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1. Function which sets the pulse as a function of time space def switch_on_pulse sim def H_ext r if r 0 lt pulse _boundary return pulse_direction else return 0 0 0 0 0 0 sim set_H_ext H_ext unit pulse_amplitude Indeed being the pulse localised and hence non uniform in space we need to define a function to be given to set_H_ext The function checks whether the x component in the given point is lower than pulse_amplitude and sets the applied field to a value differt from zero only if that is really the case 2 25 4 Postprocessing the data Once the simulations are finished the data i e the values of the magnetisation saved every 0 5 ps can be extracted from the file dynamics_dat h5 and postprocessed We use the nmagprobe command for this nmagprobe can perform several postprocessing tasks detailed documentation can be obtained by typ ing nmagprobe helgp In this context it is used to probe the magnetisation along the axis of the cylinder at regular intervals of time The values extracted are then Fourier transformed The command we use is the following nmagprobe verbose dynamics_dat h5 field m_Py time 0 100e 12 101 space 300 300 201 0 0 ref time 0 0 scalar mode component 1 out real space dat ft axes 0 1 ft out norm ft out rec space dat Here we extract data for the magnetisation option field m_Py from the file dynamics_dat h5 e We probe the field over a cubic l
2. For finite element simulations the user has to create a finite element mesh This requires some practice mostly to get used to a meshing package and in practice will take a significant amount of the time required to set up a finite element simulation 11 3 What size of the cells FD and tetrahedra FE should choose There are several things to consider the smaller the cells or tetrahedra the more accurate the simulation results e the smaller the cells or tetrahedra the more cells and tetrahedra are required to describe a geometry Memory requirements and execution time increase with the number of cells and tetrahedra In practice this will limit the size of the system that can be simulated the discretisation length this is the edge length of the cells or the tetrahedra should be much smaller than the exchange length The reason for this is that in the derivation of the micromagnetic Brown s equations one assumes that the magnetisation changes little in space there is a Taylor expansion for the exchange interaction Therefore we need to choose a discretisation length so that the direction of the magnetisation vectors varies little from one site cell center in FD node of tetrahedron in FE to the next The difference of the magnetisation vector is sometimes referred to as the spin angle a spin angle of 0 degrees means that the magnetisation at neighbouring sites points in the same direction whereas a spin ang
3. convergence Remember that you can combine time specifications using the operator or and amp and every stage 2 at convergence gt only at convergence of odd stages every step 10 at convergence gt at convergence and every 10 steps Some usage examples Save fields which implicitly will save the averages as well when the magnetisation stops changing for each applied field i e save at convergence sim hysteresis save fields at convergence Averages will be saved every 10 steps fields and implicitely averages will be saved at convergence sim hysteresis save averages every step 10 fields at convergence Each stage will not last more than 10 ps even if the magnetisation is not relaxed yet sim hysteresis do next_stage at stage_time SI le 11 s Exit hysteresis loop simulation if the total number of steps exceeds le6 save fields every 100 steps and at convergence before that sim hysteresis save fields every step 100 at convergence do exit at step le6 Save averages every 0 1 ns useful for fourier transform leave after 20 ns using the related relax_ command sim relax save averages every time SI le 10 s 1 do exit at time SI 20e 9 s
4. nsim read_h5 py in the Example 2 Computing the time development of a system directory produces output starting as follows assuming the bar_dat h5 file exists 80 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 0 0 0 O 0 70710677 0 0 70710677 1 3 00000000e 09 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 2 6 00000000e 09 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 3 9 00000000e 09 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 4 1 20000000e 08 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 5 1 50000000e 08 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 6 1 80000000e 08 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 7 2 10000000e 08 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 8 2 40000000e 08 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 9 2 70000000e 08 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 101 3 00000000e 08 0 00000000e 00 0 00000000e 00 0 70710677 0 0 70710677 111 3 00000000e 08 3 00000000e 08 1 00000000e 07 0 70710677 0 0 70710677 121 3 00000000e 08 2 70000000e 08 1 00000000e 07 0 70710677 0 0 70710677 We can see that the Site index is here just an integer the position in nanometre is shown as a triplet of three scalars and the normalised magnetisation is also a vector with three components The data in the arrays m site and positi
5. plot dat u 1 2 ti nmag with linespoints lw 3 pt 5 The resulting graph is 1 0 5 n E 0 0 5 1 1e 06 500000 Applied field A m nmag 500000 1e 06 and the comparison with the Magpar data obtained with the script make_comparison_plot gnu 34 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 set term postscript eps enhanced color set out nanodot_comparison_hyst eps set xlabel Applied field kA m set ylabel M Ms set xrang 0 2e3 0 2e3 set yrange 1 2 1 2 plot plot dat u 1 1000 2 ti nmag w lp 3 magpar dat u 1 2 ti magpar w p is shown here note that the Magpar computation only shows half of the hysteresis loop nmag o EEE ENE COSER EAA 4 2 2 200 150 100 50 0 50 100 150 200 Applied field kA m Here we can see a slight difference between nmag and Magpar in the location of the switching point probably due to different tolerances in both programs when determining time integrator convergence 2 6 Example Vortex formation and propagation in disk This example computes the evolution of a vortex in a flat cylinder magnetised along a direction orthogonal to the main axis We use the same geometry as in the Hysteresis loop for thin disk example a flat cylinder 20 nm thick and 200 nm in diameter the mesh is contained in nanodot nmesh h5 2 6 Example Vortex formation and
6. 2 4 Example Hysteresis loop for Stoner Wohlfarth particle This example is very similar to Example Simple hysteresis loop but computes the hysteresis loop of a smaller ellipsoidal magnetic object This allows to compare the results with the analytical solution given by the Stoner Wohlfarth model We use an ellipsoid whose x y z semi axes have lengths 9 nm 3 nm and 3 nm respectively The mesh is contained in el lipsoid nmesh h5 and produced with Netgen from ellipsoid geo 28 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 2 98 3 00 9 00 2 98 8 87 299 To compute the hysteresis loop for the ellipsoid we use the script el lipsoid py import nmag from nmag import SI at create simulation object sim nmag Simulation define magnetic material Py nmag MagMaterial name Py Ms SI le6 A m exchange_coupling SI 13 0e 12 J m load mesh the mesh dimensions are scaled by 0 5 nm sim load_mesh ellipsoid nmesh h5 ellipsoid Py unit_length SI le 9 m set initial magnetisation sim set_m 1 1 0 Hs nmag vector_set direction 1 1 0 norm_list 1 0 0 995 1 0 0 995 0 990 l 1 01 units le6 SI A m loop over the applied fields Hs sim hysteresis Hs save averages at convergence 2 4 Example Hysteresis loop for Stoner Wohlfarth particle 29 NMAG User Manual Documentation Release 0 2 1
7. do exit at time SI 6e 9 s run_simulation sim_name dynamics initial _m relaxed_m file damping 0 02 j 0 1e12 P 1 0 save save do do stopping_dm_dt 0 0 Here we decide to save the averages every 9 picoseconds and exit the simulation after 6 nanoseconds We use stopping_dm_dt 0 0 to disable the convergence check here we just want to simulate for a fixed amount of time We also use full spin polarisation P 1 0 we apply a current density of j 0 1e12 A m 2 and use a realistic damping parameter for Permalloy damping 0 02 For the initial magnetisa tion we pass the name of the file where the relaxed magnetisation was saved in part I and we specify a sim ulation name sim_name dynamics which is different from the one used for the relaxation which was sim_name relaxation The simulation name will decide the prefix of any filenames that are being cre ated when saving data If the simulation name is not specified the name of the script file is used We now return to discuss the function run_simulation and see how it carries out the actual simulations First the function defines the material Define the material mat nmag MagMaterial name mat Ms SI 0 8e6 A m exchange_coupling SI 13 0e 12 J m llg_damping damping llg_xi SI 0 01 llg_polarisation P It uses the variable P which is passed as an argument to the function Then the simulation object is created and the mesh
8. s set_m 1 0 0 s relax save fields at time Oxps at convergence s save_restart_file m0_filename Here we set the magnetisation along the axis of the nanopillar we then relax the system to find the equilibrium magnetisation We finally save such a configuration in the file mO_filename i e with the name specified in thesystem py 2 25 3 Part Il dynamics py The source for the file dynamics py is shown below 2 25 Example Calculation of dispersion curves 105 NMAG User Manual Documentation Release 0 2 1 from thesystem import simulate_nanowire m0_filename ps nm from nmag common import Details about the pulse pulse_boundary 300 0e 9 0 5e 9 float in nm pulse_direction 0 1 0 pulse_amplitude SI le5 A m pulse_duration 1 ps Function which sets the magnetisation to zero def switch_off_pulse sim sim set_H_ext 0 0 0 0 0 0 unit pulse_amplitude Function which sets the pulse as a function of time space def switch_on_pulse sim def H_ext r if r 0 lt pulse_boundary return pulse_direction else return 0 0 0 0 0 0 sim set_H_ext H_ext unit pulse_amplitude Here we run the simulation do is used to set the puls save is used to save the data s simulate_nanowire dynamics 0 05 s load_m_from_h5file m0_filename s relax save fields every time 0 5xps 1 do switch_on_pulse at time
9. NMAG User Manual Documentation Release 0 2 1 29 H_ext_0 lt A m gt 0 30 H_ext_1 lt A m gt 0 3 H_ext_2 lt A m gt 0 32 H_total_Py_0 lt A m gt 263661 6673782 33 H total Py 1 lt A m gt 8 212128727085 34 H_total_Py_2 lt A m gt 77027 64089399 35 E_demag_Py lt kg ms 2 gt 260346 5776034 36 H_exch_Py_0 lt A m gt 2 037901097873e 11 37 H_exch_Py_1 lt A m gt 0 38 H_exch_Py_2 lt A m gt 2 037901097873e 11 39 maxangle_m Py lt deg gt 0 40 localtime lt gt 2007 10 04 20 46 28 41 unixtime lt s gt 1191527188 269 The four columns above show the following data the first is just a line number count The second is the name of the data The third provides the units of this data type The fourth displays the first data value in the file typically corresponding to the configuration of the simulation when save_data was called the first time The meaning of the keywords time id step stage_time stage_step stage localtime and unixtime is explained in section Stage Step iteration time etc The role of the id counter is to provide a reference to the configuration that was saved and it is a unique identifier of a physical configuration It is used to identify configurations in the _dat h5 file which stores spatially resolved fields and to identify the corresponding spatially averaged data in the _dat ndt file This id is used to uniquely identify physical configurations in nmag See also Why can you no
10. time SI 6000e 12 s Here is the magnetisation at the beginning of the simulation after the first relax command whose purpose is just to find the zero field magnetisation configuration and here is the magnetisation after the write head has passed over the cubes 2 14 Applying a field that changes both in time and in space 61 NMAG User Manual Documentation Release 0 2 1 2 15 Example two different magnetic materials In this example we study the dynamics of a simple system consisting of two 15 nm x 15 nm x 15 nm cubes close to one another with 2 nm spacing along the x axis We take the right cube to be made of PermAlloy and the left cube to be made of Cobalt with the magnetic anisotropy axis pointing in z direction The mesh has been generated with Netgen from the geometry file two_cubes geo 62 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 We use the two_cubes py script to carry out the simulation import nmag from nmag import SI every at sim nmag Simulation define magnetic material Cobalt data from OOMMF materials file Co nmag MagMaterial name Co Ms SI 1400e3 A m exchange_coupling SI 30e 12 J m anisotropy nmag uniaxial_anisotropy axis 0 0 1 K1 S1 520e3 J m 3 define magnetic material Permalley Py nmag MagMaterial name Py Ms SI 860e3 A m exchange_coupling SI 13 0e 12 J m load mesh sim load_mesh
11. 28 Ruled Surface 33 33 Line Loop 37 5 36 15 32 Ruled Surface 37 37 Line Loop 41 6 40 16 36 Ruled Surface 41 41 Line Loop 45 7 19 17 40 Ruled Surface 45 45 Line Loop 46 11 12 13 14 15 16 17 172 Chapter 8 Frequently Asked Questions NMAG User Manual Documentation Release 0 2 1 Plane Surface 46 46 Surface Loop 1 9 46 21 25 29 33 37 41 4537 Volume 1 1 Physical Volume 1 1 Mesh CharacteristicLengthFactor discret www def create_mesh filename inner_size 100 0 curvature 5 0 width 10 0 thickness 20 0 discretisation 2 5 global mesh s str mesh x 0 5xinner_size variables x0 x curvature x2 x 0 5 width y1 thickness discret discretisation for variable_name variable_value in variables mE UT x qu s s replace S sS variable_name str variable_value f open filename w f write s f close create_mesh dots geo 8 17 Notes on using GMSH to create a family of related meshes 173 NMAG User Manual Documentation Release 0 2 1 174 Chapter 8 Frequently Asked Questions CHAPTER NINE USEFUL TOOLS 9 1 vtk The homepage of the Visualisation ToolKit vtk is http www vtk org VTK provides is is an open source freely available software system for 3D computer graphics image processing and visualization It also provides a f
12. 3e 09 H_demag 329997 62759666931 23 222244635691535 65 991127111463769 x 2e 09 H_demag 330013 90370482224 10 11035370824321 61 358763616681067 x le 09 H_demag 330023 50844056415 6 9714476825652287 54 900260456937708 x 0 0 H_demag 330030 98847923806 26 808832466764223 48 465748009067141 x le 09 H_demag 330062 38479507214 38 660812022013424 42 83439139610747 x 2e 09 H_demag 330093 78111090627 50 512791577262625 37 2030347831478 10 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 x 3e 09 H_demag 330150 72580001026 64 552170478617398 23 120555702674721 x 4e 09 H_demag 330226 19050178828 77 236085707456397 5 5373829923226916 x 5e 09 H_demag 330304 59300913941 90 584413821813229 14 090609104026118 x 6e 09 H_demag 330380 1392610991 115 83746059068679 37 072085708324757 x 7e 09 H_demag 330418 85831447819 122 47512022500726 62 379121138009992 x 8e 09 H_demag 330476 40747455234 110 84257225592108 108 06217226524763 x 9e 09 H_demag 330500 20126762061 68 175725285038382 162 46166752217249 x le 08 H_demag 330517 86675206106 24 351273685146875 214 40344001233677 At position le 8 there is no field defined this point lies just outside our sphere mesh and therefore the value None is returned We can see how the demagnetisation field varies slightly throughout
13. 70 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 sim nmag Simulation periodic_bc pbc structure load mesh sim load_mesh cubel nmesh h5 repeated cube 1D Py unit_length SI le 9 m set initial magnetisation along the periodic axis sim set_m 1 0 0 0 compute the demagnetising field sim advance_time SI 0 s probe demag field at the centre of the cube function returns an SI Value siv H_demag sim probe_subfield_siv H_demag 0 0 0 print H_demag_x at centre of cube H_demag 0 print H_demag_y at centre of cube H_demag 1 print H_demag_z at centre of cube H_demag Z2 Setup can be splitted into three steps In the first step we set the x_lattice parameter to be slightly larger than the dimension of the unit cell in order not to have any overlap between the cells and set the y_lattice and z_lattice parameters to zero to indicate no periodidicity along these directions x_lattice 15 01 the spacing is 0 01 y_lattice 0 0 z_lattice 0 0 In the second step we define the lattice points where we want the periodic copies to be for xi in range 3 4 lattice_points append xix xx_lattice 0 0x y_lattice 0 0xz_lattice and in the third step we define the object whose structure attribute will be used as the parameter in the definition of the simulation object pbc nmag SetLatticePoints vectorlist lattice_points scalefactor SI le 9 m
14. H_demag x 7e 09 H_demag x 6e 09 H_demag x be 09 H_demag x 4e 09 H_demag x 3e 09 H_demag x 2e 09 H_demag x le 09 H_demag x 0 0 H_demag x le 09 H_demag x 2e 09 H_demag x 3e 09 H_demag x 4e 09 H_demag x 5e 09 H_demag x 6e 09 H_demag x 7e 09 H_demag x 8e 09 H_demag x e 09 H_demag x le 08 H_demag None 333816 334670 339258 339506 344177 344725 331963 321612 2 98312 273449 293644 313838 330296 343611 348062 342272 338716 335656 334985 334441 99138074159 87148225965 77403632947 72150998382 83909963415 75257842313 49070659198 85117992124 3363571504 78240732534 21931918303 65623104072 09687372146 94111195666 40814087034 36888512014 66400897497 89887674141 59512328985 59096545313 1884 2293 3061 5316 8732 643376396662 608410913705 1708540342884 1506383768137 9787600552572 16708 164927667149 24567 078937669514 30613 873989917105 41265 117003123923 52534 176864875568 39844 049389551074 27153 921914226579 21814 293451835449 18185 932406317523 11029 603829202088 6604 3860 2610 2169 1634 210117819096 7761876767272 0345208853882 9546280837162 8337299563193 16 665519199152595 102 38526828192296 532 73877752122235 969 36630578549921 1610 433091871927
15. H_demag lt A m gt 0 00 6 81e 04 1 36e 05 2 04e 05 2 72e 05 3 4le 05 4 09e 05 4 77e 05 2 2 4 Higher level functions We now have seen an overview over the fundamental commands used to set up a micromagnetic simulation and demonstrate how to advance the configuration of the system through time In principle this is all one would need 2 2 Example 2 Computing the time development of a system 21 NMAG User Manual Documentation Release 0 2 1 to know to compute hysteresis loops and carry out most micromagnetic computations However there are more advanced functions that simplify and automatise the most frequent tasks such as computing a hysteresis loop 2 2 5 Relaxing the system The relax command takes the current magnetisation configuration of a simulation and computes the time devel opment until the torque on each mesh site is smaller than a certain threshold This is useful for this particular example as we do not know for how long we need to integrate the system until it stops in a local energy mini mum configuration We can adjust the code of this example to make use of the relax command modified source code import nmag from nmag import SI every at mat_Py nmag MagMaterial name Py Ms SI 0 86e6 A m exchange_coupling SI 13 0e 12 J m 11g_damping 0 5 sim nmag Simulation bar_relax sim load_mesh bar30_30_100 nmesh h5 Py mat_Py unit_length SI le 9 m sim set_m 1 0
16. SI 0 6 kg 1 s 2 A 1 is the code to create an SI object T that represents 0 6 kg s42 A i e 0 6 Tesla 2 A more convenient way is to first define all the base units like this these are already defined in the si submodule so instead of the following lines below we could also just write from si import meter second Ampere meter SI 1 m alternative spelling metre second SI 1 s Ampere SI 1 A and then to use these SI objects to create more complex expressions v 10 meter second B 0 6 kilogram second 2 Ampere Of course short hand notations can be defined such as T kilogram second 2 Ampere B 0 6xTesla 3 Finally there is another convenient way Instead of a SI dimension vector as in 1 it is possible to pass a string specifying dimensions Examples are A m V m J m43 m2 s 2 m2 3 s 1 etc The dimensions parser will understand in addition to m kg s A K mol cd J N W T V C Ohm H A very basic demonstration of the SI object in use gt gt gt a SI 1 m gt gt gt b SI le 3 m gt gt gt print a b lt SI 1 001 m gt 4 7 Sl 145 NMAG User Manual Documentation Release 0 2 1 gt gt gt print axb lt SI 0 001 m 2 gt gt gt gt print a b gt gt gt lt SI 1000 gt Note that this is dimensionless because we divided meters by meters 4 7 1 value Module nmag Object SI value Prop
17. Save averages every nanosecond and fields every 100 ns sim relax save averages every time SI le 9 s fields every time SI 100e 9 s 1 Save averages every nanosecond and fields every 100 ns save restart file every 1000 steps sim relax save averages every time SI le 9 s fields every time SI 100e 9 s restart every step 1000 If save is not given averages and fields will be saved whenever the stage ends this is the default behaviour 4 2 Simulation 137 NMAG User Manual Documentation Release 0 2 1 4 2 11 load_mesh Module nmag Object Simulation load_mesh Arguments self filename region_names_and_mag_mats unit_length do_reorder False manual_distribution None Parameters filename string The file that contains the mesh in nmesh format ascii or hdf5 region_names_and_mag_mats list of 2 tuples A list of 2 tuples containing the region names and the magnetic materials associated to each region For example having two spheres called region_A and region B with materials A and B in the mesh the argument would be region_A A region_B B where A and B must have been defined previ ously as nmag MagMaterial Having two Materials X and Y both defined in region A as in a magnetic two component alloy we would use region_A X Y unit_length SI object The S
18. a 4e 05 2e 05 0 5e 11 1e 10 1 5e 1 20 10 2 5e 10 3e 10 time s 1 We could in fact avoid re creating all the operator matrices and the BEM and just repeat the simulation with varying values of the tol parameter However this would mean that the data is written into the same file so is slightly less convenient here It would also be a less pedagogical example in this guided tour 2 26 Example Timestepper tolerances 111 NMAG User Manual Documentation Release 0 2 1 We can see that curves seem to coincide at this scale apart from the red tol1 1e 1 curve which deviates somewhat We zoom in to region between 1 2e 10 seconds and 2e 10 seconds and focus on the lowers curves in the main plot 10000 20000 30000 M_Py A m 40000 E 50000 60000 H 1 4e 10 1 6e 10 1 8e 10 2e 10 time s The better resolution reveals that there is a clear deviation of the various curves the red 0 1 indigo 0 01 and yellow 1e 3 curves approach the black 1e 6 curve in this order The blue 1e 4 and green le 5 curves appear to coincide with the black reference curve Another zoom at the z component of the magnetisation towards the end of the simulated time interval time gt 1 8e 10 seconds shows that the less accurate curves red and then indigo and yellow show a large amount of jitter although following the reference curve on average 112 Chapter 2 Guided Tour NMAG User Manual Documentati
19. average magnetisation 1 o A m time ns electric pinned pinned moment current moment 2 22 Example Current driven magnetisation precession in nanopillars 87 NMAG User Manual Documentation Release 0 2 1 wall We then study how such an artificial domain wall interacts with a current flowing throughout the cylinder along its axis By artificial we mean that the domain wall is developed as a consequence of the pinning which we artificially impose In real systems the pinning can be provided through interface exchange coupling or may have a geomet rical origin in combination with suitable material parameters The situation we consider here is described and studied in more detail in publications and 2 22 1 Two simulations in one single script The nanopillar is made of Permalloy and has the shape of a cylinder with radius of 10 nm and length 30 nm The mesh is loaded from the file 1030 nmesh h5 which was created using Netgen from the file 1030 geo The simulation is subdivided into two parts similarly to the previous example e In part I the system is relaxed to obtain the initial magnetisation configuration when the current is not applied e In part II the current is applied to the artificial domain wall whose shape was calculated in part I This time however we use just one single script to execute both parts of the simulation in one go In particular we define a function whic
20. create simulation object sim nmag Simulation periodic_bc pbc structure The remaining part of the script computes the demagnetisation field at the center of the cube This calculation can be carried out for a varying number of copies of the simulation cell The next figures show components of demagnetising field in the center of the cube as a function of the number of periodic copies As in the code above we impose an uniform magnetisation along the periodic x axis The first figure shows the demagnetisation field along the x axis and the second figure along the y axis In both figures we have added green crosses that have been obtained by computing the demagfield using OOMMF where in OOMMF we have actually made the simulation cell larger and larger to represent the growing number of periodic copies 2 17 Example 1D periodicity 71 NMAG User Manual Documentation Release 0 2 1 350000 300000 250000 200000 Demag field 150000 100000 50000 0 10 20 30 40 50 60 70 80 90 copies Demagnetising field as a function of the number of periodic copies with the magnetisation aligned along the periodic axis 520000 nmag oommt x 500000 pp 480000 460000 440000 420000 Demag field 400000 380000 360000 340000 320000 0 10 20 30 40 50 60 70 80 90 copies Demagnetising field as a function of the number of periodic copies with the magnetisation aligned along an axis orthogonal to the per
21. self subfieldname units None Given a subfieldname this will return a numpy array containing all the data one element for each site Parameters subfieldname string The name of the subfield for example m_Py or H_demag units SI object Optional parameter If it is provided then the entity is expressed in these units If it is not provided then the correct SI dimensions for this subfield are looked up and SE values are returned If you would like to see simulation units in the output then use ST 1 In short if you omit the second parameter you will obtain SI values Returns data numpy array 4 2 3 get_subfield_positions Module nmag Object Simulation get_subfield_positions Arguments self subfieldname pos_units SI 1 m 1 0 This function provides the positions of the sites for data obtained with get_subfield 132 Chapter 4 Command reference NMAG User Manual Documentation Release 0 2 1 Parameters subfieldname string The name of the subfield for example m_Py or H_demag pos_units SI Object Specifies the physical dimension in which positions are to be expressed Default is SI 1 m which means to return site positions in meters To obtain site positions in nanometers use SI le 9 m Returns pos numpy array Array containing a position i e 3 floating point numbers for every site 4 2 4 get_subfield_sites Module nmag Object Simulation get_subfield_sites Argume
22. 8 12 Can I save data to an arbitrary directory 8 12 1 Do you really need to do so First consider whether you really need to save data in a different directory Remember that you can run many simulation with one single script just using a different simulation name like sl Simulation one s2 Simulation two When you save the data for simulation one you get files like one_dat h5 and one_dat ndt while when dealing with simulation two you get two_dat h5 and two_dat nd5 There is no interference between the two simulations and in particular it is necessary to save thedata in different directories 8 12 2 How to save data to a different directory When you run a simulation script which saves data from a simulation the files are saved by default in the current working directory In order to change this and save data into a directory called mydir you should start your 168 Chapter 8 Frequently Asked Questions NMAG User Manual Documentation Release 0 2 1 script in the following way import nmag import nsim features fts nsim features Features fts set etc savedir mydir Alternatively you can change the current working directory at the beginning of the file with ordinary Python code import os initial_dir os path abspath os path curdir os chdir mydir os chdir initial_dir If the directory you want to write to does not exist then in both the two example
23. Python executable Technically speaking a program started under MPI control will receive extra MPI related command line arguments which upset the standard Python interpreter It so happens that by providing our own Python executable which is called ns im we have easier access to the low level library of nsim which is written in Objective Caml 8 4 What is nsim thought the package is called nmag The The nsim library is our general purpose multi physics simulation environment The corresponding executable is started through the nsim command Nmag is a collection of scripts that provide micromagnetic functionality on top of nsim For this reason nsim is being mentioned a lot in the manual 8 5 How fast is nmag in comparison to magpar Internally some of the magpar and nmag core components are structurally very similar In particular the time integration routine is almost identical up to some philosophical issues such as how to keep the length of the magnetisation vector constant and whether or not to use a symmetrical exchange matrix and a post processing step rather than combining these into an asymmetrical matrix etc The actual wall clock time used will depend to a large degree on the requested accuracy of the calculations see example timestepper tolerances Given equivalent tolerance parameters we have found the single process version of nmag to be about as fast as magpar The computation of an individual velocity dM dt is
24. We apply external magnetic fields in 110 direction i e 45 degrees between the x and the y axis to this system with strengths in the range of 1000 kA m down to 1000 kA m in steps of 5 kA m The save parameter is used to tell the hysteresis command what data to save and how often Here we are only interested in saving the spatially averaged magnetisation values for every stage i e meta stable equilibrium before the applied field is changed 2 4 1 Plotting the hysteresis loop To extract the data needed for plotting the hysteresis loop we proceed as explained in the previous example Example Simple hysteresis loop We use the ncol command and extract the data into a text file named plot dat ncol ellipsoid H_ext_0 H_ext_1 H_ext_2 m_Py_0 m_Py_1 m_Py_2 gt plot dat We then use Gnuplot to plot the loop gnuplot make_plot gnu The gnuplot script make_plot gnuis set term postscript eps enhanced color set out hysteresis eps set xlabel Applied field kA m set ylabel M Ms versor_x 1 sqrt 2 versor_y 1 sqrt 2 versor_z 0 0 scalar_prod x1 x2 x3 xl versor_x x2 versor_y X3xversor_z set mxtics 5 minor tics and grid set ytics 1 set mytics 5 set grid xtics ytics mxtics mytics lt 1 lw 0 5 It 0 plot 1050 1050 1 2 1 2 plot dat u scalar_prod 1 2 3 1000 scalar_prod 4 5 6 t Stoner Wohlfarth w lp 4 Note that within the gnuplot file we project the magnetisati
25. gt cube_hext_vs_m txt Then we compare the result with OOMMPF s result generated from the equivalent scene description oommf cube mif using the following Gnuplot script set term png giant size 800 600 set out cube_hext_vs_m png set xlabel H_ext x A m set ylabel M x A m plot cube_hext_vs_m txt t nmag w 1 2 1 oommf cube_hext_vs_m txt u 1 795 77471545947674 2 ti oommf wp 1 which gives the following result 1 8e 06 1 6e 06 1 4e 06 1 2e 06 1e 06 800000 M x A m 600000 400000 200000 200000 L L l l L 4 1 o 5000 10000 15000 20000 25000 30000 35000 40000 H_ext x A m Nmag provides advanced capabilities to conveniently handle arbitrary order anisotropy energy functions Details can be found in the documentation of the MagMaterial class 2 12 Example Arbitrary Anisotropy In this example we discuss the script coin py which shows how the user can include in his simulations a customised magnetic anisotropy 2 12 1 Arbitrary anisotropy simulation script import nmag from nmag import SI every at from nsim si_units import si import math Create simulation object no demag field 54 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 sim nmag Simulation do_demag False Function to compute the scalar product of the vectors a and b def scalar_product a b return a 0 b 0 a 1 xb 1 a 2 xb 2 Here we
26. however is much smaller Magpar is also more efficient in memory usage 8 6 How do start a time consuming nmag run in the background While this is a Unix rather than a nmag issue it comes up sufficiently often to address it here Well known techniques to run programs in the background are e Using the nohup no hangup command as in nohup nsim spherel py Using the at daemon for scheduling of command execution at given times at now warning commands will be executed using bin sh at gt nsim examplel py at gt lt EOT gt job 2 at Fri Dec 14 12 08 00 2007 Manual daemonization by using a parent process which forks amp exits as in perl e exit 0 if fork exec nsim spherel py But if you know Unix to that degree you presumably would not have asked in the first place One of the most elegant ways to start a process in the background is by using the screen utility which is installed on a number of Unix systems With screen it becomes possible to start a text terminal session in such a way that one can detach from it while keeping the session alive and even log out and log in again much later and from a different machine re attaching the terminal session and continuing work from the point where it was left While it is a good idea to read the documentation most basic usage of screen requires the knowledge of three commands only With screen R one can re atta
27. lt A m gt 8 218106743355 Tis H_demag_2 lt A m gt 77027 641984 LD dmdt_Py_0 lt A ms gt 8 250904652583e 15 13 dmdt_Py_1 lt A ms gt 2 333344983225e 16 14 dmdt_Py_2 lt A ms gt 8 250904652583e 15 153 H_anis_Py_0 lt A m gt 0 16 H_anis_Py_1 lt A m gt 0 Ps H_anis_Py_2 lt A m gt 0 18 m_Py_0 lt gt 0 7071067811865 LO m_Py_1 lt gt 0 20 m_Py_2 lt gt 0 7071067811865 21 M_Py_0 lt A m gt 608111 8318204 22 M_Py_1 lt A m gt 0 23 M_Py_2 lt A m gt 608111 8318204 24 E_anis_Py lt kg ms 2 gt 0 203 E_exch_Py lt kg ms 2 gt 5 046530179037e 17 26 rho lt A m 2 gt 0 03469702141876 27 H_ext_0 lt A m gt 0 28 H_ext_1 lt A m gt 0 29 H_ext_2 lt A m gt 0 2 2 Example 2 Computing the time development of a system 17 NMAG User Manual Documentation Release 0 2 1 30 H_total_Py_0 lt A m gt 263661 6680783 31 H_total_Py_l lt A m gt 8 218106743352 32 H_total_Py_2 lt A m gt 77027 641984 33 E_demag_Py lt kg ms 2 gt 0 2603465789714 34 H_exch_Py_0 lt A m gt 3 301942533099e 11 35 H_exch_Py_1 lt A m gt 0 36 H_exch_Py_2 lt A m gt 3 301942533099e 11 37 maxangle_m Py lt deg gt 0 38 localtime lt gt 2007 08 15 11 16 19 39 unixtime lt s gt 1187172979 6 The meaning of the various entries is discussed in detail in section ncol Here we simply note that the column indices given by the number at the beginning of every line we are most interested in are e O for the time e 21 for M_Py_0
28. see It shows a top view i e along the z axis of the rear part of the nanowire from the previous section The left hand side shows the original mesh the right hand side shows the mesh after distortion with the function g which is depicted in the middle Note that the contour of the distorted mesh follows the outline of g 0 A d avg distortion c correlation length x y The distortion functions f and g are constructed as follows First we pick equidistant nodes x_i along the x axis note that these are just auxiliary entities and completely independent from the nodes of the mesh Then random values f x_i and g x_i are assigned to each such node chosen from a normal distribution with mean 0 and a certain standard deviation that determines the amplitude of the roughness Finally these random values are interpolated smoothly to obtain the continuous distortion functions f x and g x In order to make the randomization reproducible it is possible to specify a seed for the internal random number generator by passing 2 23 Mesh distortion for edge roughness simulation 95 NMAG User Manual Documentation Release 0 2 1 any integer value as an argument to seed Otherwise the output mesh is different each time because the random number generator is seeded using the system time or something similar The reason why we need these distortion functions at all and can t just randomly displace each mesh no
29. simple moving write head example Here is a simulation of five cubes made of cobalt and a write head which moves on the top of the cubes and applies a time varying field in order to change their magnetisation At the beginning the magnetisation of all the cubes is 2 14 Applying a field that changes both in time and in space 59 NMAG User Manual Documentation Release 0 2 1 pointing in the 0 0 1 direction After the write head has passed over the cubes the magnetisation of cube 1 3 and 5 are switched in the opposite direction while cube 2 and 4 have unchanged magnetisation This is possible because the write head field which is space dependent being intense only inside a sphere of radius 15 20 nm changes also in time It indeed translates in space but also change in intensity being directed in the 0 0 1 direction when the sphere is at the center of cube 1 3 and 5 and in the 0 0 1 direction when the center of the sphere is in cube 2 and 4 Here is the geo file used to generate the mesh Netgen lt pre gt algebraic3d cubes solid cubel orthobrick solid cube2 orthobrick 20 solid cube3 orthobrick 60 20 20 20 20 20 20 20 20 20 maxh maxh maxh maxh maxh 50 80 o LLO 140 se solid cube4 orthobrick solid cube5 orthobrick OOO Oo gG O 00 SS e o O
30. 09 Time s The magnetisation field moves from its out of plane configuration into the plane and relaxes into a high remanent state which is aligned along the diagonal of the square base The plot below shows a 3d visualisation of the relaxed magnetisation field obtained with Mayavi2 for a thin film with an edge length of 130 nm 2 24 Compression of the Boundary Element Matrix using HLib 101 NMAG User Manual Documentation Release 0 2 1 800 Z x magnetisation x component 1 00 0 875 0 750 0 625 0 500 0 375 0 250 0 125 0 00 We have run the simulations on a machine with an AMD Athlon tm 64 X2 Dual Core Processor 3800 using only one core The graphs below show the results of our efficiency test of hierarchical matrices It can be seen that the memory requirements are reduced considerably While the consumed memory increases almost linearly with the number of surface nodes N for the calculation with hierarchical matrices the increase is of a higher order O N43 when using the accurate boundary element matrix B The enhanced scaling behaviour allows for simulation of larger ferromagnetic structures The graph on the memory consumption should enable users to estimate whether they can simulate a certain structure with Nmag HLib and the available hardware 102 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 1800 1600 full BEM 1400 H Matrix 1200 1000 800 600
31. 1 ps SI le 12 s sim relax save averages every time 5xps fields at convergence Note the additions to the import statement The particular relax command employed here sim relax save averages very time 5xps fields at convergence works as follows The argument save tells relax to save data according to the instructions given in the form of a python list i e enclosed by square brackets The first relax instruction is this tuple averages every time 5xps and means that the averages should be saved every 5 picoseconds The syntax used here breaks down into the following parts e averages is just the keyword a string to say that the average data should be saved e every isa special object which takes two parameters They are here time to indicate that something should be done every time a certain amount of simulated time has passed and 5 ps which is the amount of time after which the data should be saved again This has to be a SZ object which we here obtain by multiplying a number 5 with the SI object ps which has been defined earlier in our example program to represent a pico second We can provide further keywords to the every object for example to save the data every 10 iteration steps we can use every step 10 Internally the relax command uses the hysteresis command so the do
32. 297 1010e 051 6 16259262e 01 1 66071597e 02 3 29848851e 05 1 Note that within ipython one can just press the TAB key to autocomplete object names functions and commands You can leave the ipython environment by pressing CTRL D For the script shown here this will print Back in main code before the end of the script is reached The ipython command is occasionally a handy debugging feature in order to investigate the behaviour of the system on the spot one can insert an ipython call into the script which will open an interactive command line 2 9 Example Pinning Magnetisation In this example we show how to pin i e fix magnetisation in certain parts of a material 2 9 1 Pinning simulation script import nmag from nmag import SI si Create simulation object sim nmag Simulation Define magnetic material PermAlloy Py nmag MagMaterial name Py 46 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 Ms SI 0 86e6 A m exchange_coupling SI 13 0e 12 J m Load mesh sim load_mesh spherel nmesh h5 sphere Py unit_length SI le 9 m Set initial magnetisation to x direction sim set_m 1 0 0 Pin magnetisation at center in radius of 4e 9m def pin_at_center x y Z if xxx yxy z2 z lt 4e 9 x 4e 9 return 0 0 Inside the 4nm sphere gt pin else return 1 0 Outside gt do not pin sim set_pinning pin_at_center
33. 3 543451 stand dev a0 lt a0 2 gt 0 581220 2 min and max 1 953689 5 708395 6 4 Convert nmesh h5 to nmesh file and back The command nmeshpp c mesh nmesh h5 mesh nmesh converts a the mesh mesh nmesh h5 in h5 format to the mesh nmesh in ascii format Works also in the reverse way nmeshpp will save as h5 file if the last extension of the file to write is h5 6 4 1 nmeshmirror The nmeshmirror tool can create periodic meshes out of a non periodic mesh The geometry described by the non periodic mesh has to be a cuboid This can be mirrored along one or more of the planes defined by the sides of the cuboid The general usage is nmeshmirror meshfil rrorl error2 directions newfile remove where e meshfile is the original non periodic ASCII nmesh file e errorl is the maximum distance between two points in order to consider them coincident case of points on mirroring planes e error2 is the maximum distance between a point and the surface opposite to the one used as mirroring plane in order to consider the point periodic e directions isa list of values 0 1 or 1 corresponding to the direction s over which the mesh is mirrored 1 corresponds to mirroring along the positive given axis 1 along the negative given axis and 0 corresponds to no mirroring along the given axis For a three dimensional mesh there are three options to mirror the mesh along the x y and z direction In that case the direction
34. 5 nm sim load_mesh ellipsoid nmesh h5 ellipsoid Py unit_length SI le 9 m set initial magnetisation sim set_m 1 0 0 Hs nmag vector_set direction 1 0 01 0 norm_list 1 00 0 95 1 00 0 95 0 90 1 00 units le6 SI A m loop over the applied fields Hs sim hysteresis Hs save restart fields at convergence As in the previous examples we first need to import the modules necessary for the simulation at convergence allows us to save the fields and the averages whenever convergence is reached We then define the material of the magnetic object load the mesh and set the initial configuration of the magnetisation as well as the external field 2 3 2 Hysteresis loop computation We apply the external magnetic fields in the x direction with range of le6 A m down to 1e6 A m in steps of 0 05e6 A m To convey this information efficiently to nmag we use 1 a direction for the applied field here just 1 0 01 0 note that we have a small y component of 1 in the applied field to break the symmetry 2 a list of magnitudes of the field that will be multiplied with the direction vector 3 another multiplier that defines the physical dimension of the applied fields here 1000kA m given as le6 SI A m Putting all this together we obtain this command Hs nmag vector_set direction 1 0 01 0 norm_list 1 00 0 35 Ll 1
35. 5224 2484897904633 3321 016613832679 1385 6383061516099 636 60703829516081 2793 5027588779139 4310 6449471266505 5827 7871353753881 5525 7290665358933 4931 5464761658959 3781 8263522408147 50 151907623841332 485 90273674867018 586 74812908870092 542 76746044672041 627 17874011463311 44 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 The change of the magnetisation at position 0 0 0 from 1 0 0 to 0 1 0 has reduced the x component of the demag field somewhat around x 0 and has introduced a significant demag field in the y direction around x 0 Looking at the exchange field Step 9 x le 08 H_exch_Py None x 9e 09 H_exch_Py 1 26432464385698 e 09 0 0 0 0 x 8e 09 H_exch_Py 2 0419540595507732e 10 0 0 0 0 x 7e 09 H_exch_Py 1 4334754136843496e 09 0 0 0 0 x 6e 09 H_exch_Py 2 7214181426130964e 10 0 0 0 0 x 5be 09 H_exch_Py 1 6323042074911775e 09 0 0 0 0 x de 09 H_exch_Py 153858 81305452777 153858 81305452611 0 0 x 3e 09 H_exch_Py 972420 67935341748 972420 67935341166 0 0 x 2e 09 H_exch_Py 2445371 8369108676 2445371 8369108611 0 0 x le 09 H_exch_Py 5283169 701234119 5283169 7012341227 0 0 x 0 0 H_exch_Py 15888993 991894867 15888993 991894867 0 0 x le 09 H_exch_Py 8434471 7912872285 8434471 7912872266 0 0 x 2e 09 H_exch_Py 979949 59067958547 979949 59067958279 0 0
36. A J de Groot Hans Fangohr Numerical studies of demagnetizing effects in triangular ring arrays Journal of Applied Physics 103 07D932 2008 online at http eprints soton ac uk 50995 76 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 Y 15 0 4 50 The mesh is contained in periodic nmesh and has been produced using Netgen from periodic geo and the nmeshmirror command to create required periodic structure nmeshmirror netgen nmesh le 6 le 6 1 0 0 periodic nmesh 2 19 1 Relaxation script To see how the system relaxes we use the following script spinwaves py import nmag from nmag import SI import math define magnetic material Py nmag MagMaterial name Py Ms SI le6 A m exchange_coupling SI 13 0e 12 J m llg_damping SI 0 02 lattice spacings along the main axes the value must be zero for no periodic copies equal to the mesh dimension along the Se SR SR OR given axis otherwise x_lattice 30 0 y_lattice 0 0 z_lattice 0 0 list to store the lattice points where the periodic copies will be placed lattice_points for xi in range 1 2 lattice_points append xixx_lattice 0 0x y_lattice 0 0x z_lattice copies of the system along the x axis pbc nmag SetLatticePoints vectorlist lattice_points scalefactor SI le 9 m create simulation object sim nmag Simulation periodic_bc pbc structure load mesh sim load_mesh periodic
37. Apply external field in y direction unit 0 5xsi Tesla si mu0 500mT in A m sim set_H _ext Ox unit lxunit Oxunit Relax the magnetisation sim relax 2 9 2 Pinning magnetisation In order to allow the user to fix the magnetisation nmag provides a scalar field the so called pinning field its value at each site is used as a scale factor for dm dt hence by setting it to 0 at certain locations of the mesh we can force magnetisation to remain constant at these locations for the entire simulation We set the pinning field using set_pinning which is used like set_m and set_H_ ext except that it is a scalar field whereas the latter are vector fields such that magnetisation is fixed at sites with distance less than 4 nm from the sphere s center First we define a Python function which we decide to call pin_at_center def pin_at_center x y Z if x x yxy z2 z lt 4e 9 x 4e 9 return 0 0 else return 1 0 The function is called for each site of the mesh and receives the site position as an argument a 3 tuple x y z containing the three components x y and z three floating point numbers given in metres The function returns either 0 0 which means the magnetisation at this position is pinned or 1 0 in which case there is no pinning for the given position vector The formula in the if statement simply evaluates the magnitude of the vector x y z by squaring each component This number is then compared ag
38. Chapter 5 Finite element mesh generation NMAG User Manual Documentation Release 0 2 1 dim the dimensionality of the space in which the mesh is defined usually 3 as we work with meshes in 3d space nodes the number of nodes also called vertices here 79 simplices the number of simplices also called volume elements here 174 In 3d a simplex is a tetrahedron surfaces the number of surface elements here 148 In 3d the surface elements are triangles periodic the number of periodic identifications of points e The next section contains the data for all the nodes The first line of this section contains again the total number of nodes 7 9 All subsequent 79 lines in this section contain each the position of one node Because the dimensionality of space in this example is 3 there are 3 floating point numbers per node i e the x y and z component e The next section contains the data for the simplices The first line of this section contains again the total number of simplices here 17 4 The next 174 lines contain the following information each The first integer is a region identifier In this example we have only one region the sphere This is useful if different magnetic materials are simulated at the same time When the mesh is loaded into nmag one assigns material properties to these regions The next 4 integers in 3 dimensions are node identifiers The 4 nodes listed here form a simplex Note that the ve
39. Figure 2 3 Magnetisation configuration for a decreasing applied field of 10 kA m Se ey eae AA m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 2 4 Magnetisation configuration for a decreasing applied field of 30 kA m 2 6 Example Vortex formation and propagation in disk 39 NMAG User Manual Documentation Release 0 2 1 m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 2 5 Magnetisation configuration for a decreasing applied field of 95 kA m m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 2 6 Magnetisation configuration for a decreasing applied field of 100 kA m 40 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 We see that during magnetisation reversal a vortex nucleates on the boundary of the disc when the field is suffi ciently decreased from its saturation value As the field direction is aligned with the x axis the vortex appears in the disc region with the largest y component and it moves downwards towards the centre along the y axis With a further decrease of the applied field the vortex moves towards the opposite side of the disc with respect to the nucleation position and it is eventually expelled when the magnetisation aligns with the field direction over all the disc 2 7 Example Manipulating magnetisation There are two basic techniques to modify th
40. Freldsiand Subfields in Nmae ai e ion os a SG BORLA ie Re ek oe k 33 Mesh i 44 ie egos ee Ree ea ee eR SHG GOD bee wo eee eae a EA 36 SIE s x i ee te hh ee Bete eagle eth ete RAR idee Oe lay Gh ae nbs Jo hee a ge ie Se Sl ASMODJEC il A eee ee Es Re ee ee aE Aero OS be Re ee ek A SO EMS LARA Ge EIA A ne Go oe cee E ob A Av Sh RG ee eis Oe E ai 39 Solvers and tolerafice settings 24 5 5485854088 4a wake eh ee ee pe oe Re ee G 3 10 The equation of motion the Landau Lifshitz Gilbert equation oo Command reference 4 MasMatenal s socs a cc wae eee QS Rae BEG A 8 oo els Eo aS 4 2 Simulation 5064 A bb dee hee ba ee ee bebe bea 4 3 get subfield from BSfile s s wk ice sia Be Ae arg Se Ro ce eg Be GS de we ge 44 get subfield positions from hohe s s ag ece eae be eee nS See a eee 45 get subfield sites from ASE y seiste a AB ee a a es Sa a glee e eaa HO JAMatrixSenip 2 4 lt 2 asa 4 each ele a Gre eh ee Ae oe a a ee A ee eB ete Wel Ole amp aden a ee ee Bak Oa Ee ero Bale whinge hd AS O ai ate iene lt b SE BS a SA ee RR ee DS We AN 49 Command Ine options s 24 6 4 2 2 oa bee wR be HALE e ae HS w BAS Finite element mesh generation 3 1 Nmesh fileformat estirar ee RO a Se BE we dee ae doe we ee 32 MESE S176 fs ok eR cee RI Be E A ete ee a gow ES Executables Ol MO seo baa eS eR oe a Pee ea ae Oe ee eas 6 2 MMALPD oda a enh sks Bie SEES Rete eee e ea a Se ee aa 6 3 lt MMeshpp 2 os twa fae ee Pe eee Ae ba Ma
41. It can be seen that the isosurfaces are completely flat planes i e the potential is changing only along x and the demagnetisation field is perpendicular to the isosurfaces The color bar on the left refers to the magnitude of the demagnetisation field which is expressed in Ampere per meter as can be seen from the label lt A m gt Note that all the H_demag arrows are colored red as they have identical length 2 2 Example 2 Computing the time development of a system This example computes the time development of the magnetisation in a bar with x y z dimensions 30 nm x 30 nm x 100 nm The initial magnetisation is pointing in the 1 0 1 direction i e 45 degrees away from the x axis in the direction of the long z axis We first show the simulation code and then discuss it in more detail 2 2 1 Mesh generation While it is down to the mesh generation software see also Finite element mesh generation to explain how to generate finite element meshes we briefly summarize the steps necessary to create a mesh for this example in Netgen and how to convert it into an nmesh mesh 1 The finite element method requires the domain of interest to be broken down into small regions Such a subdivision of space is known as a mesh or grid We use Netgen to create this mesh Netgen reads a geometry file describing the three dimensional structure To create the mesh used here we can start Netgen and load the geometry file by using the menu File gt Load
42. Nmag uses the hybrid finite element method boundary element method hybrid FEM BEM to compute the de magnetisation field as does Magpar Not using this method one would have to discretise a large part of space arround the magnetic structure ideally all space Using the hybrid FEM BEM method it is only necessary to discretise and solve the equations for the demag field on that discretisation those parts of space that are occupied by magnetic material A disadvantage of the hybrid FEM BEM method is that it involves the assembly of a dense boundary element matrix B whose number of elements scales quadratically with the number of surface nodes N of our finite element mesh i e the matrix B has as many rows as there are surface nodes N in the mesh and also as many columns This is in particular an issue when studying flat structures such as thin films For example imagine we model a thin film of side lengths 100 nm x 100 nm x 2nm If we decide to double the side lengths to 200 nm x 200 nm x 2nm then this roughly corresponds to an increase of surface node numbers N by a factor of 4 The matrix B will then grow in size by a factor 442 16 due to the doubling of the two side lengths by a factor of 2 In practice the memory requirements of the matrix B often limit the size of a structure that can be modelled In order to improve the efficiency of the hybrid FEM BEM one can employ techniques which involve some kind of approximation of B for exampl
43. Oxps switch_off_pulse at time pulse_duration exit at time 200xps The simulation starts again importing a few entities from the file thesystem py In particular the function simulate_nanowire is used to setup the system similarly to what was done for the relaxation The next few lines define some variables which are used to define the geometry and duration of the magnetic field pulse Details about the pulse pulse_boundary 300 0e 9 0 5e 9 float in nm pulse_direction 0 1 0 pulse_amplitude SI le5 A m pulse_duration lxps In this example the pulse is obtained by switching on the applied field from 0 0 0 to 0 pulse_amplitude 0 in the region of the wire where x lt pulse_boundary which corresponds in this case to a layer of 0 5 nm thickness on one side of the cylinder The pulse is switched on at t 0 and switched off at pulse_duration We now examine the code and explain how all this is coded in the script We start explaining the last few lines Here we run the simulation do is used to set the pulse save is used to save the data s simulate_nanowire dynamics 0 05 s load_m_from_h5file m0_filename s relax save fields every time 0 5xps do set_pulse at time Oxps set_to_zero at time pulse_duration exit at time 200xps Here we use the simulate_nanowire function which we define
44. Y Z pos newx xxle9 newy yxle9 if 8 lt newx lt 14 and 3 lt newy lt 3 the magnetisation is twisted a bit return 1 0 5 math cos math pix newx 11 6 3 math cos math pix newy 6 3 0 0 else return 1 0 0 0 0 0 78 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 which is then passed on to set_m set initial magnetisation sim set_m perturbed_magnetisation 2 19 2 Visualising the magnetisation evolution Once the calculation has finished we can see how the system relaxed by means of snapshots of the magnetisation evolution The nmagpp command allows us to create vtk files from the data saved with the save option in the relax method nmagpp vtk fields spinwaves The first few frames that show the evolution of the magnetic configuration are shown below m_Py lt gt Y component 0 00 0 143 0 286 0429 0 571 0 714 0 857 1 00 Figure 2 7 Initial magnetisation configuration m_Py lt gt Y component 0 00 0 143 0 286 0429 0 571 0 714 0 857 1 00 Figure 2 8 Magnetisation configuration after 0 15 ps Itis clearly visible that the spin waves travel from the center of the disturbance to the right and penetrate the system immediately from the left due to the periodic boundary conditions in the x direction 2 19 Example Spin waves in periodic system 79 NMAG User Manual Documentation Release 0 2 1 m_Py lt gt Y component 0 00 0 143 0 2
45. a set will have mirage copies and use this information internally e g in the time integrator and when building finite element matrix operators 5 1 2 Hdf5 nmesh In addition to the Ascii nmesh format there is another binary and compressed way of storing nmesh meshes This is based on the hdf5 library which often is abbreviated as h5 We recommend that this file format to store meshes as it is a compressed binary file format and thus much more space efficient The nmeshpp tool can convert using convert ascii nmesh files into hdf5 files Likewise using the nmeshimport tool with a target file name that ends in n5 will also choose this file format We strongly recommend to use the extension nmesh h5 but h5 is sufficient to trigger saving meshes in hdf5 format For conversion of other mesh formats to a format readable by nmesh we suggest to bring data into Ascii nmesh format and then convert this ascii nmesh file to a h5 file For completeness we outline the nmesh h5 file format here Knowledge of hdf5 or pytables may be useful to understand the underlying concepts 5 1 Nmesh file format 151 NMAG User Manual Documentation Release 0 2 1 The nmesh h5 file contains the following nodes this is output from pytables s pt dump program RootGroup etc Group Configuration and version data etc filetype Array 1L data file type etc fileversion Array 1L data file type version mesh
46. and is also likely to be more efficient than running a job across the network between difference machines In that case we can run the example on 2 CPUs using gt mpirun np 2 usr bin nsim bar30_30_100 py where np is the command line argument for the Number of Processors To check that the code is running on more than one CPU one of the first few log messages will display in addition to the runid of the simulation the number of CPUs used gt mpirun np 2 which nsim bar30_30_100 py nmag 2008 05 20 12 50 01 177 setup py 269 INFO Runid name simulation is To use 4 processors if we have a quad core machine available we would use gt mpirun np 4 usr bin nsim bar30_30_100 py Assuming that the nsim executable is in the path and that we are using a bash shell we could shortcut the step of finding the ns im executable by writing gt mpirun np 4 which nsim bar30_30_100 py 116 Chapter 2 Guided Tour bar30_30_10 NMAG User Manual Documentation Release 0 2 1 To run the job across the network on different machines simultaneously we need to create a file with the names of the hosts that should be used for the parallel execution of the program If you intend to use nmag on a cluster your cluster administrator should explain where to find this machine file To distribute a job across machinel mydomain machine2 mydomain and machine3 mydomain we need to create the file machines txt with content
47. and resulted in a 5 reduction of execution time Generally the network communication that is required between the nodes will slow down the communication The smaller the system the more communication has to happen between the nodes relative to the amount of time spent on actual calculation Thus one expects a better speed up for larger systems The performance of the 118 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 network is also crucial generally we expect the best speed up on very fast networks and shared memory systems 1 e multi CPU multi core architectures We further expect the speed up to become worse in comparison to the ideal linear speed up with an increasing number of processes 2 28 Restarting MPI runs There is one situation that should be avoided when exploiting parallel computation Usually a simulation involv ing for example a hysteresis loop can be continued using the restart switch This is also true for MPI runs However the number of CPUs used must not change between the initial and any subsequent runs The reason for this is that the _dat h5 file needs to store the mesh as it has been reordered for n CPUs If we continue the run with another number of CPUs the mesh data will not be correct anymore which will lead to errors when extracting the data from the _dat h5 file Note also that there is currently no warning issued in Nmag 0 1 if a user ventures into such
48. as the stem of the name of any data files that are being written If this name is not specified as in Example demag field in uniformly magnetised sphere 1t defaults to the name of the file that contains the script but without the py extension Next we load the mesh file and set the initial normalised magnetisation to point in the 1 0 1 direction i e to have equal magnitude in the x and z direction and 0 in the y direction sim load_mesh bar30_30_100 nmesh h5 Py mat_Py unit_length SI le 9 m sim set_m 1 0 1 This vector will automatically be normalised within nmag so that 1 0 1 is equivalent to the normalised vector 0 70710678 0 0 70710678 In this example we would like to study a dynamic process and will ask nmag to compute the time development over a certain amount of time dt The line dt Sitseri2 s simply creates a SJ object which represents our timescale We then have a Python for loop in which i will take integer values ranging from 0 to 60 for subsequent iterations All indented lines are the body of the for loop In the Python programming language scoping is expressed through indentation rather than braces or other types of parentheses Text editors such as Emacs come with built in support for properly indenting Python code by pressing the Tab key on a line to be indented for i in range 0 61 sim advance_time dtx i 16 Chapter 2 Guided Tour NMAG User Manual Doc
49. b vtk a_minus_b vtk Notice that in the last version of the script we also added the line assert a structure points i b structure points i which does just check that the two files are using the same set of points i e the same mesh 8 16 How to re sample data from a saved h5 file Available in Nmag 0 2 0 You can load an h5 file like this 170 Chapter 8 Frequently Asked Questions NMAG User Manual Documentation Release 0 2 1 import ocaml from nmag h5probe import Fields handler Fields infile h5 field handler set_field_data m Py 0 And probe one of its fields position 0 1 2 In mesh units typically is nanometres value ocaml probe_field field m_Py position 0 1 This way you can create two arrays rs containing an array of points and vs containing the corresponding values You can then use pyvtk to generate a VTK file from these import pyvtk grid pyvtk UnstructuredGrid rs data pyvtk PointData pyvtk Vectors vs v pyvtk VtkData grid data v tofile outfile vtk Here is a full example which probes the magnetisation in the outer skin of a cylinder in sections which are not equally spaced Notice the usage of the function float_set to specify where the sampling should be denser originally here is where a domain wall was The script should be used as nsim probe py infile h5 outfile vtk import math import sys import pyvtk import ocaml from nmag h5
50. based on the Python programming language This seems to be a somewhat reasonable choice at present as Python is especially friendly towards casual users who do not want to be forced to first become expert programmers before they can produce any useful results Furthermore Python is quite widespread and widely supported these days 1 Thomas Fischbacher Matteo Franchin Giuliano Bordignon Hans Fangohr A Systematic Approach to Multiphysics Extensions of Finite Element Based Micromagnetic Simulations Nmag IEEE Transactions on Magnetics 43 6 2896 2898 2007 online at http eprints soton ac uk 46725 2 Thomas Fischbacher Matteo Franchin Giuliano Bordignon Andreas Knittel Hans Fangohr Parallel execution and scriptability in micromagnetic simulations Journal of Applied Physics 105 07D527 2009 online at http link aip org link JAPIAU 105 07D527 1 NMAG User Manual Documentation Release 0 2 1 1 2 How to read this document We suggest you follow the Guided Tour through a number of examples to get a quick overview of what nmag looks like in real use and to see examples that can be used to carry out typical simulations We provide a number of skeletons that are easily adapted to specific systems which show how to compute hysteresis loops do energy minimisation or compute time evolution The Command reference section explains the relevant commands provided by Nmag in full detail This should be especially useful to advanced us
51. by 1 It is available in the 45 data file and the Data files ndt data files and thus allows to match data in the ndt files with the corresponding spatially resolved field data in the h5 file stage_step The number of steps since we have started the current stage stage_time The amount of time that has been simulated since we started this stage real_time The amount of real time the simulation has been running this is the wall execution time and therefore typically of the order of minutes to days local_time A string human readable with the local time Useful in data files to see when an entry was saved unix_time The number of non leap seconds since 1 1 1970 this is the same information as lo cal_time but represented in a more computer friendly way for computing differences 3 8 2 Some geek talk deciphered nmag uses some object orientation in the high level user interface presented here There are a few special terms used in object orientation that may not be familiar and of which we attempt to give a very brief description method A method is just a function that is associated to an object 3 9 Solvers and tolerance settings There are a number of linear algebra solvers and one solver for ordinary differential equations ODEs in nmag 1 two solvers for the calculation of the demagnetisation field Default values can be modified when creating the Simulation object this user interface is not final if you really fee
52. command This will return a VumPy array that contains one 3d vector for every Site of the finite element mesh In step 5 we modify the first entry in this array which has index 0 and set its value to 0 1 0 Whereas the magnetisation is pointing everywhere in 1 0 0 because we have used the set_m command in the very beginning of the program it is now pointing in the 0 1 0 at site 0 The information which site corresponds to which entry in the data vector that we have obtained using get_subfield can be retrieved from get_subfield_sites Correspondingly the position of the sites can be obtained using get_subfield_positions We now need to set this modified magnetisation vector Step 6 using the set_m command If we save the data again to the file Step 7 we can subsequently convert this to a vtk file using for example nmagpp vtk data sphere_manipulate and visualise with MayaVi 2 7 Example Manipulating magnetisation 43 NMAG User Manual Documentation Release 0 2 1 0 00 0 143 m_Py lt gt X component 0 286 0 429 0 571 0 714 0 857 1 00 We can see one blue cone in the centre of the sphere this is the one site that he have modified to point in the y direction whereas all other cones point in the x direction As before we can probe the fields along a line through the center of the sphere Step 8 For the demag field we obtain x le 08 H_demag x 9e 09 H_demag x 8e 09
53. daemon you can use gt mpdallexit For diagnostic purposes the mpdt race command can be use to track whether a multipurpose daemon is running and which machines are part of the mpi ring Advanced usage of mpich2 To run a job across different machines one needs to start the multi purpose daemons on the other machines with the mpdboot command This will search for a file in the current directory with name mpd hosts which should contain a list of hosts to participate very similar to the machinefile in MPICH1 To trace which process is sending what messages to the standard out one can add the 1 switch to the mpiexec command then each line of standard output will be preceded by the rank of the process who has issued the message Please refer to the official MPICH2 documentation for further details 2 27 2 Using mpich1 Note Most users will use MPICH2 if they have compiled Nmag from the tar ball see Using mpich2 Suppose we would like to run Example 2 Computing the time development of a system of the manual with 2 processors using MPICH1 We need to know the full path to the ns im executable In a bash environment this is pretty much the standard on Linux and Mac OS X nowadays you can find the path using the which command On a system where nsim was installed from the Debian package gt which nsim usr bin nsim Let s assume we have a multi core machine with more than one CPU This makes the mpi setup slightly easier
54. eo Rew Ge ee ae be ae bo 6 4 Convert nmesh h5 to nmesh file and back 63 NMMESHIMPOR osorno A eee eR EEL EG 6O HSID oss u aiii a a ge Geko See Bene Dacca Daaba tee She gy ae en bh eal Ga Wedge lge ae ae ge 6 7 MSIMVEFSION 3 245 us aw oe ae Go a ee Meat ate eae a Gb a ee aie a tat Files and file names 7 1 meshfiles nmesh nmesh h5 0 0 0 e a E AE o E e E E A 1 2 Simulation ScriptS s PY s See ke a how e Beek GN a GOA aa 73 Datatilles Ade dia a a a eee A A ee ao ad TA Data filesiC sD a a aa aio Ga 73 Filenames fordata tiles ion ci eR AE wae A ee E 7 6 Filenames for loo MES s pce mocap e eo Beige ok RG Bs Rg Yh bowl e Re a eR we Frequently Asked Questions 8 1 What is the difference between the OOMMF and nmag approach 8 2 So this means the major difference is cubes vs tetrahedra o o o oo oo 8 3 Why do you have your own Python interpreter nsim 2 00 8 4 What is nsim I thought the package is called nmag o o 8 5 How fast is nmag in comparison to magpar e 8 6 How do I start a time consuming nmag run in the background 0 8 7 nmag claims to support MPI So can I run simulation jobs on multiple processors 8 8 How should Lcitenmas uc cutres a e al ea 8 9 Why can you not use the step as a unique identifier o o 8 10 How to generate a mesh wit
55. for the direc tion and magnitude of the external field The second determines the meaning of these numerical values us ing an SI object Suppose we would like an external field of le6 A m acting in the y direction then the 2 1 Example Demag field in uniformly magnetised sphere 9 NMAG User Manual Documentation Release 0 2 1 command would read sim set_H_ext 0 1e6 0 SI 1 A m However we could also use sim set_H_ext 0 1 0 SI le6 A m The default value for the external field is 0 0 0 A m so for this example we could have omitted the set_H_ext command altogether 2 1 7 Extracting and saving data We have three different ways of extracting data from the simulation 1 saving averaged values of fields which can be analysed later 2 saving spatially resolved fields which can be analysed later 3 extracting field values at arbitrary positions from within the running program In this basic example we demonstrate the use of all three methods Saving averaged data sim save_data The save_data method writes spatial averages of all fields see Fields and subfields into a text file which will be named spherel_dat ndt see below This file is best analysed using the co tool but can also just be read with a text editor The format follows OOMMP s odt file format every row corresponds to one snapshot of the system see save_data The function can also be called with parameters to save spatially resolved f
56. is loaded Create the simulation object and load the mesh sim nmag Simulation sim_name do_demag do_demag sim load_mesh mesh_name np mat unit_length mesh_unit Note that sim_name is passed to the Simulation object allowing the user to use different prefixes for the output files of the simulation For example if sim_name relaxation then the output files produced when saving the fields or their averages to disk will have names starting with the prefix relaxation_ On the other hand if sim_name dynamics the names of these files will all start with the prefix dynamics_ Using different simulation names allows us to save the data of part I and part II in different independent files The function continues with the code above Set the pinning at the left and right face of the nanopillar def pinning p X Y Z Pp tmp float SI x m mesh_unitx xhl if abs tmp gt 0 999 2 22 Example Current driven magnetisation precession in nanopillars 91 NMAG User Manual Documentation Release 0 2 1 return 0 0 else return 1 0 sim set_pinning pinning which is used to pin the magnetisation at the left and right faces of the cylinder Note here that x is the x component of the position of the mesh site and that tmp float SI x m mesh_unitx hl is equal to 1 at the right face and to 1 at the left face We then set the magnetisation If init ial_misa string then we assume it is the name of
57. list which will broadcast updates of nmag and any other relevant news To subscribe to this list send an email to nmag announce request lists soton ac uk with an empty subject and the word subscribe in the body of the email The archives can be found and searched at http groups google com group nmag announce 1 4 2 nmag users nmag users lists soton ac uk is a mailing list to discuss the use of nmag and for users to support users Any announcements to nmag announce will also be sent to this mailing list To subscribe to this list send an email to nmag users requestO lists soton ac uk with an empty subject and the word subscribe in the body of the email Information about how to unsubscribe are provided with the welcome message once you have subscribed The archives can be found and searched at http groups google com group nmag users 4 Chapter 1 Introduction NMAG User Manual Documentation Release 0 2 1 1 5 Support Support will be provided within our limited resources which may be None After consulting the manual please feel free to use the Mailing list nmag users lists soton ac uk to seek advice or contact the nmag team directly 1 6 License and Disclaimer This software was developed at the University of Southampton United Kingdom It is released under the GNU General Public License GPL as published by the Free Software Foundation either version 2 or at your option any later version Nmag is an exper
58. must be polynomial in the components of m a m that computes anisotropy energy density as a function of the normalised magnetisation direction m If you specify a custom anisotropy function you also need to pass the order of the polyno mial in the anisotropy_order parameter Default value is None that is no anisotropy term is used anisotropy_order int If a custom polynomial anisotropy function a m is specified the order of the polynomial must be given in this parameter This is not required for pre defined uniaxial_anisotropy or cubic_anisotropy anisotropy functions Default value is None do_precession True or False Boolean that can switch off the precessional term in the LLG equation This is useful to improve convergence speed when studying metastable configu rations properties list of strings default magnetic material A list of additional properties this material will be associated with Normally users do not have to change this but it 1s used internally when setting up discretized operators Example and default value True 4 1 1 uniaxial_anisotropy Module nmag Object uniaxial_anisotropy Arguments axis K1 K2 0 Returns a predefined anisotropy modelling an uniaxial anisotropy energy density term E_anis Kl x lt axis m gt 2 K2 x lt axis m gt 4 where m is the normalised magnetization Parameters axis vector list Easy axis or hard axis if K1 lt 0 will be
59. name of the log file starts with the name of the simulation script without the py extension and ends with _log log For example a simulation script with name mybar py will have an associated log file with name mybar_log log Another three files will be created if the undocumented dumpconf switch is provided This are primarily of use to the developers and can usually be ignored e mybar_log conf This can be used to configure what data is logged e mybar_ocaml conf Configuration of some variables used in the ocaml code mybar_nmag conf Some variables used in the nmag code 164 Chapter 7 Files and file names CHAPTER EIGHT FREQUENTLY ASKED QUESTIONS What is the difference between the OOMMF and nmag approach So this means the major difference is cubes vs tetrahedra Why do you have your own Python interpreter ns im What is nsim I thought the package is called nmag How fast is nmag in comparison to magpar How do I start a time consuming nmag run in the background nmag claims to support MPI So can I run simulation jobs on multiple processors How should I cite nmag Why can you not use the step as a unique identifier How to generate a mesh with more than one region using GMSH Can I run more than one simulation in one directory Can I save data to an arbitrary directory Do you really need to do so How to save data to a different directory How to check the convergence of a sim
60. nmesh periodic film Py unit_length SI le 9 m print ocaml mesh_plotinfo_periodic_points_indices sim mesh raw_mesh 2 19 Example Spin waves in periodic system 77 NMAG User Manual Documentation Release 0 2 1 function to set the magnetisation def perturbed_magnetisation pos X Y Z pos newx x le9 newy yxle9 if 8 lt newx lt 14 and 3 lt newy lt 3 the magnetisation is twisted a bit return 1 0 5 x x math cos math pix newx 11 6 3 math cos math pix newy 6 3 0 0 else return 1 0 0 0 0 0 set initial magnetisation sim set_m perturbed_magnetisation let the system relax generating spin waves s SI s from nsim when import every at sim relax save averages fields every time 0 05e 12xs at convergence do exit at time 10e 12xs To execute this script we call the nsim executable for example on linux nsim spinwaves py As in the previous examples we first need to import the modules necessary for the simulation define the material of the magnetic object load the mesh and set the initial configuration of the magnetisation Here we start from a spatially non homogeneous configuration in order to excite spin waves Nmag allows us to provide a function to be sampled on the mesh that defines a particular magnetisation configuration In our case we use the function def perturbed_magnetisation pos X
61. of the spin current llg xi is the degree of non adiabadicity HB is the Bohr magneton is the electron charge e is positive e e 5 S Zhang and Z Li Roles of Nonequilibrium Conduction Electrons on the Magnetization Dynamics of Ferromagnets Physical Review Letters 93 127204 2004 online at http link aps org doi 10 1103 PhysRevLett 93 127204 2 21 Example Spin transfer torque Zhang Li model 81 NMAG User Manual Documentation Release 0 2 1 In this and in the next examples we show how to set up a micromagnetic simulation including such spin transfer torque effects We show how the current density can be specified and how the required parameters can be included in the material definitions As a first example we consider a thin Permalloy film which develops a vortex in the center We compute the dynamics of the vortex as a response to the application of a current 2 21 1 Current driven motion of a vortex in a thin film The system under investigation is a 100 x 100 x 10 nm Permalloy film The mesh is stored in the file pyfilm nmesh h5 The simulation is subdivided in two parts e In part I the system is relaxed to obtain the initial magnetisation configuration when the current is not applied which is just a vortex in the center of the film e In part II the vortex magnetisation obtained in part I is loaded and used as the initial magnetisation configu ration A current is applied and the magnetisation d
62. oo ae ea ew ee RS RR Se ee Pe eS E 57 2 14 Applying a field that changes both in time and in Space ooo o 59 215 Example two different magnetic materials scsi r pay Se 224 8 ee Ne ee ee Oe 62 2 16 Examples Larmor precession ed ro BASE Oh e BESS A Be bw A 67 2 17 Example ID periodicity sos psss ee ae bb eee ee ee ee a a we 69 2 18 Example 2D periodicity iyos erde be ba Oe Le eA a ee ee ea 73 2 19 Example Spin waves in periodic system 2 2 e 76 2 20 Example post processing of saved field data oo 80 2 21 Example Spin transfer torque Zhang Li model o e 81 2 22 Example Current driven magnetisation precession in nanopillars 86 2 23 Mesh distortion for edge roughness simulation 94 2 24 Compression of the Boundary Element Matrix using HLib o 96 2 29 Example Calculation of dispersion Curves 20245 348i pee Sey eee eee a w as 103 2 26 Example Timestepper tolerances load rear aa Gee ee e ee 108 22 Example Parallelexecution MPD i c 2225424554 4452 04 44 oe ba eee be ead 114 2 28 Restarting MPI runs 3 5 52 6 Gs ew p e tS o we ee ae a e 119 2 29 More than one magnetic material exchange coupled o ooo 119 3 Background 121 Sul ATCHILECITCOVEIVIEW 25 5 e e EOE A a di ja A 122 32 Themsun library oks tr OR A A E 122 33 Fieldsandsubnelds S ezar es a a sado A 123 SA
63. periodicity demonstrates the macro geometry concept for a thin film This is followed by the Spin waves example which includes exchange coupling between periodic copies and is of more practical value The mesh of the central simulation cell used is described in cube geo which reads algebraic3d prism solid prism orthobrick 7 50 Ps D0 T90 7 50 7 50 750 maxh 1 80005 tlo prism Note that the mesh is centered around the origin This is recommended for periodic simulations We need to document this better The resulting mesh is this the periodic copies are not shown The script periodicl py reads import nmag from nmag import SI define magnetic material Py nmag MagMaterial name Py Ms SI 1le6 A m exchange_coupling SI 13 0e 12 J m size of simulation cell plus extra spacing to avoid exchange interaction across interfaces between repeated copies of the simulation cell x_lattice 15 01 the spacing is 0 01 y_lattice 0 0 z_lattice 0 0 list to store the lattice points where the periodic copies will be placed lattice_points for xi in range 3 4 lattice_points append xi x_lattice 0 0 y_lattice 0 0 z_lattice create data structure pbc for this macro geometry pbc nmag SetLatticePoints vectorlist lattice_points scalefactor SI le 9 m create simulation object passing macro geometry data structure http link aip org link JAP 105 07D529
64. propagation in disk 35 4 NMAG User Manual Documentation Release 0 2 1 Z 0 100 0 100 1 00 1 00 1 00 To simulate the magnetised disc we use the following script nanodot py import nmag from nmag import SI at create simulation object sim nmag Simulation define magnetic material Py nmag MagMaterial name Py Ms SI 795774 A m exchange_coupling SI 13 0e 12 J m load mesh the mesh dimensions are scaled by 100nm sim load_mesh example_vortex nanodot nmesh h5 cylinder Py unit_length SI 100e 9 m set initial magnetisation eim set_m 1 0 0 lt Hs nmag vector_set direction 1 0 0 norm_list 12 0 7 0 200 0 units le3 SI A m loop over the applied fields Hs sim hysteresis Hs save averages at convergence fields at convergence restart at convergence 36 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 We would like to compute the magnetisation behaviour in the applied fields ranging from 12e3 0 0 A m to 200e3 0 0 A min steps of 5e3 A m The command for this is Hs nmag vector_set direction 1 0 0 norm_list 12 0 7 0 200 01 units 1e3xS1I A m sim hysteresis Hs save averages at convergence fields at convergence restart at convergence The col co
65. properties of PermAlloy The third argument to load_mesh is an SI object which defines what physical distance should be associated with the length 1 0 as given in the mesh file In this example the mesh has been created in nanometers i e the distance 1 0 in the mesh file should correspond to 1 nanometer in the real world We thus use a SI object representing 1 nm 2 1 5 Setting the initial magnetisation To set the initial magnetisation we use the set_m method sim set_m 1 0 0 The field m describes the direction of magnetisation as a field of normalised vectors whereas the field M contains the magnetisation with its proper magnitude So M is the saturation magnetisation in Amperes per meter whereas m is dimensionless with m 1 0 There are different ways to set a particular magnetisation in the simplest case of a homogeneously magnetised body it is sufficient to provide the magnetisation vector So in this example we provide a unit vector pointing in positive x direction We could provide a vector with non normalised magnitude which would be normalised automatically This is convenient for say setting an initial magnetisation in the x y plane with a 45 degree angle towards the x axis by specifying 1 1 0 2 1 6 Setting the external field We can set the external field using the set_H_ext command sim set_H_ ext 0 0 0 SI A m In contrast to se _m this method takes two arguments The first defines numerical values
66. results obtained for the dynamics The average magnetisation as a function of time can be extracted using ncol dynamics time M_mat_0 M_mat_1 M_mat_2 gt m_of_t dat We can use the following gnuplot script set term postscript color eps enhanced solid set out m_of_t eps set xlabel time ns set ylabel average magnetisation 10 6 A m plot 0 6 m_of_t dat u 1 1e9 2 1e6 t lt M_x gt wl u lx x1e9 3 1e6 t lt M_y gt w 1 u S1 1le9 4 1e6 t lt M_z gt w 1 and obtain the following graph 92 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 y component of magnetisation 0 00 0 143 0 286 0 429 0571 0 714 0 857 1 00 average magnetisation 1 o A m time ns 2 22 Example Current driven magnetisation precession in nanopillars 93 NMAG User Manual Documentation Release 0 2 1 The sinusoidal dependence of the y and z magnetisation components suggests that the magnetisation rotates around the nanopillar axis with a frequency which increases to approach its maximum value A more detailed discussion of results and interpretation is provided in the publ
67. same mesh First save the data into two ASCII VTK files For example nmagpp vtk m vtk vtkascii fields m simulation_name Note the option vtkascii to force the creation of a ASCII file Let s say this command created the two files m 000000 vtk and m 000001 vtk You can now use the library pyvtk to load the two files compute the difference and save it back to a third file import numpy pyvtk a pyvtk VtkData m 000000 vtk b pyvtk VtkData m 000001 vtk va a point_data data 0 vectors vb b point_data data 0 vectors for i in range len va va i list numpy array va i numpy array vb i a tofile difference vtk Save this text to a file named diff py and run it as python diff py You ll get a third file with name difference vtk containing the difference of the two fields If you are repeating this operation many times it may become annoying to open again and again the diff py file to change the names of the input files You can then modify the script as follows import sys numpy pyvtk a pyvtk VtkData sys argv 1 b pyvtk VtkData sys argv 2 va a point_data data 0 vectors vb b point_data data 0 vectors for i in range len va assert a structure points i b structure points i va i list numpy array va i numpy array vb i a tofile sys argv 3 The name of the files are taken from the command line You can then compute the difference using python diff py a vtk
68. size of 5e3 A m to resolve this applied field range better This will take us through zero applied field 0 0 0 A m Now symmetrically to the positive field values we would like to use a step size of 100e3 A m again to go from 100e3 0 0 A mto 1le6 0 0 A m At this point we would like to reverse the whole sequence to sweep the field back to the initial value The information we need for the hysteresis command includes 1 a direction for the applied field here just 1 0 0 2 a list of magnitudes of the field this is the norm_1i st that will be interpreted and then multiplied with the direction vector As in the Example Simple hysteresis loop and in the Example Hysteresis loop for Stoner Wohlfarth par ticle we employ a special notation for ranges of field strengths understood by nmag vector_set The expression 1000 0 900 0 95 0 means that we start with a magnitude of 1000 the next magnitude is 900 The empty brackets indicate that this sequence should be continued i e 800 700 600 500 400 300 200 100 up to but not beyond the next value given i e 95 3 another multiplier that defines the strength of the applied fields here 1e3 SI A m The corresponding command is Hs nmag vector_set direction 1 0 0 norm_list 1000 0 900 0 95 0 9020 Ly 100 0 2000 C 1000 0 90007 11 90 50 90 0 1 100 0 200 0 1000 0 units 1e6xS1I A m
69. the Exchange length or even about the Exchange length is chosen If the spin angle stays sufficiently low during the whole simulation including intermediate non equilibrium configurations then this may be acceptable The ultimate test recommended by among others M Donahue and the nmag team is the following cell size dependence test The best way to check whether the cell size has been chosen small enough is to perform a series of sim ulations with increasing cell size Suppose we are simulating Permalloy Ni80Fe20 with Ms 8e5 A m A 1 3e 11 and the Exchange length l is about 5nm Suppose further we would like to use a cell size of 5nm for our simulations We should then carry out the same simulation with smaller cell sizes for example 4nm 3nm 2nm Inm Now we need to study typically plot some scalar entity of the simulation such as the coercive field or the remanence magnetisation as a function of the cell size Ideally this entity should converge towards a constant value when we reduce the simulation cell size below a critical cell size This critical cell size is the maximum cell size that should be used to carry out the simulations Be aware that 1 it is often nearly impossible to carry out these simulations at smaller cell sizes because of a lack of computational power and ii this method is not 100 fool proof the observed entity may appear to converge towards a constant but actually start changing again if
70. the file and load the magnetisation with the method load_m_from_h5file otherwise we assume it is just a function and set the magnetisation in the usual way using the method set _m if type initial_m str Set the initial magnetisation sim load_m_from_h5file initial_m a from file if a string is provided else sim set_m initial_m b from function vector otherwise We then set the current density along the x direction only if 3 is not zero if j 0 0 Set the current if needed sim set_current_density j 0 0 0 0 unit SI A m 2 Finally we set tolerances the stopping criterion and launch the simulation Set additional parameters for the time integration and run the simulation sim set_params stopping_dm_dt stopping_dm_dt ts_rel_tol le 7 ts_abs_tol le 7 sim relax None save save do do return sim The relax function carries out the simulation taking into account the stopping criterion and save and do actions Finally the function returns the simulation object which it created 2 22 2 Results precession of the magnetisation We launch the script with nsim stt_nanopillar py The script runs both part I output files starting with relaxation_ and part II output files starting with dynamics_ The relaxed magnetisation can be extracted and saved into a vtk file using the command nmagpp relaxation vtk m vtk MayaVi can then be used to obtain the following picture We can now take a look at the
71. the section of the code that starts with def run_sim tol defines a function with name run_sim which will carry out a complete simulation every time it is called It takes one argument the parameter tol The simulation name which is re used in the name of the Data files ndt data file contains the value of tol For example if the to1 0 1 then the name of the simulation is bar_0 100000 and the name of the ndt data file is bar_0 100000_dat ndt We can thus call this function repeatedly for different values of to1 and each time a complete simulation will be run and new data files created 11 The main loop of the script main program tols 1e 1 1e 2 1e 3 1e 4 1e 5 1e 6 1 0 for tol in tols run_sim tol simply iterates over values 0 1 0 01 0 001 0 0001 0 00001 and 0 000001 and calls the func tion run_sim with a different tolerance value in every iteration of the for loop Once the program has finished we have data files bar_0 000001_dat ndt bar_0 000010_dat ndt and bar_0 100000_dat ndt that can be analysed and plotted in the usual way We show a plot of the x y and z components of the magnetisation against time as in Example 2 Computing the time development of a system for each of the tolerance values The run with tol 1e 6 is the most accurate and the corresponding black line has been tagged with little characters 8e 05 ai tol 1e 1 tol 1e 2 tol 1e 3 tol 1e 4 tol 1e 5 6e 05 tol 1e 6 E lt
72. the visualisation without further manual intervention However we expect that this is not a show stopper and will dedicate our time to more pressing issues User feedback and suggestions for improvements are of course always welcome 2 27 4 Performance Here is some data we have obtained on an IBM x440 system with eight 1 9Ghz Intel Xeon processors We use a test simulation located in tests devtests nmag hyst hyst par which computes a hysteresis loop for a fairly small system 4114 mesh nodes 1522 surface nodes BEM size 18MB We use overdamped time integration to determine the meta stable states Both the setup and the time required to write data will not become significantly faster when run on more than one CPU We provide total time this includes setup time time for the main simulation loop and time for writing data measured in seconds total speedup The speed up for the total execution time i e ratio of execution time on one CPU to execution time on n CPUs sim time this is the time spend in the main simulation loop and this is where expect a speed up sim speedup the speedup of the main simulation loop CPUs total time total speedup sim time sim speedup 1 4165 1 00 3939 1 00 2 2249 1 85 2042 1 93 3 1867 2 23 1659 2 37 4 1605 2 60 1393 2 83 The numbers shown here have been obtained using mpich2 and using the ssm device instead of the default sock device this is available on Linux
73. thesystem py to setup the system loads the initial magnetisation configuration from the file m0 h5 produced by relaxation py It then applies a localised pulse of the applied magnetic field on one side of the wire and compute the dynamical response of the system saving the result to files Consequently in order to run the full simulation the user will have to type two commands on the shell one for each part of the simulation nsim relaxation py nsim dynamics py there is no need to type nsim thesystem py as this file is implicitly included by the other two In the next sections we will go through the three files which make up the numerical experiment 2 25 1 The system thesystem py The system under investigation is a cylindrical nanopillar of radius r 3 nm and length 1 600 nm The mesh file cylinder nmesh h5 is obtained using Netgen The figure shows a cylinder that is 100nm long The geometry file given to Netgen cylinder geo is shown below algebraic3d solid nanopillar cylinder 300 0 0 0 300 0 O 07 3 0 and plane 300 0 0 0 1 O 0 and plane 300 0 0 0 1 O 0 maxh 1 0 tlo nanopillar The cylinder is made of Permalloy and as specified in the file thesystem py shown below In this file we define the material parameters and geometry of the system so that we can use it in two simulations first during the relaxation then during the dynamics from nmag common impo
74. to be processed For example to convert every second saved configuration i e ids 0 20 40 into vtk files we could use nmagpp range range 0 60 20 vtk x vtk bar The string range 0 60 20 is a Python expression and will evaluate to 0 20 40 because it is the list of integers starting from 0 going up to but not including 60 in steps of 20 This will create files x 000000 vtk x 000020 vtk and x 000040 vtk 6 2 5 Other features Use nmagpp help to get an overview of other features of nmag and further details 6 2 nmagpp 157 0 831957 0 833272 NMAG User Manual Documentation Release 0 2 1 6 3 nmeshpp The nmeshpp program is the NMESHPreProcesser and NMESHPostProcessor It provides quick access to some statistical information about nmesh meshes The basic usage is nmeshpp OPTIONS INPUTFILE OUTPUTFILI where INPUT is the name of a nmesh file either in ascii or hdf5 format OUTPUTFILE is the name of the file to be written to if required this depends on the OPTIONS and OPTIONS can be one or several of the options listed in the following subsections We use the mesh file bar30_30_100 nmesh h5 from Example 2 to illustrate the usage of nmeshpp E 6 3 1 General information info The command nmeshpp info bar30_30_100 nmesh h5 produces the following output Info output 3 dimensional mesh 18671 volume elements 3d 3438 surface elements 2d
75. two_cubes nmesh h5 cubel Py cube2 Co unit_length SI le 9 m set initial magnetisation along the positive x axis for both cubes slightly off in z direction sim set_m 0 999847695156 0 0 01745240643731 ns SI le 9 s corresponds to one nanosecond sim relax save averages every time 0 0lx ns fields every time 0 05 ns at convergence The script is very similar to the one used in Example 2 Computing the time development of a system However here we have two materials The related changes are that we define two magnetic materials and assign them to objects Co and Py When loading the mesh sim load_mesh two_cubes nmesh h5 cubel Py cube2 Co unit_length SI le 9 m 2 15 Example two different magnetic materials 63 NMAG User Manual Documentation Release 0 2 1 we need to assign regions 1 and 2 in the mesh file which correspond to the two cubes to the materials This is done with this list of tuples cubel Py cube2 Co The first list entry is cubel Py and tells nmag that we would like to refer to the region 1 as cubel and that we would like to assign the material P y to this region This entry refers to region 1 because it is the first entry in the list The second list entry is cube2 Co and tells nmag that we would like to refer to the region 2 as cube2 and that we would like to assign the ma
76. very similar in nmag and magpar and about equally efficient However we observe that depending on the particular problem subtle differences in the philosophies underlying time integration can lead to noticeable differences in the number of individual steps required to do some particular simulation which can be up to about 25 of simulation time in either direction Setup time is a different issue nmag derives its flexibility from abstract approaches where magpar uses hard coded compiled functions Where magpar uses a hand coded Jacobian nmag employs the nsim core to symbolically compute the derivative of the equations of motion There is a trade off the flexibility of being able to introduce another term into the equations of motion without having to manually adjust the code for the Jacobian comes at a price in execution time Therefore nmag s setup time at present is far larger than magpar s This can be alleviated to a considerable degree by providing hard coded bypass routines which can be used as alternatives to the symbolically founded methods for special situations that are frequently encountered such as setting up a Laplace operator matrix Conceptually it is easy to add support for this but due to limited manpower it has not happened yet 166 Chapter 8 Frequently Asked Questions NMAG User Manual Documentation Release 0 2 1 In short once the setup stage is over nmag is about as fast as magpar Magpar s setup time
77. which computes a list of vectors Hs The hysteresis command takes this list of applied fields Hs as one input parameter and will compute the hysteresis loop for these fields sim hysteresis Hs save averages fields restart at convergence Again the second parameter save is used to tell the hysteresis command what data to save and how often We request that the averages of the fields the fields and the restart data should be saved at those points in time where we reach convergence See also Restart example 2 5 Example Hysteresis loop for thin disk 33 NMAG User Manual Documentation Release 0 2 1 2 5 1 Thin disk hysteresis loop Once the calculation has finished we can plot the hysteresis loop i e the graph of the magnetisation computed along the direction of the applied field as a function of the applied field strength We use the ncol command to extract the data into a text file plot dat ncol nanodotl H_ext_0 m_Py_0 gt plot dat This file starts as follows 1000000 0 9995058139817 1000000 0 9995058139817 900000 0 9994226410102 900000 0 9994226410102 800000 0 9993139080655 We use Gnuplot to plot the hysteresis loop gnuplot make_plot gnu using the gnuplot script make_plot gnu set term postscript eps enhanced color set out nanodot_hyst eps set xlabel Applied field A m set ylabel M Ms set xrang 1 2e6 1 2e6 set yrange 1 2 1 2 plot
78. which is the x component of the magnetisation of the Py material e 22 for M_Py_1 which is the y component of the magnetisation of the Py material and e 23 for M_Py_2 which is the z component of the magnetisation of the Py material We can use ncol to extract this data into a file data_M dat which has the time for each time step in the first column and the x y and z component of the magnetisation in columns 2 3 and 4 respectively ncol bar 0 21 22 23 gt data_M txt This creates a text file data_M txt that can be read by other applications to create a plot Note however that the order of the entries in the ndt file is not guaranteed 1 e the numbers corresponding to fields may change with different versions of the software or different simulations for example the user may add extra fields Therefore the recommended approach is to directly specify the names of the columns that are to be extracted i e time M_Py_0 M_Py_1 M_Py_2 ncol bar time M_Py_0 M_Py_1 M_Py_2 gt data_M txt We use the xmgrace command xmgrace nxy data_M txt to create the following plot manually adding the legend and axis labels T 8e 05 D D o a 4e 05 Magnetisation A m 2e 05 0 1e 10 2e 10 3e 10 time s 18 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 Comparison with OOMMF and Magpar We have carried out the same simulation with Magpar and OOMME The following plot shows
79. x a oO SS OBE OGIO AEG OBOE 300 HOCICO ER 0 5e 11 je 10 1 5e 10 2e 10 2 5e 10 3e 10 3 5e 10 4e 10 time s From this plot we can see that with using only the unit cell the magnetisation aligns along the x axis at equilibrium We now move to the macro geometry of a thin film with dimensions 400x300x10nm 3 which is realised in periodic2 py import nmag from nmag import SI every at define magnetic material Py nmag MagMaterial name Py Ms SI le6 A m exchange_coupling SI 13 0e 12 J m size of the simulation cell plus extra spacing x_lattice 30 01 the spacing is 0 01 to avoid exchange coupling y_lattice 10 01 between repeated copies of the simualtion cell z_lattice 0 0 list to store the lattice points where the periodic copies of the simulation cell will be placed lattice_points for xi in range 4 6 for yi in range 19 21 lattice_points append xi x_lattice yixy_lattice 0 0 z_lattice create data structure pbc for this macro geometry pbc nmag SetLatticePoints vectorlist lattice_points scalefactor SI le 9 m fcreate simulation object passing macro geometry data structure sim nmag Simulation periodic_bc pbc structure load mesh 74 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 sim load_mesh prism nmesh h5 repeated prism 2D Py unit_length SI le 9 m set initial magnetisation sim set_m 1
80. x 3e 09 H_exch_Py 1112837 3087986181 1112837 3087986207 0 0 x 4e 09 H_exch_Py 193877 66176242317 193877 6617624248 0 0 x 5e 09 H_exch_Py 1 6602158583197139e 09 0 0 0 0 x 6e 09 H_exch_Py 1 8844573960991853e 09 0 0 0 0 x 7e 09 H_exch_Py 6 2460015649740799 e 09 0 0 0 0 x 8e 09 H_exch_Py 1 1231714572170603e 08 0 0 0 0 x 9e 09 H_exch_Py 7 3643182171284044e 09 0 0 0 0 x le 08 H_exch_Py 3 4351784609779937e 09 0 0 0 0 We can see that the exchange field is indeed very large around x 0 Note that one of the fundamental problem of micromagnetic simulations is that the magnetisation must not vary significantly from one site to another In this example we have manually violated this requirement only to demon strate how the magnetisation can be modified and to see that this is reflected in the dependant fields such as demag and exchange immediately 2 8 Example IPython The basics of this file are as in Example Demag field in uniformly magnetised sphere a ferromagnetic sphere is studied and initially configured to have homogeneous magnetisation Here is the source code of sphere_ipython py import nmag from nmag import SI Create simulation object sim nmag Simulation Define magnetic material Py nmag MagMaterial name Py Ms SI 1le6 A m exchange_coupling SI 13 0e 12 J m Load mesh sim load_mesh spherel nmesh h5 sphere P
81. 0 0 0 x 6e 09 H_exch_Py 2 7214181426130964e 10 0 0 0 0 x 5be 09 H_exch_Py 1 6323042074911775e 09 0 0 0 0 x de 09 H_exch_Py 1 6243345875473033e 09 0 0 0 0 x 3e 09 H_exch_Py 5 6526341264934703e 09 0 0 0 0 x 2e 09 H_exch_Py 6 1145979552370084e 09 0 0 0 0 x le 09 H_exch_Py 3 0929969691649876e 09 0 0 0 0 x 0 0 H_exch_Py 9 2633407053741312e 10 0 0 0 0 x le 09 H_exch_Py 1 9476821552904271e 09 0 0 0 0 x 2e 09 H_exch_Py 2 9690302400434413e 09 0 0 0 0 x 3e 09 H_exch_Py 2 6077357277001043e 09 0 0 0 0 x 4e 09 H_exch_Py 1 5836815585162886e 09 0 0 0 0 x 5e 09 H_exch_Py 1 6602158583197139e 09 0 0 0 0 x 6e 09 H_exch_Py 1 8844573960991853e 09 0 0 0 0 x 7e 09 H_exch_Py 6 2460015649740799e 09 0 0 0 0 x 8e 09 H_exch_Py 1 1231714572170603e 08 0 0 0 0 x 9e 09 H_exch_Py 7 3643182171284044e 09 0 0 0 0 x le 08 H_exch_Py 3 4351784609779937e 09 0 0 0 0 Note that the subfield name we are probing for the exchange field is H_exch_Py whereas the subfield name we used to probe the demag field is H_demag without the extension _Py The reason for this is that the exchange field is a something that is associated with a particular material here Py whereas there is only one demag field that is experienced by all materials see also Fields and subfields 2 7 1 Modifying the magnetisation In step 4 we use the get_subfield
82. 0 nmesh h5 we can use the program bar30_30_100 py to run the simulation import nmag from nmag import SI mat_Py nmag MagMaterial name Py Ms SI 0 86e6 A m exchange_coupling SI 13 0e 12 J m lig_damping 0 5 sim nmag Simulation bar sim load_mesh bar30_30_100 nmesh h5 Py mat_Py 2 2 Example 2 Computing the time development of a system 15 NMAG User Manual Documentation Release 0 2 1 unit_length SI le 9 m sim set_m 1 0 1 dt SL 36 12 s for i in range 0 61 sim advance_time dt i compute time development if i 10 0 every 10 loop iterations sim save_data fields all save averages and all fields spatially resolved else sim save_data fotherwise just save averages As in Example demag field in uniformly magnetised sphere we start by importing nmag and creating the material object import nmag from nmag import SI mat_Py nmag MagMaterial name Py Ms SI 0 86e6 A m exchange_coupling SI 13 0e 12 J m lig_damping 0 5 We set the 11g_damping parameter to 0 5 As this is a dimensionless parameter we can pass a number Alter natively we may give it as SI 0 5 Note that in this example we give the appropriate physical value for the saturisation magnetisation of PermAlloy The next line creates the simulation object sim nmag Simulation bar Here we provide a name for the simulation which is bar This will be used
83. 00 0 95 0 90 li 2 00 units le6 SI A m which computes a list of vectors Hs Each entry in the list corresponds to one applied field The hysteresis command takes this list of applied fields Hs as one input parameter and computes the hysteresis loop for these fields sim hysteresis Hs save restart fields at convergence The save parameter is used to tell the hysteresis command what data to save and how often We have come across this notation when explaining the relax command in the section Relaxing the system of the previous example In the example shown here we request that the fields and the restart data should be saved at the point in time where we reach convergence The spatially averaged data is saved automatically to the Data files ndt file when the fields are saved This is done in a compact notation shown above which is equivalent to this more explicit version 26 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 sim hysteresis Hs save restart at convergence fields at convergence The compact notation can be used because here we want to save fields and restart data at the same time The hysteresis command computes the time development of the system for one applied field until a convergence criterion is met It then proceeds to the next external field value provided in Hs We run the simulation as usual using
84. 001 300 200 100 0 100 200 300 position in axis nm Fourier transform 500 1 8e 0i 1 6e 0 400 1 4e 0 NW 1 2e 0 y le 08 O 8e 09 200 O 6e 09 100 4e 09 2e 09 0 0 1 5 1 0 5 0 0 5 1 k 1 nm 2 26 Example Timestepper tolerances 109 NMAG User Manual Documentation Release 0 2 1 It is common that the amount of time simulated per iteration varies throughout a simulation as different time step sizes are required to resolve the physics to the same accuracy level The Data files ndt data file contains one column last_step_dt which provides the size of the time step Use ncol to extract this data conveniently The sundials tolerance parameters rtol and atol can be set in nmag using the ts_rel_tol and ts_abs_tol arguments in the set_params function The letters ts ints_rel_tolandts_abs_tol stand for Time Stepper The integration of the Landau Lifshitz and Gilbert equation is carried out on the normalised magnetisation and the corresponding field see Fields and Subfields in Nmag is called m the magnetisation with the saturation magnetisation magnitude is called capital M in nmag Because this field is normalised we set rtol and atol to the same value in this example and refer to the value just as tol We use the program bar_tol py that e re uses the bar studied in Example 2 Computing the time development of a system but e carries out the time integration for a number of different tolerance values import nma
85. 00142 0 00236 0 00330 We first need to select phi as the data source for scalar visualisation modules Through clicking on the Configure Data button in the DataVizManager section of MayaVi s user interface we can select phi lt A gt as the data source for scalar visualisations The lt A gt simply indicates that the units of the potential are Ampere To show the scalar potential we use the Visualize gt Module gt SurfaceMap module We can see that the potential varies along the x direction The legend at the bottom of the figure shows the colour code used We can also see from the legend title that the physical dimension of the potential phi is Ampere this is the lt A gt Unless the user specifies a particular request for physical dimensions the following rules apply for vtk files e position are given in the same coordinates as the mesh coordinates that is why in this example the x y and z axis have values going from 10 to 10 e all field data are given in SI units The next plot shows the demag field the vectors together with isosurfaces of the magnetic potential 2 1 Example Demag field in uniformly magnetised sphere 13 NMAG User Manual Documentation Release 0 2 1 H_demag lt A m gt 3 33e 05 9 93 2 86e 05 Ao 108 2 38e 05 1 90e 05 Z 1 430 05 9 9 52e 04 2799 4 760 04 Y 0 00 9 96 phi lt A gt 0 00328 0 00234 0 00140 0 000458 0 000482 0 00142 0 00236 0 00330
86. 1 1 loop over the applied field s SI 1 s sim relax save averages fields every time 5e 12 s at convergence As in the previous example we first define the three unit vectors of the lattice again slightly larger than the dimension of the unit cell to avoid overlapping and thus to eleminate any exchange coupling across the interfaces for this demonstration of the demagnetisation effects x_lattice 30 01 the spacing is 0 01 y_lattice 10 01 the spacing is 0 01 z_lattice 0 0 Then we define where the copies will be placed for xi in range 4 6 for yi in range 19 21 lattice_points append xi x_lattice yixy_lattice 0 0 z_lattice copies of the system along the x axis pbc nmag SetLatticePoints vectorlist lattice_points scalefactor SI le 9 m The simulation cell is always the one at the 0 0 0 lattice point The for loops therefore place 4 copies of the simulation cell in the negative x direction i e 4 0 0 3 0 0 2 0 0 and 1 0 0 and 5 in the positive the x direction i e 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 The translation vector 0 0 0 corresponds to the actual simulation cell Similarly the inner for loop places 20 copies along the positive y axis and 19 along the negative one We set the same initial configuration as before with a uniform magnetisation along 1 1 1 and let the system evolve towards the equilibrium The outcome is s
87. 19285767062581 22 213920341440794 x 4e 09 H_demag 330220 13307247689 76 54950394725968 5 0509172407556262 x 5e 09 H_demag 330298 69089200837 90 534514175273259 13 57279800234617 x 6e 09 H_demag 330375 34327985492 117 01128011426778 35 262477275758371 x 7e 09 H_demag 330415 38940687838 123 68558207391983 60 580352625726341 x 8e 09 H_demag 330474 37719032855 112 22952205433305 106 13032196062491 x 9e 09 H_demag 330499 64039893239 69 97070465326442 160 41688110297264 x le 08 H_demag 330518 649930441 26 536490670368085 212 32392103651733 The data is approximately 1 3 Ms 333333 A m in the direction of the magnetisation and approximately zero in the other directions as we would expect in a homogeneously magnetised sphere The deviations we see are due to i the shape of the sphere not being perfectly resolved ie we actually look at the demag field of a polyhedron and ii numerical errors 42 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 In step 3 we probe the exchange field along the same line The exchange field is effectively zero because the magnetisation is pointing everywhere in the same direction x le 08 H_exch_Py None x 9e 09 H_exch_Py 1 26432464385698 e 09 0 0 0 0 x 8e 09 H_exch_Py 2 0419540595507732e 10 0 0 0 0 x 7e 09 H_exch_Py 1 4334754136843496e 09 0
88. 3 NMAG User Manual Documentation Release 0 2 1 It is worth noting that the names of the fields are fixed whereas the subfield names are often material dependent and given by e the name of the field and the material name joined through _ if there is one material specific subfield for every magnetisation or e the name of the field if there is only one subfield such as the demagnetisation field or the applied external field This may seem a little bit confusing at first but is easy to understand once one accepts the general rule that the material dependent quantities and only those contain a material related suffix All atomic species experience the demagnetisation field in the same way so this has to be H_demag 1 e non material specific On the other hand anisotropy depends on the atomic species so this is H_anis_Py and therefore the total effective field also has to be material specific H_total_Py All this becomes particularly relevant in systems where two types of magnetic atoms are embedded in the same crystal lattice 3 4 2 Example two magnetic materials This table from the Example two different magnetic materials shows the fields and subfields when more than one material is involved Field Subfield s Comment m m_Py m_Co normalised magnetisation M M_Py M_Co magnetisation H_total H_total_Py H_total_Co total effective field H_ext H_ext external applied field only
89. 400 200 Memory MB 800 600 400 200 Setup Time s 0 4000 8000 12000 16000 20000 24000 28000 Number of Volume Nodes Besides the savings in memory hierarchical matrices also reduce the time needed for the simulation setup consid erably see the bottom graph 2 24 6 HLib and MPI The HLib library that is available for academic use does not support parallel execution It is thus stored on the master node and cannot be distributed over several nodes Simulations using the Hlib library can use MPI for all other calculations 2 25 Example Calculation of dispersion curves Nmag can be used to study the propagation of spin waves and to calculate dispersion curves Here we consider a simulation script which shows how to do that In particular we study a long cylindrical wire made of Permalloy We assume the magnetisation in the wire is relaxed along one axial direction i e there are no domain walls inside the wire One side of the wire is perturbed at time t 0 by a pulsed magnetic field The spin waves generated on this side propagate towards the other We want to study the propagation of spin waves and obtain the dispersion relation i e a relation between the wave vector and the frequency of the spin waves which propagate in the considered media To calculate the dispersion relation we use the method developed by V Kruglyak M Dvornik and O Dmytriiev In order to carry out such a numerical experiment we first n
90. 4086 points 1 simplex regions 1 2 point regions 1 1 2 region volumes 0 0 89999 999999999782 1721 boundary points gt BEM size lt 22MB 0 periodic points mirage 0 total 0 a0 average 3 543451 std 0 581220 min 1 953689 max 5 708395 Starting from the top of the output we are given the information that this is a three dimensional mesh with its number of volume elements i e tetrahedra in 3d surface elements i e surface triangles and points We are also given a list of simplex regions which is just 1 here If we had more than one region defined say two disconnected spheres that are to be associated with different material then we would have two entries here The numbers given in this list are the identifiers of the regions in this example there is only one region and it has the identifier 1 The point regions is a list of all regions in which points are located This includes of course region 1 Region 1 represents the vacuum around the meshed region The points that are located on the surface of the bar are located both in the bar region 1 and in the vacuum region 1 Other negative region numbers 2 3 can be used to discern different pieces of a boundary While this feature is at present not used by Nmag the underlying nsim framework provides capabilities to e g associate Dirichlet boundary conditions to a 1 1 boundary and von Neumann boundary conditions to a 1 2 boundary The region volumes p
91. 44 x le 09 H_demag 333064 22835497675 0 79797869001455679 74 851480234723581 x 2e 09 H_demag 333060 20872696047 2 9088218728650852 77 0823444044496 x 3e 09 H_demag 333056 59267071093 5 064110260421554 80 187548021318634 x 4e 09 H_demag 333052 97641355224 7 2199889195136837 83 294534914159939 x 5e 09 H_demag 333051 27043353132 9 4396856537516776 85 662174893158024 This shows that the error introduced by the HLib is of the order of 10 in 333333 in this example Note that the y and z component theoretically should be zero for both calculations with and without HLib and that the error we see there of the order of 60 333333 in the z component is coming from approximating the spherical shape with tetrahedra and approximating the magnetisation with a piecewise linear function not primarily from using the HLib approximation of the BEM HLib Memory usage Nmag will also provide information on the memory requirements for the hierarchical matrix First it will print to stdout and here exceptionally not write to the log file the following lines to the screen which are each preceded by HLib HLib Memory footprint of hierarchical matrix 10 523720 MB HLib Equivalent full matrix would require 98 273628 MB HLib The compression rate is 10 71 The first line states the amount of memory required for the storage of the hierarchical matrix the second one states the equivalent m
92. 7 1 mesh files nmesh nmesh h5 Files that contain a finite element mesh See Nmesh file format 7 2 Simulation scripts py Files that contain simulation program code The ending is by convention py which reflects that the program ming language used is Python All the example codes provided in the Guided Tour are such simulation scripts 7 3 Data files ndt ndt stands for Nmag Data Table analog to odt files OOMMF Data Table for the OOMMEF project In fact ndt and odt files are very similar ndt files are ascii files where each row corresponds to one time step or more generally configuration of the system The columns contain e metadata such as a unique identifier for every row the time at which the row was written e spatially averaged field data The first two lines contain information about what data is stored in the various columns 1 The first line provides a header 2 The second line provides the SI units All other lines contain the actual data The file can be loaded into any data processing software such as MS Excel Origin Matlab Gnuplot How ever often it is more convenient to use the ncol tool to select the relevant columns and only to pass the filtered data to a post processing e g plotting program Data is written into the ndt file whenever the save_data method of the simulation object is called 163 NMAG User Manual Documentation Release 0 2 1 7 4 Data files
93. 707107 Oy 0 707107 3 3 E dy 0 0 0 707107 0 0 707107 The first few rows provide some metadata such as which field and subfield the data is about at what simulation time it was saved here O seconds what the id step and stage is It further shows the field unit and the position unit These give the physical dimensions with which the numerical quantities from the table have to be multiplied to get dimensionful physical quantities For example the positions in the table are provided as 0 0 0 3 0 0 6 0 0 etc These numbers have to be multiplied by lt SI le 09 m gt le 9 meters to obtain the actual positions in SI units In other words the position coordinate data is expressed in nanometers In this particular example the field data the normalised magnetisation is dimensionless Followed by the keyword Start the actual data starts in the next line The format of the subsequent data lines 1s as follows e Column 1 index of the site in the h5 file This mostly relevant for developers e Column 2 the index of the site As long as we are dealing with first order basis functions as is nearly always the case in micromagnetics this is equivalent to the node id in the mesh e Columns 3 4 5 enclosed in parentheses the position of the site is expressed in units of the position unit e Columns 6 7 8 enclosed in parentheses the actual field data expressed in units of the field unit In short the first line of the
94. 86 0429 0 571 0 714 0 857 1 00 Figure 2 9 Magnetisation configuration after 0 25 ps 2 20 Example post processing of saved field data Suppose we have saved spatially resolved fields as for example in Example 2 Computing the time development of a system and we would like to read those from the data file to process the data further We can use the nmagpp tool if it provides the required functionality Alternatively we can write a Python script that 1 reads the data from the _dat h5 file 2 carries out the required post processing and or saves the data in another format The program read_h5 py demonstrates how to read the saved configuration with id 0 of the m_Py subfield and to print this to the screen import nmag read data positions and sites from h5 file m nmag get_subfield_from_h5file bar_dat h5 m_Py id 0 pos nmag get_subfield_positions_from_h5file bar_dat h5 m_Py site nmag get_subfield_sites_from_h5file bar_dat h5 m_Py can carry out some sanity checks but is not necessary assert m shape pos shape assert len m len site print the data for i in range len m print site i pos i m i The functions get_subfield_from_hSfile get_subfield_positions_from_h5file and get_subfield_sites_from_hSfile al low in principle to retrieve all the field data from the h5 files and stores this in the variables m pos and site respectively The program when run like this
95. E_anis E_demag E_exch E_ext E_total H_anis H_demag 60 gt 1 762 3e 10 E_anis E_demag E_exch E_ext E_total H_anis H_demag The id is the same unique identifier id used in the Data files ndt files that can be read with the ncol command In particular its purpose is to identify time steps saved in the ndt file with the corresponding data saved in the h5 data file Columns t ime measured in seconds step and stage are just providing some further information see Stage Step iteration time etc Finally the available i e saved fields for every configuration are listed The list of fields is not displayed completely if it is long unless the printall switch is used 6 2 2 Dumping data Suppose we are interested in the magnetisation data stored at id 0 We restrict the data to the m field using the fields m switch and restrict the number ids to dump using range 0 6 2 nmagpp 155 phi phi phi phi phi phi phi pin pin pin pin pin pin pin rr rr rH rr rr rr rr NMAG User Manual Documentation Release 0 2 1 nmagpp fields m range 0 dump bar produces output that starts like this field m subfield m_Py time OD SSIS Ss 2 id 0 step 0 stage 0 field unit lt SI 1 gt position unit lt SI le 09 m gt row 0 Start index in h5 table dofsite pos data O Os O 0 0 0 707107 0 0 707107 Ek T o 3z O IN 0 707107 0 0 707107 Zs ZA U 6 0 0 0
96. Export Filetype and ensure that Neutral Format is selected Then export the mesh with File gt Export Mesh See also Mesh generation which is part of the Guided Tour e There is a contributed import module for Gambit Use at your own risk e Gmsh meshes written file format version 1 0 can be imported If you already have the Gmsh mesh file in format 2 0 then you can use gt gmsh 3 format mshl o outfile msh infile msh to create outfile msh which contains the mesh in the gmesh file format 1 0 that can be imported If you create the mesh interactively then choose FILE gt SAVE AS select Gmsh mesh msh from the drop down list choose filename and click OK When the MSH Options box appears choose Version 1 0 from the drop down list in the Format field click OK If you create your meshes automatically from the command line then add format msh1 to the com mand line to instruct Gmsh to write in the 1 0 format 5 1 Nmesh file format There are two nmesh file formats Ascii nmesh and Hdf5 nmesh 149 NMAG User Manual Documentation Release 0 2 1 5 1 1 Ascii nmesh This section describes the syntax of the nmesh ascii files You only need to read this if you would like to know what the nmesh ascii format looks like This is only necessary if you i need to convert nmesh ascii files into other mesh formats or ii if you have generated a mesh in a format that is not supported by nmeshimport Y
97. Finite element mesh generation CHAPTER SIX EXECUTABLES 6 1 ncol ncol is a utility to conveniently analyse Data files ndt files Suppose we have data file with name X_dat ndt We can then use ncol X_dat ndt or simply ncol X to display the content of the file This is useful to quickly gain an overview of the data in the file For the Example 2 Computing the time development of a system the command is ncol bar which produces this output 0 time lt s gt 0 1 id lt gt 0 2 step lt gt 0 3 last_step_dt lt s gt 0 4 stage_time lt s gt 0 5 stage_step lt gt 0 6 stage lt gt 0 7 E_total_Py lt kg ms 2 gt 260346 5776034 8 phi lt A gt 2 50626665111e 07 9 s E_ext_Py lt kg ms 2 gt 0 10 H_demag_0 lt A m gt 263661 6673782 lal H_demag_1 lt A m gt 8 212128727093 12 H_demag_2 lt A m gt 77027 64089399 Tos dmdt_Py_0 lt A ms gt 8 250903922407e 15 14 dmdt_Py_1 lt A ms gt 2 333345040949e 16 15 dmdt_Py_2 lt A ms gt 8 250903922407e 15 16 pin lt gt 1 173 H_anis_Py_0 lt A m gt 0 18 H_anis_Py_1 lt A m gt 0 19 H_anis_Py_2 lt A m gt 0 20 m_Py_0 lt gt 0 7071067811865 Zils m_Py_1 lt gt 0 22 m_Py_2 lt gt 0 7071067811865 23 M_Py_0 lt A m gt 608111 8318204 24 M_Py_1 lt A m gt 0 25 M_Py_2 lt A m gt 608111 8318204 26 E_anis_Py lt kg ms 2 gt 0 27 E_exch_Py lt kg ms 2 gt 3 114630036477e 11 28 rho lt A m 2 gt 3 469702141876e 13 153
98. G OGOOGO OO 00 S 0 0 0 0 N NN Ny yy tlo cubel tlo cube2 tlo cube3 tlo cube4 tlo cube5 And here is the full listing of the example from nmag common import x import math Define magnetic material data from OOMMF materials file mat_Co MagMaterial name Co Ms SI 1400e3 A m exchange_coupling SI 30e 12 J m anisotropy uniaxial_anisotropy axis 0 0 1 K1 SI 520e3 J m 3 sim Simulation sim load_mesh cubes nmesh h5 cubel mat_Co cube2 mat Coy cube4 mat_Co cube5 mat_Co unit_length SI le 9 m cube3 mat_Co sim set_m 0 0 1 sim relax save fields at convergence tO sim time def set_H sim t float sim time t0 0 SI le 9 s get time in ns width 10 0 nm v 25 0 nm ns m s H_amplitude 4 0e6 math sin math pix t A m center v t 20 10 print CENTER IN center def H r x y Zz ri le 9 ci for ri ci in zip r center factor H_amplitude math exp x x yxy z z width width return 0 0 factor sim set_H_ext H unit SI A m set_H sim 60 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 sim set_params stopping_dm_dt 0 degrees_per_ns sim relax save fields every time SI 200e 12 s first t0 0 do set_H every time SI 50e 12 s first t0 0 exit at
99. Geometry We then tell Netgen that we like the edge length to be shorter than 3 by going to Mesh gt Meshing Options gt Mesh Size and enter 3 0 in the max mesh size box Then a click on the Generate Mesh button will generate the mesh Finally using File gt Export will save the mesh as a neutral file this is the default 14 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 under the name bar30_30_100 neutral We provideagzipped version of this filefor completeness 2 This neutral file needs to be converted into a nmesh file We do this using the command nmeshimport netgen bar30_30_100 neutral bar30_30_100 nmesh h5 By providing the n5 extension we tell nmeshimport to write a compressed mesh file which is significantly smaller than an ascii file see mesh file size The generated mesh looks like this s We can examine the mesh using nmeshpp to obtain information about mesh quality the statistical distribution of edge lengths the overall number of points and elements etc If you like to script the mesh generation starting from a Netgen geometry file and ending with the nmesh file you could use for the example above the following shell commands netgen geofile bar30_30_100 geo meshfiletype Neutral Format meshfile bar30_30_100 neutral b nmeshimport netgen bar30_30_100 neutral bar30_30_100 nmesh h5 2 2 2 The simulation Having obtained the mesh file bar30_30_10
100. Group Mesh data mesh points CArray 1154L 3L shuffle zlib 5 Positions of mesh nodes points mesh simplices CArray 4953L 4L shuffle zlib 5 Indices of nodes starting from zero Each row is one simplex mesh simplicesregions CArray 4953L shuffle zlib 5 Region ids one for each simplex In short the position of the mesh nodes are stored in mesh points as 8byte floats The simplices i e tetra hedra in 3d are stored in mesh simplices as a set of integers 4 in 3d per simplex which are the indices of the mesh nodes that form the simplex We also need to store to what physical region each simplex belongs Regions are coded by integer values with 0 being vacuum and 1 the area outside the mesh and stored in mesh simplicesregions 5 2 mesh file size The following table shows the size of the mesh file used in Example 2 Computing the time development of a system stored in various formats Filename size kB type bar30_30_100 neutral 1036 ascii bar30_30_100 neutral gz 246 gzipped ascii bar30_30_100 nmesh 794 ascii bar30_30_100 nmesh h5 203 hdf5 The neutral file is the mesh as written by Netgen in this particular format The second line shows the file size of the same file after compressing with gzip The third line shows the size of the mesh stored as an Ascii nmesh file while the last line gives the size of the corresponding Hdf5 nmesh file 152 Chapter 5
101. I object defines what a length of 1 0 in the mesh file corresponds to in reality If the length 1 0 in the mesh corresponds to a nanometer then this SI object would be given as SI 1e 9 m do_reorder bool If set to True metis will be called to reorder the mesh aiming to bring together node ids that correspond to node locations that are spatially close to each other If this doesn t make sense to you you should probably leave the default which is False Generally we recommend to order a mesh using nmeshpp reordernodes mesh nmesh orderedmesh nmesh and not to use this reodering option here if you think you need to order it If you know nmag really well you are probably a member of the core team then read on The use of do_reorder can make sense if either your mesh is not ordered already or you provide a manual_distribution of nodes The use of do_reorder makes no sense if you run on more than one CPU and leave the distribution of the nodes to nmag ie you use the default manual_distribution None manual_distribution list of integers This list if provided describes how many nodes are to be put onto which CPU under MPI parallelized execution If this is None i e the default then the distribution is done automatically through metis This parameter should generally not be used unless you really know what you are doing Returns mesh mesh object 4 2 12 load_m_from_hb5file Module nmag Object Simulat
102. NMAG User Manual Documentation Release 0 2 1 Hans Fangohr Thomas Fischbacher Matteo Franchin Giuliano Bordignon Jacek Generowicz Andreas Knittel Michael Walter Maximilian Albert January 15 2012 CONTENTS 1 Introduction 3 1 1 Nmag Philosophy e so e RA GA e A AE AOS 3 12 How toread this document 422 0 e E e E A o eas 4 1 3 DevelopmentistatUs y soss os apa a wa pa we ld ews 4 LA Malme Gsto da E ESS bee aee She eeee E 4 DS SUPPO 3 taux e DS be eee a E Se te EN ee A 5 L6 Tacense and Disclaimer sa coeso 0 se G4 be ee ee ee Be Re ee ee 5 2 Guided Tour 7 2 1 Example Demag field in uniformly magnetised sphere 0 7 2 2 Example 2 Computing the time development of a system aoaaa 14 23 Example Simple hysteresis loop e se exe a e a a e E ad e as 25 2 4 Example Hysteresis loop for Stoner Wohlfarth particle o o 28 23 Example Hysteresis loop for thimdisk eos o e Se 32 2 6 Example Vortex formation and propagation in disk o o 35 2 7 Example Manipulating magnetisation 2 e 41 28 Example IPythom oia aa be 8S aaa BEG Bhs doe OS 45 2 9 Example Pinning Magnetisation s lt ece ceite eetere eune ee ee 46 2 10 Example Uniaxial anisotropy 205 ra es Oe a Se ee ee we 49 2 111 Example Cubic Anisotropy c 2 3G a4 be oe a a ee a oe ee al a 53 2 12 xamplesArbitrary AMSOWOpY re ue eA eee ad Ge BA EL a ale a yen amp se Aw 54 2 19 Restartexample
103. ROMAGNETIC MODELLING This section is intended for researchers who are just beginning to explore micromagnetic modelling It is assumed that you have some knowledge on micromagnetics We advise to read this whole section and then to look the Guided Tour examples or to explore other Micromagnetic packages at that point 11 1 Introduction micromagnetic modelling To carry out micromagnetic simulations a set of partial differential equations have to be solved repeatedly In order to be able to do this the simulated geometry has to be spatially discretised The two methods that are most widely spread in micromagnetic modelling are the so called finite difference FD method and the finite element FE method With either the FD or the FE method we need to integrate the Landau Lifshitz and Gilbert equation numerically over time this is a coupled set of ordinary differential equations All these calculations are carried out by the Micromagnetic packages and the user does not have to worry about these The finite difference method subdivides space into many small cuboids Sometimes the name cell is used to describe one of these cuboids Warning in finite difference simulations the simulated geometry is typically enclosed by a big cuboid which is also referred to as simulation cell Usually it is clear from the context which is meant Typically all simulation cells in one finite difference simulation have the same geometry A typical size for
104. Timestepper tolerances The tolerance settings of a simulation can greatly affect the performance the accuracy and the usefulness of a simulation Section Solvers and tolerance settings provides an overview In this example we demonstrate e how the time integrator s tolerances can be set and e how these tolerances affect the simulation results and performance The time integrator we use is the PVODE solver from the SUNDIALS package It is optimised to deal with stiff systems of ordinary differential equations and is therefore very suited for micromagnetic simulations It can also execute in parallel i e across several CPUs at the same time using MPI The computational challenge of the time integration lies in the different time scales associated with the fast exchange field and the slower demagnetisation field Sundials provides two parameters rtol and atol see sundials documentation to control the required accuracy of the calculations Sundials uses these parameters to determine the number of iterations required to simulate a given amount of real time for example one pico second Equivalently these parameters determine the amount of real time that can be simulated per iteration 108 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 y component of magnetisation variation 100 0 001 90 0 000 80 0 000 70 0 0004 T 60 0 0002 au 50 0 E 40 0 0002 30 0 0004 20 0 000 10 0 000 0 0
105. _dat h5 In addition to the field data that is saved it also stores the finite element mesh in the order that was used when the file was created In this example this is the mesh ordered according to the output from the ParMETIS package The first 177 nodes of the mesh in this order are assigned to CPUO the next 185 are assigned to CPU1 and the next 178 are assigned to CPU2 We can visualise this partition using the nmeshpp command which we apply here to the mesh that is saved in the spherel_dat h5 file gt nmeshpp partitioning 177 185 178 spherel_dat h5 partitioning vtk The new file partitioning vtk contains only one field on the mesh and this has assigned to each mesh node the id of the associated CPU We can visualise this for example using gt mayavi d partitioning vtk m SurfaceMap 2 27 Example Parallel execution MPI 117 NMAG User Manual Documentation Release 0 2 1 cpu_id_ lt gt 0 00 0 286 0 571 0 857 1 14 1 43 1 71 2 00 The figure shows that the sphere has been divided into three areas which carry values 0 and 2 corresponding to the MPI CPU rank which goes from 0 to 2 for 3 CPUs Actually in this plot we can only see the surface nodes but the volume nodes have been partitioned accordingly The process described here is a bit cumbersome to visualise the partition This could in principle be streamlined so that we save the partition data into the _dat h5 data file and can generate
106. a simulation 2 29 More than one magnetic material exchange coupled To be written 2 28 Restarting MPI runs 119 NMAG User Manual Documentation Release 0 2 1 120 Chapter 2 Guided Tour CHAPTER THREE BACKGROUND In this section we list some background information on the simulation package some explanation of the philos ophy behind it which may explain some of the user interface choices that have been made and explanation of some terms that are relevant 121 NMAG User Manual Documentation Release 0 2 1 3 1 Architecture overview Sequential execution Parallel execution all compiled The Nmag environment that is described in this manual is shown as the blue box labelled Nmag Simulation Script This is importing the nmag library which is a Python library This in turn is built on the Nsim library Python module The nsim Python module uses compiled code which is written in Objective Caml At this level the execution can be parallel and this is also used to link together existing libraries yellow boxes 3 2 The nsim library Nmag is the high level user interface that provides micromagnetic capabilities to a general purpose finite element multi physics field theory library called nsim Therefore many of the concepts used by Nmag are inherited from nsim This manual documents the high level Nmag userinterface it does not document nsim Some of the internal details of nsim are explained in htt
107. ached we ll tell the relax method to exit after a fixed amount of time has been simulated sim relax save fields at convergence very time SI 1 0e 9 s averages every time SI 0 05e 9 s at stage_end do exit at time SI 10e 9 s We run the simulation for just 10 nanoseconds by forcing an exit with exit at time SI 10e 9 s We also save the fields every nanosecond and save the averages more often every 50 picoseconds The relax method will simulate a vortex hit by a spin polarised current and will save the averages so that we can see how the magnetisation changes in time To run the script which takes of the order of half an hour we use as usual nsim stt py The output files for this simulation will start with the prefix stt The script saves the average magnetisation periodically in time We can therefore plot it using the following gnuplot script set term postscript color eps enhanced set out m_of_t eps set xlabel time ns set ylabel average magnetisation 10 6 A m plot 0 10 m_of_t dat u lx 1e9 2 1e6 t lt M_x gt w lp u lx x1e9 3 1e6 t lt M_y gt w lp u lx x1e9 4 1e6 t lt M_z gt w lp to obtain the following graph 2 21 4 Standard problem The simulation carried out here is a coarse version of the recently proposed standard problem for spin transfer torque micro
108. actual data 0 A Op 20 Oyo 0 707107 0 0 707107 tells us that the normalised magnetisation at node id 0 and position 0 0 0 nm is pointing in the direction 0 707107 0 0 707107 Another example Suppose we are interested in the magnetisation field M this is the non normalised magnetisation measured in Ampere per meter at time le 10 seconds i e id 20 We use this command nmagpp fields M dump range 20 bar to obtain output beginning like this field sm subfield m_Py time le 10 x lt SI 1 s gt id 20 step 495 stage ll field unit lt SI 1 gt position unit lt SI le 09 m gt row 2 Start index in h5 table dofsite pos data 0 0 0 0 0 0 182556 0 525948 1 1 3 0 0 0 165008 0 534525 156 Chapter 6 Executables 0 830694 0 828888 NMAG User Manual Documentation Release 0 2 1 2 2 6 0 0 0 104837 0 544846 3 3 9 0 0 0 029925 0 552054 4 In principle this output data can be parsed by other tools to extract the positions and the data However it is hoped that other options of the nmagpp tool such as the vtk switch already cover most of the situations where the need to convert data may arise If you would like to export the raw data into another file format or application please contact the nmag team to request this feature as it may be of interest to other people as well It is further possible to access the data in the _dat h5 files directly
109. ainst 4nm 2 As a result the magnetisation is pinned at all the mesh nodes that are located within a sphere with center 0 0 0 and radius 4 nm All the nodes that are located outside this sphere can change their magnetisation as usual Second we need to tell nmag that it should use this function to decide where the magnetisation should be pinned sim set_pinning pin_at_center Note the slightly counterintuitive fact that value 1 means no pinning Finally we apply an external field of 0 5 T in y direction and use relax to compute the equilibrium configuration The relax command sim relax will save the fields and averages at convergence this is the default of the relax command 2 9 Example Pinning Magnetisation 47 NMAG User Manual Documentation Release 0 2 1 2 9 3 Visualisation After running the example via nsim sphere py we convert the equilibrium data to VTK format nmagpp vtk sphere vtk sphere We would first like to verify that the pinning field has been set up properly Hence we use MayaVi to visualise it by showing an isosurface of the pinning field shown in blue together with the magnetisation vector field 9 96 19 0 9 99 i 9 93 10 0 pin lt gt 0 00 0 143 0 286 0 429 0 571 0 714 0 857 1 00 The blue blob in the center of the sphere is the collection of those tetrahedra that have corners just inside the 4nm sphere Because we have not generated the mesh to have nodes coinci
110. ameters e The specification of units is more important when the micromagnetism is extended with other physical phenomena moving towards multi physics calculations for which in principle the software cannot predict what units these will have e Some convenience in having a choice of how to specify for example magnetic fields i e A m T mu0 Oe See also comments in set_H_ext 3 7 1 Library of useful si constants The si name space in nmag provides the following constants Some useful SI constants import math from lib import SI kilogram SI 1 0 kg 1 meter SI 1 0 m 1 metre meter Ampere SI 1 0 A 1 Kelvin SI 1 0 K 1 second SILO ls 2 candela SI 1 0 cd 1 mol SI 1 0 mol 1 The kilogram The meter alternative spelling The Ampere The Kelvin The second The candela The mol i i i Se specific units for magnetism Newton kilogram meter secondxx 2 Newton mu0 SI 4 0e 7 math pi N A 2 vacuum permeability mu0 Tesla kilogram Ampere second 2 Tesla Gauss le 4 kilogram Ampere secondx x2 Gauss Oersted Gauss mu0 Oersted Oe Oersted Oersted gamma0 SI 2 2137286285040001e5 m A s gyromagnetic ratio gamma0 units degrees nanosecond Useful to specify the stopping_dm_dt degrees_per_ns SI math pi 180 0 SI le 9 s other units and constants Joule SI J bohr_magneton 9 2740094980e 24 Joule Tesla Bohr magneton p
111. and performance of the simulation Parameters ts_rel_tol float the relative error tolerance default is 1e 6 for the timestepper ts_abs_tol float the absolute error tolerance default is 1e 6 for the timestepper stopping_dm_dt SI object the value used in the hysteresis and relax functions to decide whether convergence has been reached If the largest value for dm dt drops below stopping_dm_dt then convergence has been reached The default value for stopping_dm_dt this is that the magnetisation changes less than one degree per nanosecond i e stopping_dm_dt ST 17453292 519943293 s 1 exact_tstop bool the value of exact_tstop which is used by the advance_time method when the optional argument is not given This is also the value used by the relax and hysteresis methods See the documentation of advance_time for further details Note that this command has to be issued after having created an m field with the set_m command 142 Chapter 4 Command reference NMAG User Manual Documentation Release 0 2 1 4 3 get_subfield_from_h5file Module nmag Object get_subfield_from_h5file Arguments xargs x x nargs Retrieve data from h5 file Data are returned as an array of floating point number in SI units This function should be used with care as the order of the entries in the returned array depends on the partitioning of the mesh used when saving the data Analog to get_subfield which returns subfield
112. and their averages are saved at the end of each stage The third line specifies that the restart file should be saved at the end of each stage and also every 1000 steps For convenience the modified script cube_restartable py is shown below import nmag from nmag import SI si Create the simulation object sim nmag Simulation Define the magnetic material data from OOMMF materials file Fe nmag MagMaterial name Fe Ms SI 1700e3 A m exchange_coupling SI 2le 12 J m anisotropy nmag cubic_anisotropy axisl 1 0 0 axis2 0 1 0 K1 SI 48e3 J m 3 Load the mesh sim load_mesh cube nmesh cube Fe unit_length SI le 9 m Set the initial magnetisation sim set_m 0 0 1 Launch the hysteresis loop Hs nmag vector_set direction 1 0 0 0 0001 nortm_last 0 1 Dl 19 29 1 Dlhy 21 22 17 5015 units 0 001xsi Tesla si mu0 from nmag import every at sim hysteresis Hs save averages fields at stage_end restart at stage_end every step 1000 2 13 Restart example 57 NMAG User Manual Documentation Release 0 2 1 2 13 2 Starting and restarting the simulation We will now demonstrate how the discussed nmag script can be restarted To do that we will have to interrupt it artificially We start the simulation in the usual way nsim cube_restartable py We interrupt the execution after the hysteresis loop has starte
113. as saved see Restart example This continuation is activated with the restart switch Example nsim X py restart Note that this functionality is only available for the hysteresis loop The command line options can be combined for example nsim X py clean loglevel debug There are a few other switches mostly for debugging which can be seen using nsim X py help 148 Chapter 4 Command reference CHAPTER FIVE FINITE ELEMENT MESH GENERATION Finite element mesh generation is a difficult business and one needs to get used to using at least one mesh generating software package to be able to create meshes for the geometries one wants to simulate A list of available free and commercial mesh generators is available at http www andrew cmu edu user sowen softsurv html For nmag one needs to create unstructured meshes which means for three dimensional simulations that the mesh simplices are tetrahedra and the surface elements are triangles We are not recommending any mesh generating software We have used Netgen to generate most of the meshes for this manual The Vienna Sheffield group Fidler and Schrefl use the commercial mesh generator GID http gid cimne upc es The mesh format used by nmag is called nmesh and described in Nmesh file format The nmeshimport tool provides conversion from the following mesh formats into nmesh files e Netgen neutral Create mesh in Netgen then go to File gt
114. at_Py nmag MagMaterial name Py Ms SI 0 8e6 A m exchange_coupling SI 13 0e 12 J m 119_gamma_G SI 0 2211e6 m A s lig_damping 1 0 Define the simulation object and load the mesh sim nmag Simulation sim load_mesh pyfilm nmesh h5 Py mat_Py unit_length SI le 9 m Set a initial magnetisation which will relax into a vortex def initial_m p X Yr ZSP return y 50 0e 9 x 50 0e 9 40 0e 9 sim set_m initial_m Set convergence parameters and run the simulation sim set_params stopping_dm_dt 1 0 degrees_per_ns 82 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 sim relax save fields at step 0 at stage_end Write the final magnetisation to file vortex_m h5 sim save_restart_file vortex_m h5 After importing the usual Nmag module and helper objects we define the material create the simulation object and load the mesh similar to what is shown in previous examples Define the material mat_Py nmag MagMaterial name Py Ms SI 0 8e6 A m exchange_coupling SI 13 0e 12 J m 1llg_gamma_G SI 0 2211le6 m A s lig_damping 1 0 Define the simulation object and load the mesh sim nmag Simulation sim load_mesh pyfilm nmesh h5 Py mat_Py unit_length SI le 9 m Notice that the damping parameter 11g_damping is set to a high value to allow for quick relaxation of the magnetisation We write a
115. ather to be used in part I and II 2 25 2 Part l relaxation py The source for the file relaxation py is shown below This script is used to compute the equilibrium configuration for the magnetisation which is then used in the second part of the simulation where the dynamics is actually studied from thesystem import simulate_nanowire m0_filename ps from nmag common import simulate_nanowire name relaxation damping 0 5 NOTE the high damping set_m 1 0 01 relax save fields at time Oxps at convergence Save_restart_file m0_filename The first two lines are used to import entities defined elsewhere In particular the first line in from thesystem import simulate_nanowire m0_filename ps from nmag common import x tells to Python to load the file thesystem py and extract from it the entities simulate_nanowire m0_filename ps The second line does a similar thing and extracts all the quantities defined in the Nmag module nmag common This module defines some entities which are commonly used in simulations such as every at SI etc The simulation is then set up using s simulate_nanowire name relaxation damping 0 5 NOTE the high damping This line invokes the function simulate_nanowire which does load the mesh and associate the material to it The function returns the simulation object which is stored inside the variable s and is used in the following lines
116. ation is virtually identical with H_demag E_demag and the related charge density rho and magnetic scalar potential phi All the other relevant fields in this example turn out to be related to a particular magnetic component Field Subfield s Comment m m_Py m_Co normalised magnetisation M M_Py M_Co magnetisation H_total H_total_Py H_total_Co total effective field H_ext H_ext external applied field only one E_ext E_ext_Py E_ext_Co energy density of Py due to external field H_anis H_anis_Py H_anis_Co crystal anisotropy field E_anis E_anis_Py E_anis_Co crystal anisotropy energy density H_exch H_exch_Py H_exch_Co exchange field E_exch E_exch_Py E_exch_Co exchange energy H_demag H_demag demagnetisation field only one E_demag E_demag Py E_demag_Co demagnetisation field energy density phi phi scalar potential for H_demag tho tho magnetic charge density div M H_total H_total_Py H_total_Co total effective field The issue of multiple magnetic components becomes much more interesting when we study multi component alloys i e if we associate more than one type of magnetisation to a single region in the mesh Usually we will then also have to introduce some generalized anisotropy energy term of the form E c M_axM_b that depends on more than a single magnetisation subfield see More than one magnetic material exchange coupled Once we have run the simulation using nsim
117. ation to zero llg_damping SI 0 0 We set saturation magnetisation to Js 1 T see Library of useful si constants Ms 1 0 si Tesla si mu0 We use a sphere as the magnetic object and starting from a uniform magnetic configuration along the 1 1 1 direction sim set_m 1 1 1 To compute the time development in the presence of a static field pointing in the z direction we abuse the hysteresis command because this way we can conveniently save the data at equidistant time intervals To do this we need to find the sequence of applied fields here it is only one of course 2 16 Example Larmor precession 67 NMAG User Manual Documentation Release 0 2 1 Hs nmag vector_set direction 0 0 1 norm_list 1 0 units le6 SI A m and then use the hysteresis command sim hysteresis Hs save averages every time 0 1 ps do exit at time 300 ps The hysteresis command will save the averages which is what we need to for the fit below every 0 1 pico seconds Once we reach the time of 300 pico seconds the method will exit The dynamics of the magnetisation is driven only by the Zeeman effect with a torque T pom x Hext acting on the magnetisation m which is orthogonal to both m and H thus causing the magnetisation to precess around the applied field direction The frequency of the precession called f_Larmor is given by y FLarmor 57 HO Hoxe 27
118. attice in space and time The lattice is four dimensional and consists of the points t x y z with t 0 1 ps 2 ps 100 ps 101 values x 300 nm 297 nm 294 nm 300 nm 201 values and y z 0 The lattice is fully determined by the options t ime and space In particular the option time 0 100e 12 101 states that the lattice consists of 101 equispaced values going from 0 to 100e 12 s The option space accepts a similar expressions for each spatial coordinate separated by Ee e ref time 0 0 tells to nmagprobe that after extracting the values for the field m t x y z it should compute the difference with respect to the given time i e dm t x y z m t x y z m 0 x y z We 2 25 Example Calculation of dispersion curves 107 NMAG User Manual Documentation Release 0 2 1 add this option to nmagprobe because we are interested in the variation of the magnetisation with respect to the equilibrium configuration t 0 rather than on its absolute value e scalar mode component 1 induces nmagprobe to extract the y component of dm and to use it as a scalar when writing the output and when doing the fourier transform to ex tract the x component one should use scalar mode component 0 We could also write scalar mode component y and scalar mode component x e out real space dat induces nmagprobe to save to file the data selected by the options discussed so far In par
119. ault settings in a new script sphere_h1lib2 py we add one line to create an HMatrixSetup object create an HLib object hms nmag HMatrixSetup nmin 50 eps_aca 1e 5 quadorder 2 This object is then passed to the Simulation object sim nmag Simulation phi_BEM hms In order to make the time measurement you can just run the nsim command with a preceding time i e time nsim sphere_hlib2 py clean do the same with the sphere_hlib py script and compare the execution times Alternatively search for the string like Populating BEM took 25 094362 seconds in the log file output The execution time of the second script should be smaller see also Using HLib Example 2 Thin Films For completeness the Hdemag values computed with this script are x 5be 09 H_demag 333060 73884748813 5 7471691393211453 56 164777361260889 x 4e 09 H_demag 333062 34355895646 4 6973695734449556 58 19523338342605 x 3e 09 H_demag 333063 7357911733 4 2543955018989577 60 199068292632305 x 2e 09 H_demag 333064 14913635491 3 5107100192801424 62 841949236542568 x le 09 H_demag 333062 54691465426 2 1473409122582736 66 824386136704007 x 0 0 H_demag 333060 94469295366 0 78397180523640564 70 806823036865438 x le 09 H_demag 333059 14023403701 0 15188988623380831 75 030255790251871 x 2e 09 H_demag 333055 17692864774 2 2289146769013355 77 213961296827563 x 3
120. be_H_demag_siv Arguments self pos pos_unit SI 1 m 1 0 epsilon 1e 07 ME this function returns a wrong value for points outside the mesh For a sphere uniformly magnetised along x the x component of the demag field outside should be positive while it is negative Compute the demag field at given position Works inside and outside of magnetic materials Note that most fields can only be probed where they are defined This function computes the demag field at the given position on the fly based on the boundary element method Note that for large distances away from the magnetic material we expect this not to be very accurate Furthermore there is an awkward technical problem whenever the probe point lies in plane with any of the surface triangles These awkward limitations are strongly linked to the method used to compute the scalar potential internally and are intrinsically difficult to avoid They will go away in the future when potential computations will be performed with Hlib Also this function should at present not be used to probe the demag field for periodic structures Parameters pos list of floats The SI numbers described the position in meters A command like probe_H_demag_siv 0 0 1e 9 would thus probe the demag field one nanome ter away in z direction from the origin pos_unit SI object Optional argument that defaults to SI m The full SI position is computed as pos pos_unit The above example co
121. cate that the results are probably reliable The smaller the value the more accurate the results will be If this is new to you you may want to read the Mini tutorial micromagnetic modelling and in particular the section What size of the cells FD and tetrahedra FE should I choose The general syntax for calling ncol is ncol OPTIONS datafile COLS A list of options can be obtained with ncol help Available options include h help show this help message and exit scale col1 factor1l col2 factor2 col3 factor3 scale coll by factorl col2 by factor 2 etc last of column Select only the rows where column changes Select only the last row for each stage i e typically the relaxed state mod field Compute the magnitude of given field i e mod H_demag computes sqrt H_demag_0 2 H_demag_1 2 H_demag_2 2 More than one field can be provided comma separated but there 154 Chapter 6 Executables NMAG User Manual Documentation Release 0 2 1 must be no spaces between the fields I e mod m_Py H_ext These modulus entries will be printed last after any other COLS that have been provided and in the order given in the mod switch odt Expect to process odt file as produced by OOMMF see http math nist gov oommf and http math nist gov o ommf doc userguidel2a3 userguide Data_Table_File_Forma t_ODT html 6 2 nmagpp The stage nmagpp pro
122. ce that the user interface might change in the future when more functionality such as surface roughness is added In this section we go into the details of the distortion process and explain the relevant command line options The general usage is nmeshpp front rear axis X Y Z distort along axis X Y Z distort D correlation length C seed S mesh_orig nmesh mesh_distorted nmesh Only distort correlation length and the name of the input mesh are required arguments The overall distortion process works as follows First the surface nodes of the mesh are divided into front and rear depending on which side of the mesh they lie on By default this distinction is based on their y coordinate as in the example in the previous section but this can be changed using the option front rear axis Next a univariate distortion function f x is constructed based on the given command line parameters the details of this process will be explained in a moment This function specifies the amount by which each front node is displaced in y direction as a function of the x coordinate of the node Analogously the rear nodes are displaced using a second independently constructed distortion function g x so that both sides of the mesh are distorted differently The intermediate parts of the mesh are stretched to fit nicely between the new distorted sides The whole procedure is illustrated in the following picture
123. ch to a running session automatically creating a new one if none was created before Within a screen session Control a is a prefix keyboard command for controlling screen Pressing Control a and then Control d will detach the session Control a will being up a help screen showing all screen keyboard commands 8 7 nmag claims to support MPI So can run simulation jobs on multiple processors Yes See Example Parallel execution MPI 8 8 How should cite nmag Please cite e Thomas Fischbacher Matteo Franchin Giuliano Bordignon and Hans Fangohr A Systematic Approach to Multiphysics Extensions of Finite Element Based Micromagnetic Simulations Nmag in IEEE Transactions on Magnetics 43 6 2896 2898 2007 Available online 8 6 How do start a time consuming nmag run in the background 167 NMAG User Manual Documentation Release 0 2 1 8 9 Why can you not use the step as a unique identifier There are two reasons Firstly nmag may be extended in future to support effective energy minimisation in which case the step becomes somewhat meaningless although it could probably still be used as an identifier if we identify minimisation iterations with steps Secondly and more importantly in nmag the user can modify the magnetisation directly using set_m either scripted or interactively This will change the configuration of the system without increasing the step counter of the time integra
124. contains one or more Subfields For example a simulation with two different types of magnetic material for example Fe and Dy has a field m for the normalised magnetisation and this would contain two subfields m_Fe and m_Dy It is partly a question of philosophy whether different material magnetisations are treated as subfields in one field or whether they are treated as two fields For now we have chosen to collect all the material magnetisations as different subfields in one field Often a field contains only one subfield and this may carry the same name as the field 3 4 Fields and Subfields in Nmag 3 4 1 Example one magnetic material Assuming we have a simulation of one material with name PermAlloy Py we would have the following Fields and Subfields Field Subfield Comment m m_Py normalised magnetisation M M_Py magnetisation H_total H_total_Py total effective field H_ext H_ext external applied field only one E_ext E_ext_Py energy density of Py due to external field H_anis H_anis_Py crystal anisotropy field E_anis E_anis_Py crystal anisotropy energy density H_exch H_exch_Py exchange field E_exch E_exch_Py exchange energy H_demag H_demag demagnetisation field only one E_demag E_demag_Py demagnetisation field energy density for Py phi phi scalar potential for H_demag tho tho magnetic charge density div M H_total H_total_Py total effective field 3 3 Fields and subfields 12
125. cumentation of hysteresis should be con sulted for a more detailed explanation of parameters 22 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 The second relax instruction is fields at convergence which means that the fields should be saved at convergence i e when the relaxation process has finished and the magnetisation has converged to its meta stable configuration e fields is a string that indicates that we would like to save all the defined fields e at convergence is a special object that indicates that this should happen exactly when the relax ation process has converged After running this program we can use the ncol tool to look at the averages saved ncol bar_relax step tim gives output which starts like this 0 0 82 5e 12 120 le 11 146 Ll 96 12 176 2e 11 201 2 456 11 227 3e 11 248 3 56 11 Here we see the iterations on the left and the simulated time in seconds on the right As requested there is one data entry i e line every 5 picoseconds Note that it may happen that the system saves the data not exactly at the requested time i e 532 6 5e 11 580 7 047908066945e 11 620 Yoel The middle line shows that the data has been saved when the simulated time was approximately 7 05e 11 seconds whereas we requested 7e 11 seconds Such small deviations are tolerated by the system to improve performance l From the data saved we can obtai
126. d Tour NMAG User Manual Documentation Release 0 2 1 Create the simulation object and load the mesh sim nmag Simulation sim_name do_demag do_demag sim load_mesh mesh_name np mat unit_length mesh_unit Set the pinning at the top and at the bottom of the nanopillar def pinning p X Y Z Pp tmp float SI x m mesh_unitxhl if abs tmp gt 0 999 return 0 0 else return 1 0 sim set_pinning pinning if type initial_m str Set the initial magnetisation sim load_m_from_h5file initial_m a from file if a string is provided else sim set_m initial_m b from function vector otherwise if j 0 0 Set the current if needed sim set_current_density j 0 0 0 0 unit SI A m 2 Set additional parameters for the time integration and run the simulation sim set_params stopping_dm_dt stopping_dm_dt ts_rel_tol le 7 ts_abs_tol le 7 sim relax save save do do return sim If the initial magnetisation has not been calculated and saved into the file relaxed_m_file then do it now if not os path exists relaxed_m file Initial direction for the magnetisation def m0 p X Y Z Pp tmp min 1 0 max 1 0 float SI x m mesh_unitx xhl angle 0 5 math pixtmp return math sin angle math cos angle 0 0 save fields at step 0 at stage_end averages every time SI 5e 12 s sim run_simulation sim_name relaxation init
127. d and several stages have been computed Do this by pressing simultaneously the keys CTRL and C in the same terminal window where nsim was started thus simulating what could have been the result of a power cut We then use the command ncol cube_restartable stage step time to see at what point of the hysteresis loop the simulation was interrupted We obtain for this particular interrup tion 1 330 3 320127110062e 11 2 480 5 042492488627e 10 3 640 9 926580643272e 10 4 805 1 464971830453e 09 5 980 1 927649646634e 09 6 1150 2 406521613682e 09 7 1340 2 882400372552e 09 8 1515 3 371522550051e 09 9 1705 3 863380029345e 09 10 1920 4 365560120394e 09 11 2095 4 893234441813e 09 T2 2295 5 436617525896e 09 13 2480 5 997866344586e 09 14 2680 6 570733097131e 09 LS 2890 7 172534305054e 09 16 3100 7 803577637245e 09 17 3315 8 462827284047e 09 The simulation was interrupted at the seventeenth stage We now try to run the simulation again with the command nsim cube_restartable py obtaining the following output lt snip gt NmagUserError Error Found old file cube_restartable_dat ndt cannot proceed To start a simulation script with old data files present you either need to use clean and then the old files will be deleted or use restart in which case the run will be continued nsim suggests the possible alternatives We can start the simulation from scratch with the command but this will ov
128. d in the file thesystem py to setup the system and the materials We then set the initial magnetisation configuration from the file saved in part I and carry out the time integration by calling the relax method of the simulation object s The pulse is switched on and switched off by the instruction passed in the do argument In particular the argument do accepts a list of pairs things to be done at a given time The code 106 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 do switch_on_pulse at time Oxps switch_off_ pulse at time pulse_duration exit at time 200xps specifies that e the function switch_on_pulse should be executed at time t 0 ps e the function switch_off_pulse should be executed at time t pulse_duration e the simulation should terminate at time t 200 ps At the same time the argument save fields every time 0 5 ps of the relax method saves the field every 0 5 ps Let s now see how the pulse is actually switched on and off To switch off the pulse we provide the function Function which sets the magnetisation to zero def switch_off_pulse sim sim set_H_ext 0 0 0 0 0 0 unit pulse_amplitude The function gets the simulation object sim as an argument and uses it together with the method set_H_ext to set the applied magnetic field to zero everywhere The function to set up the simulation is a little bit more complicated
129. dM_ml dt llg_ gamma_G_ml M_m1 x H_ml llg_ damping m1 M_ml x dM_ml dt dM_m2 dt lIlg_gamma_G_m2 M_m2 x H_m2 llg_damping_m2 M_m2 x dM_m2 dt determine the dynamics of M_m1 and M_m2 Here H_m1 and H_m2 are the effective fields relative to the two components while with dM_m1 dt and dM_m2 dt we denote the two time derivatives The constant 119_gamma_G_XX in front of the precession term in the LLG equation is often called gyromagnetic ratio even if usually in physics the gyromagnetic ratio of a particle is the ratio between its magnetic dipole moment and its angular momentum and has units A s kg It is then an improper nomenclature but it occurs frequently in the literature The 11g_damping_XX constant is called damping constant Notice that these two constants are specified on a per material basis This means that each material has its own pair of constants 11g_gamma_G_ml 1llg_damping_m1 and llg_gamma_G_m2 11g_damping_m2 The two constants are specified when the corresponding material is created using the MagMaterial class 128 Chapter 3 Background CHAPTER FOUR COMMAND REFERENCE 4 1 MagMaterial Module nmag Object MagMaterial Class constructor information self name Ms SI 0 86e6 A m llg_damping SI 0 5 llg_gamma_G SI 2 210173e5 m A s exchange_coupling SI 1 3e 11 J m anisotropy None anisotropy_order None do_precession True Parameters name string Th
130. d_mesh spherel nmesh h5 sphere Py l unit_length SI le 9 m set initial magnetisation NMAG User Manual Documentation Release 0 2 1 sim set_m 1 0 0 set external field sim set_H _ext 0 0 0 SI A m Save and display data in a variety of ways sim save_data fields all save all fields spatially resolved together with average data sample demag field through sphere for i in range 10 11 x ixle 9 position in metres H_demag sim probe_subfield_siv H_demag x 0 0 print x x H_demag H_demag To execute this script we have to give its name to the nsim executable for example on linux nsim spherel py Some simulations produce output files which nsim will refuse to overwrite when run for a second time The rationale is that big simulations may have to run for a long time and so there should be a safeguard against accidental destruction of data In order to re run a simulation removing all old output data files the extra option clean should be given as in nsim spherel py clean Let us discuss the spherel py script step by step 2 1 1 Importing nmag First we need to import the nmag module and any subpackages of nmag that we want to use In this basic example this is just the SI module for dimensionful physical quantities import nmag from nmag import SI 2 1 2 Creating the simulation object Next we need to create a simulatio
131. data for a subfield of a simulation object but will retrieve data from saved _dat h5 file Note that the entries of the returned array are ordered accordingly to the mesh used in this simulation object Parameters filename string The full name of the _dat h5 data file subfieldname string The name of the subfield to be retrieved id integer The id of the configuration to return defaults to 0 row integer If the id is not specified the row can be used to address the data row with index row For example the magnetisation may have been saved at some point during the simulation into a file for example using the Restart example functional ity or using the save_data method for the first time to save the m field i e sim save_data fields m into a new file We can use row 0 to read the first magnetisation configuration that has been written into this file and row 1 to access the second etc Returns numpy array 4 4 get_subfield_positions_from_h5file Module nmag Object get_subfield_positions_from_h5dfile Arguments filename subfieldname Analogous to get_subfield_positions which returns the positions of nodes for a subfield of a simulation object but will retrieve data from saved _dat h5 file Parameters filename string The full name of the _dat h5 data file subfieldname string The name of the subfield to be retrieved Returns numpy array The positions are returned as si values 4 5 get_subfie
132. de indi vidually is because then the result would strongly depend on the mesh spacing and the overall quality of the mesh However since we usually want roughness on a scale independent from the mesh spacing we need some kind of correlation between the displacements of adjacent mesh nodes hence the need for the distortion functions The parameters in the construction of f and g are e the distance between the nodes x_i which can be controlled with the flag correlation length e the standard deviation of the underlying normal distribution which must be specified using the command line switch d or distort Note that depending on which edges of the mesh the roughness should be applied to and on the way the mesh is oriented in the coordinate system it may be necessary to apply the distortion in a direction different from the y direction and also to consider f and g as functions of a different input axis distinct from the x axis The first can again be controlled using the option front rear axis which was already mentioned above The second can be adjusted using distort along axis For instance if the roughness should displace the nodes in z direction and if the amount of displacement should be a function of their y coordinates the command line arguments would be front rear axis Z distort along axis Y 2 24 Compression of the Boundary Element Matrix using HLib 2 24 1 Hierarchical Matrices in Micromagnetism
133. define a function which returns the energy for a uniaxial anisotropy of order 4 K1 SI 43e3 J m 3 K2 SI 21e3 J m 3 axis 0 0 1 The normalised axis def my_anisotropy m a scalar_product axis m return Klxaxx2 K2xaxx 4 my_material nmag MagMaterial name MyMat Ms SI le6 A m exchange_coupling SI 10e 12 J m anisotropy my_anisotropy anisotropy_order 4 Load the mesh sim load_mesh coin nmesh h5 coin my_material unit_length SI le 9 m Set the magnetization sim set_m 1 0 0 Compute the hysteresis loop Hs nmag vector_set direction 1 0 0 0 0001 norm_litst 0 4 0 35 1 0 0 005 ly 0 15 0 2 y 0 4 units si Tesla si mu0 sim hysteresis Hs save fields averages at convergence We simulate the hysteresis loop for a ferromagnetic thin disc where the field is applied orthogonal to the axis of disc This script includes one main element of novelty which concerns the way the magnetic anisotropy is specified In previous examples we found lines such as my_material nmag MagMaterial name MyMat Ms SI le6 A m exchange_coupling SI 10e 12 J m anisotropy nmag uniaxial_anisotropy axis 0 0 1 K1 SI 43e3 J m 3 K2 SI 21e3 J m 3 where the material anisotropy was specified using the provided functions nmag uniaxial_anisotropy uniaxial_anisotropy and nmag cubic_anisotropy cubic_anisotropy In this examp
134. ding with the 4nm sphere the shape of the blue region is not particularly spherical In the above diagram we also see the magnetisation vectors of the final configuration Their colour corresponds to the pinning field at their location It can be seen that the blue magnetisation vectors emerging from the central region of the sphere are all pointing strictly in the x direction The magnetisation vectors outside the blue sphere are coloured red The applied field drives these vectors to point into the y direction However the magnetisation in the centre is pinned and the exchange interaction requires a gradual spatial change of magnetisation This explains the spatial variation of the magnetisation The next figure shows the same data as the last figure but in addition a ScalarCutP lane in MayaVi terminol ogy has been introduced which is coloured according to the x component of the magnetisation Red corresponds 48 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 to 1 0 and blue corresponds to 0 73 we have not shown the legend to provide a larger main plot This demon strates the gradual change from the pinned magnetisation in the centre to the outside YA A 2 10 Example Uniaxial anisotropy In this example we would like to simulate the development of a Bloch type domain wall on a thin cobalt bar of dimension 504 x 1 x 1 nm bar nmesh h5 due to uniaxial anisotropy 2 10 1 Uniaxial anisotropy sim
135. do list of pairs thing_to_do when is very similar to the save argument but is usu ally used for other purposes thing_to_do is either a string or a function provided by the user and when is an instance of the class When Possible string values for thing_to_do are e next_stage induces the hysteresis method to advance to the next stage e exit induces the hysteresis method to exit even if the hysteresis computation has not still reached its end The user can provide his own function to save data For example the following three lines def my_fun sim sim save_data sim hysteresis save my_fun every step 10 are equivalent to sim hysteresis save averages very step 10 To specify when something has to be saved the module when is used The functions at and every provided by this module can refer to the following time variables 136 Chapter 4 Command reference NMAG User Manual Documentation Release 0 2 1 e step the step number from the beginning of the simulation e stage_step the step number from the beginning of the current stage e time the simulation time passed from the beginning of the simulation measured in SI objects e stage_time the simulation time passed from the beginning of the current stage e stage the number of the current stage convergence a boolean value which is True if the convergence criterion is satis fied Use in this way at
136. dreas Knittel Michael Walter Maximilian Albert Licence GNU General Public License GPL version 2 Version 0 2 1 Date Manual generated on 2012 01 14 at 23 38 Home page http nmag soton ac uk CONTENTS 1 NMAG User Manual Documentation Release 0 2 1 2 CONTENTS CHAPTER ONE INTRODUCTION Nmag is a flexible finite element micromagnetic simulation package with an user interface based on the Python programming language If you use Nmag in your published work please cite e Thomas Fischbacher Matteo Franchin Giuliano Bordignon and Hans Fangohr A Systematic Approach to Multiphysics Extensions of Finite Element Based Micromagnetic Simulations Nmag in IEEE Transactions on Magnetics 43 6 2896 2898 2007 Available online 1 1 Nmag Philosophy Many specialized simulation codes used in research today consist of a highly specialized core application which initially was written to simulate the behaviour of some very specific system Often the core application then evolved into a more broadly applicable tool through the introduction of additional parameters Some simulation codes reach a point where it becomes evident that they need an amount of flexibility that can only be provided by including some script programming capabilities The approach underlying Nmag turns this very common pattern of software evolution which we also have seen in web browsers CAD software word processors etc on its head rather than gradua
137. e 09 H_demag 333051 63216875959 4 3434799953307275 80 273150211395659 x 4e 09 H_demag 333048 08718075219 6 4586908275326955 83 334113807086638 x 5e 09 H_demag 333046 47566667694 8 6375699926922742 85 648195356633963 2 24 5 Using HLib Example 2 Thin Films In this example we consider square thin films with a thickness of 10 nm in z direction and a varying edge length in x and y directions between 20 and 130 nm The magnetisation within those films is initially homogeneously aligned and points out of plane We then use Nmag s relax routine in order to evolve the magnetisation field to an energetically meta stable state In order to estimate the efficiency benefits of hierarchical matrices the simulations are executed twice i with and ii without hierarchical matrices Optimal damping is ensured by setting the damping constant of the LLG equation to 1 To increase the efficiency of the relaxation the tolerance of the time stepper has been increased to le 5 see Example Timestepper tolerances For our estimation of the efficiency we measure the time needed for the setup of our simulation basically the time for populating the finite element and boundary element matrices the time for relaxing the system and the memory consumption at the end of the simulation which should be roughly equal to the maximal value throughout the simulation For each film size and either use of the full BEM or the approximatio
138. e Physical Volume 1 1 to make sure that the mesh region is labeled starting from region number 1 mesh cll 1 Point 1 x2sS 0 0 ell Point 2 25 Sx2S 0 el Point 3 0 x2S 0 ell Point 4 10 x15 0 cll Point 5 1 x18 0 0 all Point 6 x0S x0 0 cll Point 7 x0 x15 0 cil Point 8 Sxl x0 0 G11 Point 9y 52857 O SyS ell Point 10 x1 0 y1 cl1 Point 14 x1 x0 y1 cll Point 18 x0 x0 y1 cll Point 19 Sx0 SxlsS SylLS cli Point 23 0 Sxls Syil cll Point 27 0 228 Sys ell Point 31 x287 Sx28 Sy1S EIL LDine 1 1 5 Line 2 5 i Circle 3 8 6 7 Line 4 7 4 Line 5 4 3 Lane 6 13 247 Line 7 2 1 Line 11 19 LO Line 12 10 14 Circle 13 14 18 19 Line 14 19 23 Dine 15 23 27 Line 16 27 31 Line 17 31 9 Line 19 11 QF Line 20 5 10 Line 24 8 14 Line 28 7 19 Line 32 4 23 Line 306 137 2743 Line 40 2 31 Line Loop 9 1 2 3 4 5 6 Tiy Plane Surface 9 9 Line Loop 21 1 20 11 19 Ruled Surface 21 21 Line Loop 25 2 24 12 20 Ruled Surface 25 25 Line Loop 29 3 28 13 24 Ruled Surface 29 29 Line Loop 33 4 32 14
139. e magnetisation on the one hand we can use the set_m method to replace the current magnetisation configuration with a new one We can use sef_m to specify both homogeneous see Setting the initial magnetisation and non homogeneous magnetisations see the Spin waves example Alter natively we can selectively change magnetic moments at individual mesh sites This example demonstrates how to use the latter technique The basics of this system are as in Example Demag field in uniformly magnetised sphere we study a ferromagnetic sphere with initially homogeneous magnetisation The corresponding script file is sphere_manipulate py import nmag from nmag import SI Create simulation object sim nmag Simulation Define magnetic material Py nmag MagMaterial name Py Ms SI le6 A m exchange_coupling SI 13 0e 12 J m Load mesh sim load_mesh spherel nmesh h5 sphere Py unit_length SI le 9 m Set initial magnetisation sim set_m 1 0 0 Set external field sim set_H_ext 0 0 0 SI A m Save and display data in a variety of ways Step 1 save all fields spatially resolved sim save_data fields all Step 2 sample demag field through sphere for i in range 10 11 x ixle 9 position in metres H_demag sim probe_subfield_siv H_demag x 0 0 print x x H_demag H_demag Step 3 sample exchange field through sphere for i in range 10 11 x i
140. e name of the material This will be used in the names of material dependent fields and subfields Must be alphanumeric i e contain only the characters 0 9_a zA Z Examples Py Fe_1 Fe_2 Ms SI Object The saturation magnetisation of the material in Ampere per meter Example and default PermAlloy value ST 0 86e6 A m llg_ gamma_G SI Object The constant in front of the precession term in the LLG equation dM dt llg_gamma_G Mx H llg_damping M x dM dt It is often called gyromagnetic ratio even if usually in physics the gyromagnetic ratio of a particle is the ratio between its magnetic dipole moment and its angular momentum and has units A s kg It is then an improper nomenclature but it occurs frequently in the literature Example and default value SI 2 210173e5 m A s llg_damping SI Object The damping parameter often called alpha Optimum damping for 1 0 realistic values are of the order of 0 01 The default value as in OOMMFP is 0 5 Example and default value SI 0 5 exchange_coupling SI Object The coupling strength for the exchange interaction in Joule per meter Example and default value SI 1 3e 11 J m 129 NMAG User Manual Documentation Release 0 2 1 anisotropy PredefinedAnisotropy Object or function vector gt SI Object Either a predefined anisotropy such as returned by uniaxial_anisotropy or cubic_anisotropy or a custom func tion which
141. e using hierarchical matrices The basic idea is to approximate submatrices of B by a data sparse approximation where possible within user provided tolerance margins In general the complexity of the storage requirements and execution time of simple operations like the matrix vector product scale as O N log N as compared to the quadratical costs N 2 using the standard matrix representation For the use of HLib hierarchical matrices in micromagnetic simulations we are often mostly interested in the their reduced memory requirements The library HLib contains implementations of this hierarchical matrix methodology and can be used with Nmag in order to run micromagnetic simulations in a more memory efficient way see for example Knittel et al 105 07D542 2009 postprint pdf 2 24 2 Installation of HLib In order to be able to use the HLib library and to obtain the HLib source code you have to apply for an HLib licence as explained on http hlib org license html 96 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 Once the HLib authors grant a licence they will send their HLib tarball Nmag will have to be compiled from source see install from source in the presence of this tarball to make use of the HLib matrix compression Nmag will compile happily in the absence of this file and in that case the boundary element matrix is stored in the normal way as a full matrix We describe the required step
142. ecompression algorithm which op timises a given hierarchical matrix The default value is 0 001 Parameters influencing the tree structure cluster_strategy string algorithm to be used for creating the cluster tree Available choices are regular cluster constructed splitting the bounding box of the surface in two smaller bounding boxes with half the size along x then y z x and so on geometric similar to regular but the splitting is done along longer dimension of the bounding box regu lar_box behaves similarly to regular cardinality the bounding box is split into two bounding boxes containing the same number of points cyclically along each dimension pca clustering based on principal directions default uses the default The default clustering strategy is regular eta float eta is a parameter which influences the so called admissibility criterion As explained above a subblock of the boundary element matrix basically describes the dipole potential at a cluster of surface nodes A generated by a different cluster B The subblock can only be approximated when both cluster are spatially well separated To have an objective measure of what well separated means an admissibility criterion has been introduced The smaller the parameter eta is chosen the more restrictive is the admissibility criterion The default value is 2 0 nmin int In order to be able to adjust the c
143. eed to calculate the relaxed equilibrium magnetisation i e the one which we perturb with the application of a pulsed field Consequently the simulation is split into two parts e In part I the system is relaxed to obtain the initial magnetisation configuration for zero applied field Such a state is then saved into a file to be used in part II e In part II the magnetisation obtained in part I is loaded and used as the initial magnetisation configuration A pulsed external magnetic field localised on one side of the wire is applied The Landau Lifshitz Gilbert equation is integrated in time to compute the dynamical reaction to the applied stimulus The configuration of the magnetisation is saved frequently to file so that it can be studied and processed later The two parts are two simulations of the same system under different conditions If we then decide to write two separate files for the two parts we end up duplicating the fragment of code which defines the materials and load the mesh For this reason we split the simulation in three files e thesystem py defines the material which composes the nanowire and loads the mesh e relaxation py uses thesystem py to setup the system and performs a relaxation with zero applied field It saves the final magnetisation configuration to a file m0 h5 2 25 Example Calculation of dispersion curves 103 NMAG User Manual Documentation Release 0 2 1 e dynamics py uses
144. elds a list of list of SI objects for rank 2 tensor fields etc 4 2 8 probe_subfield_siv Module nmag Object Simulation probe_subfield_siv Arguments self subfieldname pos unit None The same behaviour as get_subfield but the pos and return data are S values not SI objects If the subfield is not defined at that part of space None is returned If the subfield does generally not exist then a KeyError exception is thrown The input position and returned data is expressed in SI units but of type float Parameters subfieldname string The name of the subfield pos list of floats The position for which the data should be returned in meters 134 Chapter 4 Command reference NMAG User Manual Documentation Release 0 2 1 unit SI object If you request the value for a subfield of a field that is part of nmag i e fields M m H_demag etc then you do not need to provide this object If you request data of any other multi physics fields then this function needs to know the SI dimensions of that field for the correct conversion from simulation units to SI units If incorrect dimensions are provided the returned data is likely to be wrongly scaled Returns data list of list of float The returned object is a float for scalar subfields a list of floats for vector fields a list of list of floats for rank 2 tensor fields etc 4 2 9 probe _H_demag_siv Module nmag Object Simulation pro
145. elease 0 2 1 3 5 Mesh In finite element calculations we need a mesh to define the geometry of the system For development and de bugging purposes nsim includes some at present undocumented capabilities to generate toy meshes directly from geometry specifications but for virtually all nsim applications the user will have to use an external tool to generate a tetrahedral mesh file describing the geometry 3 5 1 Node Roughly speaking a mesh is a tessellation of space where the support points are called mesh nodes nmag uses an unstructured mesh i e the cells filling up three dimensional space are tetrahedra 3 5 2 node id Each node in the finite element mesh has an associated node id This is an integer starting from 0 for the first node This information is used when defining which node is connected to which see Finite element mesh generation for more details and when defining the sites at which the field degrees of freedom are calculated 3 5 3 node position The position as a 3d vector in space of a node 3 6 Site A Mesh has nodes and each node is identified by its node id If we use first order basis functions in the finite element calculation then a site is exactly the same as a node In micromagnetism we almost always use first order basis functions because the requirement to resolve the exchange length forces us to have a very fine mesh and usually the motivation of using higher order basis functions
146. ely create this file is to do the following cd SHOME touch mpd conf chmod 600 mpd conf and then use an editor to insert a line like MPD_SECRETWORD mr45 39z into the file Of course use some other secret word than mr45 39z If you don t have this file in your home directory just follow the instructions above to create it with some secret word of your choice Note that the above example is from a Mac OS X system on Linux the home directory is usually under home USERNAME rather than Users USERNAME as shown here Let s assume we have a multi core machine with more than one CPU This makes the mpi setup slightly easier and is also likely to be more efficient than running a job across the network between difference machines First we need to start the multi purpose daemon gt mpd It will look for the file mpd conf as described above If found it will start silently Otherwise it will complain Testing that nsim executes in parallel First let s make sure that ns im is in the search path The command which nsim will return the location of the executable if it can be found in the search path For example gt which nsim home fangohr new nmag 0 1 bin nsim To execute nsim using two processes we can use the command gt mpiexec n 2 nsim There are two useful commands to check whether nsim is aware of the intended MPI setup The fist one is ocaml mpi_status which prov
147. emag 333060 29023012909 23 736721821840622 68 984395930340639 x le 09 H_demag 333058 66039082204 24 758745874347209 69 6797361890888 x 2e 09 H_demag 333055 87727687479 24 635979967196079 70 705429412122513 x 3e 09 H_demag 333054 17167091055 24 9868363963913 73 501799477569747 x 4e 09 H_demag 333052 78687652596 25 388604442091431 76 097088958697071 x 5e 09 H_demag 333051 43416558538 25 507782471847442 77 792885797356391 As in Example Demag field in uniformly magnetised sphere of our guided tour we should obtain a constant magnetic induction of about 333333 0 0 A m Deviations from that value can be mainly ascribed to the dis cretisation errors of the finite element method rather than the error due to the approximation with hierarchical matrices To see this we use sphere_full1BEM py which carries out the same calculation but uses the normal full BEM It reports x 5be 09 H_demag x le 09 H_demag 333065 71403658605 5 2685406972238447 55 70105442854085 333067 37484881631 4 2116117445407726 57 778611300679266 x 3e 09 H_demag 333068 83107133937 3 7372238611028603 59 825445387210245 x 2e 09 H_demag 333069 28217968839 2 9635031726006642 62 513814422201456 x le 09 H_demag 333067 6639511605 1 5730916838594211 66 546659227740889 x 0 0 H_demag 333066 04572263273 0 18268019511817793 70 5795040332803
148. emory requirements when using the full boundary element matrix and the last line gives the corresponding compression rate Furthermore Nmag creates the file memory_info dat which in our example looks like Number of surface nodes 3589 Size of hierarchical matrix 10 52 MB Total size of inadmissible leaves 1 40 MB Total size of admissible leaves 8 96 MB While the first two lines should be relatively self explanatory the third line states the total amount of memory needed to store the matrix blocks which cannot be approximated while the fourth line gives the equivalent number for the approximated matrix blocks Additionally one can obtain the memory used for the hierarchical tree structure itself by computing the difference between the size of the hierarchical matrix and the sum of the total sizes of the admissible and inadmissible leaves 2 24 Compression of the Boundary Element Matrix using HLib 99 NMAG User Manual Documentation Release 0 2 1 Changing the Parameters of HLib Let us assume we want to run the simulation of the last section again but this time we would like to reduce the time needed to assemble our hierarchical matrix To achieve this we coarsen the hierarchical tree by increasing the parameter nmin to 50 reassign the parameter eps_aca to le 5 in order to decrease the accuracy of the HCA II algorithm and reduce the accuracy of the numerical integration by setting the parameter quadorder to 2 To use non def
149. ence_check every object The default value every step 5 specifies that we ask the time integrator to carry out 5 steps before we check for convergence If in doubt ignore this feature 4 2 Simulation 139 NMAG User Manual Documentation Release 0 2 1 4 2 15 save data Module nmag Object Simulation save_data Arguments self fields None avoid_same_step False Save the averages of all defined subfields into a ascii data file The filename is composed of the simulation name and the extension _dat ndt The extension ndt stands for Nmag Data Table analog to OOMMFs odt extension for this kind of data file If fields is provided then it will also save the spatially resolved fields to a file with extensions _dat h5 Parameters fields None all or list of fieldnames If None then only spatially averaged data is saved into ndt and x h5 files If all i e the string containing all then all fields are saved If a list of fieldnames is given then only the selected fieldnames will be saved i e lm H_demag avoid_same_step bool If True then the data will only be saved if the current clock step counter 1s different from the step counter of the last saved configuration If False then the data will be saved in any case Default is False This is internally used by the hysteresis command which uses avoid_same_step True to avoid saving the same data twice The only sit
150. equirements of boundary element matrix The boundary element matrix is densely populated matrix with s rows and s columns where s is the number of surface nodes in the mesh Strictly it is only the number of surface nodes that enclose a ferromagnetic material Assuming we use 8 bytes to store one floating point number we can thus estimate the memory required to store this matrix In the example above we have 1721 boundary points and thus 1721 1721 2961841 matrix entries Each entry requires 8 byte so the total memory requirement is 23694728 bytes or approximately 23139 kilobytes or 23 megabytes The nmeshpp i command can be used to quickly check how big the BEM matrix is A computation is only feasible if the RAM of the computer can hold the boundary element matrix When carrying out a distributed calculation it is sufficient if the total RAM of all machines can hold the matrix 6 3 3 Inspecting the quality of a mesh The quality of a mesh can be defined in various ways In micromagnetics we usually want tetrahedra that have edges of nearly identical length i e we do not want the tetrahedra to be flat nmeshpp uses the ratio of the radius of the in sphere the sphere that can just fit into a tetrahedron so that it touches the sides to radius of the circumsphere the sphere passing through the four corners multiplied by the number of dimensions This number is 1 0 for a perfect tetrahedron with identical edge lengths and O for a compl
151. erion how to decide when the simulation has reached a meta stable state and when the relaxation at a given applied field should be considered to have been reached A common approach which is used by OOMMF and nmag for example is to monitor the change of the normalised magnetisation with respect to time i e dm dt If the absolute value of this drops below a given threshold then one considers the system as converged the relax command will return at this point while the hysteresis command will move to the next field This threshold can be changed from its default value with the set_params simulation method the attribute is stopping_dm_dt The choice of the tolerances ts_rel_tol and ts_abs_tol must respect the chosen stopping_dm_dt value or con versely the stopping_dm_dt needs to be adapted to work with the chosen tolerances large values for the tolerances correspond to lower accuracy and to larger random fluctuations of dm dt which consequently may never become lower than stopping_dm_dt In such a case the simulation never returns from the re ax command because the convergence criterion is never satisfied In all the examples we have studied we have found that the default parameters work fine However if you find that a simulation never returns from the hysteresis or relax command it is worth reducing the tolerances for the time stepper on increasing stopping_dm_dt to see whether this resolves the problem 2 27 Example Para
152. erride any data from the previous run nsim cube_restartable py clean or we can continue from the configuration which was last saved nsim cube_restartable py restart Here we choose the second possibility After the simulation has finished we issue again the command ncol cube_restartable stage step time obtaining the following output 1 330 3 320127110062e 11 2 480 5 042492488627e 10 3 640 9 926580643272e 10 4 805 1 464971830453e 09 5 980 1 927649646634e 09 6 1150 2 406521613682e 09 7 1340 2 882400372552e 09 58 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 8 1515 3 37152255005le 09 9 1705 3 863380029345e 09 10 1920 4 365560120394e 09 11 2095 4 893234441813e 09 Te 2295 5 436617525896e 09 13 2480 5 997866344586e 09 14 2680 6 570733097131e 09 15 2890 7 172534305054e 09 16 3100 7 803577637245e 09 L 3315 8 462827284047e 09 stage step time lt gt lt gt lt s gt 18 3715 8 519843629989e 09 19 3975 9 300878866142e 09 The two lines between stage 17 and 18 stand as a reminder that the simulation was restarted at that point They need to be removed manually from the cube_restartable_dat ndt file before ncol can work in the usual way on the ndt file 2 14 Applying a field that changes both in time and in space 2 14 1 Idea pass simulation object to field setting function You can simulate an applied field which both changes in space and time this may be useful to mimic the ef
153. ers who want to design sophisticated simulation scripts in Python If you are new to micromagnetic modelling you may want to start with the Mini tutorial micromagnetic modelling 1 3 Development status The first Nmag release was late in 2007 and many bugs have been fixed since then Having said that without doubt there are bugs left in the system and there is a long list of wishes for extra features changes improvements Currently there is no significant amount of funding or man power available to support Nmag users or develop it further The software should thus be seen to be provided as is Should you use Nmag for your work please cite e Thomas Fischbacher Matteo Franchin Giuliano Bordignon and Hans Fangohr A Systematic Approach to Multiphysics Extensions of Finite Element Based Micromagnetic Simulations Nmag IEEE Transactions on Magnetics 43 6 2896 2898 2007 online preprint and http dx doi org 10 1109 TMAG 2007 893843 to demonstrate the value of open source infrastructure in the community We should also cite the corresponding recommended publications when using OOMMF Magpar Mumax MicroMagnum etc 1 4 Mailing list If you are using nmag we recommend that you subscribe to at least one of these following two lists If you have a question about how to use the software we suggest you subscribe to nmag users and post it there 1 4 1 nmag announce nmag announce lists soton ac uk is a low traffic read only mailing
154. erty information None Read only attribute to obtain dimensionless value of Physical Object Returns value float The numerical value Example gt gt gt from nmag import SI gt gt gt H SI 10 A m gt gt gt print H value 10 0 gt gt gt print H lt SI 10 A m gt 4 7 2 units Module nmag Object ST units Property information None Read only attribute to obtain units of Physical Object returned as list of pairs of dimension name and power 4 7 3 in_units_of Module nmag Object SI in_units_of Arguments self unit_quantity The object will be expressed in multiplies of unit_quantity This is useful to convert from one measurement convention such as m s to another one such as km h The return value is just a float The units of unit_quantity have to be compatible with the units of the object itself otherwise an exception is raised A simple example gt gt gt d SI 10 m gt gt gt inch SI 2 54e 2 m gt gt gt d in_units_of inch 393 70078740157478 Another example 146 Chapter 4 Command reference NMAG User Manual Documentation Release 0 2 1 gt gt gt m SI 1 m gt gt gt s SI 1 s gt gt gt velocity 2 m s gt gt gt print velocity lt SI 2 m s gt gt gt gt km 1000xm gt gt gt h 3600xs gt gt gt print velocity in_units_of km h 8 2 Parameters unit_quantity SI Object The SI object itself i e se1
155. esh cube Fe unit_length SI le 9 m Set the initial magnetisation sim set_m 0 0 1 Launch the hysteresis loop Hs nmag vector_set direction 1 0 0 0 0001 norm_listsl0 1 ly 19 9 25 y 21 227 ll S01 units 0 001 si Tesla si mu0 sim hysteresis Hs We will now discuss the cube py script step by step After creating the simulation object we define a magnetic material Fe with cubic anisotropy representing iron Fe nmag MagMaterial name Fe Ms SI 1700e3 A m exchange_coupling SI 2le 12 J m anisotropy nmag cubic_anisotropy axisl 1 0 0 axis2 0 1 0 K1 SI 48e3 J m 3 We load the mesh and set initial magnetisation pointing in z direction that is in a local minimum of anisotropy energy density Finally we use hysteresis to apply gradually stronger fields in x direction up to 50 mT Hs nmag vector_set direction 1 0 0 0 0001 norm list 0 1 1 19 19 1 Ilg 21l 22 17 501 units 0 001xsi Tesla si mu0 Note that we sample more often the region between 19 and 21 mT where magnetisation direction changes rapidly due to having crossed the anisotropy energy barrier between z and x as can be seen in the graph below 2 11 2 Analyzing the result First we extract the magnitude of the applied field and the x component of magnetisation 2 11 Example Cubic Anisotropy 53 NMAG User Manual Documentation Release 0 2 1 ncol cube H_ext_0 M Fe_0
156. eshpp distort 0 4 correlation length 2 0 seed 23 nanowire_800x20x5 nmesh nanowire_800x20x5_distorted nmesh Intuitively what this command does is to randomly displace the front and rear nodes of the mesh and to stretch shrink the middle bits accordingly The details of this process as well as meaning of all the command line switches are explained in the next section The original and distorted mesh look like this only part of each mesh is shown 2 Maximilian Albert Matteo Franchin Thomas Fischbacher Guido Meier and Hans Fangohr Domain wall motion in perpendicular anisotropy nanowires with edge roughness J Phys Condens Matter 24 024219 14 pages 2012 postprint pdf 10 The mesh file for the nanowire was produced using the examesh tool which is included in the nmag distribution in the directory utils cubicmesh note that it needs to be compiled before it can be used just cd into this directory and type make The exact command used to produce the mesh file was examesh nanowire_800x20x5 nmesh 800 450 20 15 5 3 94 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 This figure shows a smooth nanowire top and then the same mesh after having been distorted using the nmesh command shown above The figure is taken from 2 23 2 Details and command line options Preliminary remark As mentioned above nmeshpp can only produce edge roughness at the moment There is a slight chan
157. etely flat effectively 2 dimensional tetrahedron The command nmeshpp q bar30_30_100 nmesh h5 computes a histogram of the distribution of this quality parameter for the bar mesh and produces this output Quality output qual interval counts probability 0 000 0 100 0 0 00 0 100 0 200 0 0 00 0 200 0 300 0 0 00 0 300 0 400 0 0 00 0 400 0 500 1 0 01 x 0 500 0 600 42 0 22 x 0 600 0 700 364 1 95 xx 0 700 0 800 2420 12 96 KxKKKKKKKKKK 0 800 0 900 8252 44 20 eK kk KR IR OR RAR RRA RRA 0 900 1 000 7592 40 66 xxx k k k k xxkkxxxxkxxkRRRARARAKA KR kkk 6 3 4 Histogram of edge lengths The command nmeshpp a bar30_30_100 nmesh h5 computes a histogram of the edge length distribution of the mesh a0 output a0 interval counts probability 1 954 2 329 234 0 63 xx 2 329 2105 1424 3 81 xxxxx x 2 705 3 080 7921 21 17 mR KR KKK KR KKK KR RK RK OK KK 3 080 3 456 8790 23 D0 Kx KKK KK KKK KKK KK KK KEK KK RK OK R OK EK RA A l 3 456 3 831 7573 20 243 xxx xx kkxk k kxxkxkkkkHARAKKAKK KARA RAR 6 3 nmeshpp 159 NMAG User Manual Documentation Release 0 2 1 3 831 4 207 5884 15 73 KKK KKK KKK KKK KKK EK KEKE KEKE 4 207 4 582 3769 10 08 k x x x x k x x x x x 4 582 4 957 1385 3 70 xxxxxx xx 42957 5 333 365 0 98 xx 5 333 5 708 63 0 17 x average a0 lt a0 gt
158. fect of a write head on the magnetic grains of an hard disk while the head is moving The way we do this is by changing the applied field every delta_t picoseconds This means that the applied field won t change continuously in time it will be piecewise constant in time but in general it can be non uniform in space You can do something like import math def set_H sim width 10 0 nm v 100 0 nm ns m s H_amplitude 0 5e6 A m t float sim time SI le 9 s get the time in ns center vx t 0 0 center of the applied field region def H r x y Zz ri le 9 ci for ri ci in zip r center factor H_amplitude math exp xxx yxy ZxZ width width return factor factor factor sim set_H ext H unit SI A m sim relax do set_H very time SI 50e 12 exit at time SI 1000e 12 s sui The function set_His called every 50 ps and does the following it sets a new field from the function H r This function sets a field which directed along the direction 1 1 1 and almost vanishes outside a sphere with radius 30 0 nm The center of this sphere moves along the direction 1 0 0 with velocity 100 nm ns thus simulating the motion of a write head in a hard disk Obviously the piece of code is not complete it shows only the technique in order to have a field changing in time and space For a complete example see the next section 2 14 2 Complete example
159. from left to right as the position changes from the left face to the right face of the cylinder Here x is the x coordinate of the position vector p and tmp min 1 0 max 1 0 float SI x m mesh_unitx hl1 is a continuous function which changes linearly from 1 to 1 when going from the left to the right face keeping constant outside the cylinder In the code above we also define the variable save which is used to specify when and what should be saved to disk Here we save the fields before and after the relaxation and save the averages every 5 picoseconds 90 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 We then call the run_simulation function we defined above to relax the magnetisation This function returns the simulation object sim which we use to save the magnetisation using the save_restart_file function Once this is done we delete the simulation object releasing resources memory we have used for the simulation of part I Note that for the relaxation we use 3 0 0 zero current density damping 0 5 fast damping to reach convergence quickly and stopping_dm_dt 1 0x degrees_per_ns this means that the simulation should end when the magnetisation moves slower than 1 degree per nanosecond The following part of the script deals with part II the computation of the current driven dynamics Now we simulate the magnetisation dynamics save averages every time SI 9e 12 s
160. from tailor written post processing scripts See example post processing of saved field data 6 2 3 Range of data to be processed The range switch allows a variety of ways to express which of the ids in the data file should be selected for dumping to the screen or conversion to a vtk file Here are some examples range 17 will select 17 range range 5 10 will select 5 6 7 8 9 range 2 5 10 42 will select 2 5 10 42 range range 10 20 25 31 42 will select 0 1 2 3 9 10 20 25 31 42 range max ids will select the last saved id 6 2 4 Conversion to vtk file The command nmagpp range O vtk test vtk bar will take the dataset with id 0 in the bar_dat h5 file and convert it to a binary vtk file with name test vtk For vtk files the default is to convert all fields However if a field or a list of fields is specified using the field option then only this field is converted This may be useful if disk space or conversion time is an issue We can convert multiple time steps into a set of vtk files with one command For example to convert for all saved configurations all fields into vtk files use nmagpp vtk alltest vtk bar This will create files alltest 000000 vtk alltest 000010 vtk alltest 000020 vtk alltest 000030 vtk alltest 000040 vtk alltest 000050 vtk and alltest 000060 vtk The conversion to vtk can be combined with the range command See Range of data
161. function initial_m that is being given the position of each site in the mesh as a vector p with three components and which returns an initial magnetisation vector This vector is chosen such that the initial magnetisation that is described by this function is likely to relax into a vortex configuration def initial_m p X Y Zz pP return y 50 0e 9 x 50 0e 9 40 0e 9 The magnetisation at point p is obtained from a 90 degree rotation of the vector which connects p to the center of the film This vector doesn t have to be normalised Nmag will take care of normalising it for us We need to instruct the simulation object sim to use this function to set the magnetisation sim set_m initial_m We set the criterion to be used to decide when the magnetisation has relaxed The value used here in set_params 1 e one degree per nanosecond is the default value so we could omit this but we change the value in the second part of this example sim set_params stopping_dm_dt 1 0 degrees_per_ns We finally run the simulation using the relax command until the convergence criterion dm dt lt 1 degree per nanosecond is fullfilled In the process we save spatially resolved data for all fields at step 0 and the same data at the end of the stage i e when an equilibrium has been reached just before the relax function returns sim relax save fields at step 0 at stage_end We finally save the relaxed magnetisat
162. g from nmag import SI import time python standard modules used to measure run time def run_sim tol Function that is called repeatedly with different tolerance values Each function call is carrying out one simulation oon mat_Py nmag MagMaterial name Py Ms SI 0 86e6 A m exchange_coupling SI 13 0e 12 J m 11g_damping 0 5 compose name of simulation to inlude value of tolerance fu o sim nmag Simulation bar_3 6f tol sim load_mesh bar30_30_100 nmesh h5 Py mat_Py unit_length SI le 9 m sim set_m 1 0 1 set tolerance has to be called after set_m sim set_params ts_abs_tol tol ts_rel_tol tol dt Si 2 56 1Z2 s timing 0 initialise variable to measur xecution time for i in range 0 121 timing time time start measuring time sim advance_time dt i compute time development for 300ps timing time time stop measuring time fwe exclude time required to save data sim save_data save averages every 2 5 ps fat end of simulation write performance data into summary file f open resultsummary txt a open file to append f write g d g n tol sim clock step timing f close fmain program tols 1le 1 1e 2 1e 3 1e 4 1e 5 1e 6 110 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 for tol in tols run_sim tol From a conceptual point of view we see something new here
163. gohr 31 05 2008 4 2 17 set_H_ext Module nmag Object Simulation set_H_ext Arguments self values unit None Parameters values vector list function or numpy array See set_m for an explanation of possible values unit SI Object An SI Object that is used as a multiplier for the values This unit has to be physically compatible with Ampere per meter To set an applied field that is homogenous and points in x direction one can use sim set_H_ext le6 0 0 SI A m which is equivalent to 4 2 Simulation 141 NMAG User Manual Documentation Release 0 2 1 sim set_H ext 1 0 0 SI le6 A m However we could also define the field in Oersted from nmag si import Oe sim set_H_ext 100 0 0 08 e or in Tesla mu0 from nmag si import Tesla mu0 sim set_H_ext l 0 0 Tesla mu0 4 2 18 set_pinning Module nmag Object Simulation set_pinning Arguments self values Parameters values vector list function or numpy array This method sets the scalar pinning field which defines a local scale factor for dm dt Default value is 1 0 use 0 0 to force dm dt to zero that is to pin fix magnetisation at a certain position Semantics of the values parameter match set_m 4 2 19 set_params Module nmag Object Simulation set_params Arguments self stopping_dm_dt None ts_rel_tol None ts_abs_tol None exact_tstop None Set the parameters which control the accuracy
164. gram is the NMAG data PostProcessor It can be used to convert data stored in RUNID_dat h5 files into vtk files e dump the data to the screen The documentation is available with the help switch nmagpp help 6 2 1 Inspecting the content We describe some typical scenarios using the data file bar_dat h5 that is generated in Example 2 Computing the time development of a system The bar_dat h5 file contains spatially resolved data for all fields in the simulation because we have used the save_data fields all command Some of the functions of nmagpp apply to one or more fields such as dump and vtk and these can be specified through a fields command line parameter Similarly the range command will limit the number of saved configurations which will be processed Try nmagpp help for further documentation Some examples e Checking what at what configurations have been saved nmagpp idlist bar produces id stage step time fields 0 gt 1 0 0 E_anis E_demag E_exch E_ext E_total H_anis H_demag 10 gt 1 312 5e 11 E_anis E_demag E_exch E_ext E_total H_anis H_demag 20 gt 1 495 le 10 E_anis E_demag E_exch E_ext E_total H_anis H_demag 30 gt 1 603 1 5e 10 E_anis E_demag E_exch E_ext E_total H_anis H_demag 40 gt 1 678 2e 10 E_anis E_demag E_exch E_ext E_total H_anis H_demag 50 gt 1 726 2 5e 10
165. guration of the system We can use the range argument to select entries for further processing The stage is only relevant for calculations of hysteresis curves see Example Simple hysteresis loop The step is the time stepper iteration counter for this calculation The time is given in seconds lt s gt Note the 5 pico second interval between entries The stage step and time data is provided for convenience What follows is a list of fields that have been saved for each of these configurations We convert the first saved time step into a vtk file with base name bar_initial vtk using nmagpp range 0 vtk bar_initial vtk bar and we also convert the last saved time step at 300 picoseconds to a vtk file with base name bar_final vtk using 2 2 Example 2 Computing the time development of a system 19 pin pin pin pin pin pin pin rho rho rho rho rho rho rho NMAG User Manual Documentation Release 0 2 1 nmagpp range 60 vtk bar_final vtk bar The actual file names that are created by these two commands are bar_initial 000000 vtk and bar_final 000060 vtk The appended number is the id of the saved configuration This is useful if one wants to create vtk files for all saved configurations For example nmagpp vtk bar vtk bar will create the files bar 000000 vtk bar 000010 vtk bar 000020 vtk bar 000030 vtk bar 000040 vtk bar 000050 vtk bar 000060 vtk Using MayaVi we can display this data in a
166. h it created We now comment the code which follows the function run_simulation If the initial magnetisation has not been calculated and saved into the file relaxed_m file then do it now if not os path exists relaxed_m file Initial direction for the magnetisation def m0 pos X Y Z pos tmp min 1 0 max 1 0 float SI x m mesh_unitxhl angle 0 5 math pixtmp return math sin angle math cos angle 0 0 save fields at step 0 at stage_end averages every time SI 5e 12 s sim run_simulation sim_name relaxation initial_m m0 damping 0 5 j 0 0 save save stopping_dm_dt 1 0x degrees_per_ns sim save_restart_file relaxed_m_file del sim This piece of code carries out part I of the simulation it relaxes the system starting from a sensible initial guess for the magnetisation and saves the relaxed magnetisation configuration so that it can be used in part II In more detail it starts by checking using the function os path exists if a file containing the initial mag netisation exists If this is not the case then the following indented block will be executed which computes and saves this initial magnetisation If the file exists the whole indented block is skipped and we go straight to part IT of the calculation In order to compute the relaxed configuration an initial guess mO for the magnetisation is defined Such magneti sation linearly rotates
167. h more than one region using GMSH 8 11 Can Irun more than one simulation in one directory ooo e 8 12 Can save datato an arbitrary directory 2 044 rss Be ee ER A 8 13 How to check the convergence ofa simulation lt lt e so e cacaredda a ki ke e 8 14 What to do in case of convergence problems e 8 15 How to visualise the difference between two fields defined over the same mesh 8 16 How to re sample data from a saved h5 file o 8 17 Notes on using GMSH to create a family of related meshes oo 129 129 131 143 143 143 144 145 147 147 149 149 152 153 153 155 158 160 161 161 161 163 163 163 163 164 164 164 9 Useful tools 175 A IEC 175 92 MayaVi se rrea le ac a e Be a lo oe id e a 175 03 INUNDA AA 175 10 Contact 177 11 Mini tutorial micromagnetic modelling 179 11 1 Introduction micromagnetic modelling lt se eere s tese reent eat terer iea 179 11 2 What is better finite differences or finite elements o o o 180 11 3 What size of the cells FD and tetrahedra FE should I choose o 180 IA Micromagnetic packages s cos gorai de B a e Be Ee ee E a 182 IES AE AA 182 12 Acknowledgements 183 NMAG User Manual Documentation Release 0 2 1 Authors Hans Fangohr Thomas Fischbacher Matteo Franchin Giuliano Bordignon Jacek Gen erowicz An
168. h pi Mx math cos angle My math sin angle Mz 0 return magnetisation vector for position x y z return Mx My Mz sim set_m my_magnetisation The function my_magnetisation returns the magnetisation vector corresponding to the given 3d posi tion in space This position x y z as given to the function is expressed in meters 3 Providing a numpy array If a numpy array is provided to set the values of the subfield then the shape of this array has to match the shape of the subfield data For example if the subfield is the magnetisation of material X and this material is defined on n mesh sites then the array needs to have n entries Each of those has to be a 3 component array as the magnetisation vector has three components Note the Simulation get_subfield function can be used to obtain exactly such a numpy array for the relevant subfield To read such a numpy array from a file you can use the get_subfield_from_h5file function However you have to be sure that the node order in the mesh that is stored in the _dat h5 file is the same as the mesh you are currently using in your simulation This should certainly be the case if 1 both runs 1 e the saved and the current are based on the same mesh and ii you only us one CPU as using more than one results in repartitioning and reordering of the mesh We aim to not allow setting wrong data here in the future but currently such checking is not implemented fan
169. h takes some input parameters such as the current density the damping etc and uses them to carry out a simulation We then call this function twice once for part I and once for part II The full listing of the script stt_nanopillar py import nmag os math from nmag import SI every at from nsim si_units si import degrees_per_ns 1 30 0 The nanopillar thickness is 30 nm hl 1 2 hl is half the nanopillar thickness relaxed_m_file relaxed_m h5 File containing the relaxed magnetisation mesh_name 1030 nmesh h5 Mesh name mesh_unit SI le 9 m Unit length for space used by the mesh def run_simulation sim_name initial_m damping stopping_dm_dt j P 0 0 save do do_demag True Define the material mat nmag MagMaterial name mat Ms SI 0 8e6 A m exchange_coupling SI 13 0e 12 J m 11g_damping damping 11g_xi SI 0 01 lig_polarisation P 7 Matteo Franchin Thomas Fischbacher Giuliano Bordignon Peter de Groot Hans Fangohr Current driven dynamics of domain walls constrained in ferromagnetic nanopillars Physical Review B 78 054447 2008 online at http eprints soton ac uk 59253 8 Matteo Franchin Giuliano Bordignon Peter A J de Groot Thomas Fischbacher Jurgen P Zimmermann Guido Meier Hans Fangohr Spin polarized currents in exchange spring systems Journal of Applied Physics 103 07A504 2008 online at http link aip org link JAPIAU 103 07A504 1 88 Chapter 2 Guide
170. h5 The h5 data files store spatially resolved fields The format is a binary and compressed hdf5 format to which we have convenient access via the pytables package for Python The user should not have to worry about reading this file directly but use the nmagpp tool to access the data 7 5 File names for data files The filenames for the Data files ndt and Data files h5 are given by concatenation of the simulation name the extension dat and the extension h5 or ndt When a simulation object is created for example in a file called mybar py starting like this import nmag sim nmag Simulation name bar then the simulation name is bar If no name is provided i e the file mybar py starts like this import nmag sim nmag Simulation then the simulation name will be the run id The run id is the filename of the simulation script without the py extension 1 e the simulation name then will be mybar Let us assume for the rest of this section that the simulation name is bar Once we use the save_data command for example like this sim save_data an ndt file will be created with name bar_dat ndt bar _dat ndt Similarly if we write the fields spatially resolved sim save_data fields all a h5 data file with name bar_dat h5 bar _dat h5 will be created 7 6 File names for log files A log file is created that stores most of the messages displayed to stdout i e the screen The
171. hat here we also provide an anisotropy order To understand what this number is we have to explain briefly what is going on behind the scenes nsim calculates the values of the user provided function for an appropriately chosen set of normalised vectors it then finds the polynomial in mx my and mz the components of the normalised magnetisation of the specified order which matches the sampled values The strength of this approach stands in the fact that the user has to provide just the energy density for the custom anisotropy nsim is taking care of working out the other quantities which are needed for the simulation such as the magnetic field resulting from the provided anisotropy energy which would require a differentiation of the energy with respect to the normalised magnetisation However the user must be sure that the provided function can be expressed by a polynomial of the specified order in mx my and mz In the present case we are specifying anisot ropy_order 4 because the energy for the uniaxial anisotropy can be expressed as a 4th order polynomial in mx my and mz In some cases the user may find useful to know that the functions nmag uniaxial_anisotropy and nmag cubic_anisotropy can be added the resulting anisotropy will have as energy the sum of the en ergies of the original anisotropies 2 12 2 The result The steps involved to extract and plot the data for the simulation discussed in the previous section should be familiar to t
172. he user at this point of the manual We then just show the graph obtained from the results of the script coin py 1 5 0 5 56 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 During the switching the system falls into an intermediate state where the magnetisation is nearly aligned with the anisotropy easy axis 2 13 Restart example Micromagnetic simulations can last for many hours or even many days It is then important to be able to save periodically the state of the simulation in such a way that if a hardware failure or a power cut occurs the simulation can be restarted exactly at the point where its state was last saved In this example we show how an nmag script can be modified to be restartable The only thing the user needs to do is to periodically save the state of the simulation in what we call a restart file The simulation can then be restarted using the appropriate command line option The restart feature applies only to the hysteresis method 2 13 1 Saving the state of the simulation We re consider the cubic anisotropy example Cubic anisotropy simulation script and replace the last line sim hysteresis Hs with the following lines from nmag import every at sim hysteresis Hs save averages fields at stage_end restart at stage_end every step 1000 The first two lines reproduce the default behaviour the fields
173. hod grow as the square of the number of surface points Note that for simulation of thin films the hybrid Finite Element Boundary Element as used by nmag and Magpar is likely to require a lot of memory see Memory requirements of boundary element matrix 165 NMAG User Manual Documentation Release 0 2 1 There are other points that are related to the fundamentally different discretisation approach used to turn a field the ory problem with a conceptually infinite number of degrees of freedom into a finite problem OOMMF assumes the magnetisation in every cell to be constant with jumps at boundaries while Nmag assumes magnetisation to be continuous and vary linearly within cells thus slightly violating the constraint of constant magnitude within a cell of non constant magnetisation 8 2 So this means the major difference is cubes vs tetrahe dra No Simplicial mesh discretisation is fundamentally different from finite difference discretisation With OOMME say magnetisation degrees of freedom are associated with the centers of the cells while with nmag they are associated with corners This conceptual difference has many implications e g for the question how to conceptually deal with the exchange interaction between different materials 8 3 Why do you have your own Python interpreter sim In order to provide the ability to run code in a distributed environment using MPI we cannot use the standard
174. hown in the following figure 2 18 Example 2D periodicity 75 NMAG User Manual Documentation Release 0 2 1 M Ms 0 2e 10 4e 10 6e 10 8e 10 te 09 1 2e 09 1 4e 09 1 6e 09 1 8e 09 2e 09 time s where we notice that the final configuration is now with the magnetisation aligned along the negative y axis and not along the x axis as before The alignment along the y direction is expected as now the macro geometry has a total size of 300 09 nm times 400 39 nm 30 nm x 10 copies plus spacings along the x direction times 10 nm x 40 copies plus spacings along the y direction times 10nm no periodic copies along the z direction so the longest side now is along the y direction The demagnetisation energy of the macro geometry drives the alignment of the magnetisation with the y direction Other usage examples include this study of an array of interacting triangular rings 2 19 Example Spin waves in periodic system Starting from a magnetisation out of equilibrium we study the time development of the magnetisation and track visually the spin waves The geometry is a thin film with dimensions 30 nm x 9 nm x 0 2 nm along the x y and z axes respectively The mesh is centered at 0 0 0 and periodic along the x direction so that the nodes with coordinates 15 0 y z will be considered as equivalent to the nodes with coordinates 15 0 y z 4 Giuliano Bordignon Thomas Fischbacher Matteo Franchin Jurgen P Zimmermann Peter
175. i in range 0 504 xX array i 0 5 0 5 0 5 le 9 M sim probe_subfield_siv M_Co x print gt gt f x 0 M 0 M 1 M 2 Relax the system sim relax save save_magnetisation_along_x at convergence We shall now discuss the bar py script step by step In this particular example we are solely interested in energy terms resulting from exchange interaction and anisotropy Hence we disable the demagnetisation field as follows sim nmag Simulation do_demag False We then create the material Co used for the bar cobalt in this case which exhibits uniaxial_anisotropy in z direction with phenomenological anisotropy constant K1 SI 520e3 J m 3 Co nmag MagMaterial name Co Ms SI 1400e3 A m exchange_coupling SI 30e 12 J m anisotropy nmag uniaxial_anisotropy axis 0 0 1 K1 SI 520e3 J m 3 After loading the mesh we set the initial magnetisation direction such that it rotates from z to z while staying in the plane normal to x direction hence suggesting the development of a Bloch type domain wall def sample_m0 x y 2 relative position goes linearly from 1 to 1 in region B relative_position 2x x offset length 1 mz min 1 0 max 1 0 relative_position return 0 math sqrt 1 mzxmz mz 50 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 We further pin the magnetisation at the very left x lt offset 2 nm and right
176. ial_m m0 damping 0 5 3 0 0 save save stopping_dm_dt 1 0x degrees_per_ns sim save_restart_file relaxed_m file del sim Now we simulate the magnetisation dynamics save averages every time SI 9e 12 s do exit at time SI 6e 9 s run_simulation sim_name dynamics initial_m relaxed_m_file damping 0 02 j 0 1e12 P 1 0 save save do do stopping_dm_dt 0 0 After importing the required modules we define some variables such as the length of the cylinder 1 the name of the file where to put the relaxed magnetisation relaxed_m_file the name of the mesh mesh_name its unit length mesh_unit 1 30 0 The nanopillar thickness is 30 nm hl 1 2 hl is half the nanopillar thickness relaxed_m_file relaxed_m h5 File containing the relaxed magnetisation mesh_name 1030 nmesh h5 Mesh name mesh_unit SI le 9 m Unit length for space used by the mesh 2 22 Example Current driven magnetisation precession in nanopillars 89 NMAG User Manual Documentation Release 0 2 1 These quantities are used later in the script For example knowing the length of the nanopillar is necessary in order to set a proper initial magnetisation for the relaxation By making this a parameter at the top of the program we can change it there 1f we wan to study the same system for a different 1 and just run the script again We define the function run_simulation we teach Python h
177. ications and mentioned in section Example Current driven magnetisation precession in nanopillars 2 23 Mesh distortion for edge roughness simulation The meshes used in micromagnetic simulations usually represent idealized geometries for example a nanowire might be modeled using a completely smooth cuboid mesh Real world materials on the other hand possess imperfections on various scales caused by fabrication processes e g electron beam lithography or sputter depo sition This can potentially have a significant impact on the magnetization dynamics The advantage of finite element based simulations is that such effects can be simulated at least qualitatively by distorting the mesh in a suitable way nmeshpp provides a means of distorting a given mesh in order to imitate roughness so that the resulting effects on simulations can be explored Note that at the moment only edge roughness is supported We first present an example in the following section and then go into the details of the command line interface and how the distortion process works The appropriate reference for this mesh distortion is Albert et al where the method is described and used to study domain walll motion in the presence of edge roughness 2 23 1 Example Consider a nanowire with dimensions 800nm x 20nm x 5nm for convenience we provide the corresponding mesh in the file nanowire_800x20x5 nmesh We distort this mesh using the following command nm
178. ides the total number of processes in the MPI set up gt mpiexec n 2 nsim gt gt gt ocaml mpi_status MPI status There are 2 nodes this is the master rank 0 gt gt gt The other command is ocaml mpi_hello and prints a short hello from all processes gt gt gt ocaml mpi_hello gt gt gt Node 0 2 Hello from beta kk soton ac uk Node 1 2 Hello from beta kk soton ac uk For comparison let s look at the output of these commands if we start ns im without MPI in which case only one MPI node is reported gt nsim gt gt gt ocaml mpi_status MPI status There are 1 nodes this is the master rank 0 gt gt gt ocaml mpi_hello Node 0 1 Hello from beta kk soton ac uk Assuming this all works we can now start the actual simulation To use two CPUs on the local machine to run the bar30_30_100 py program we can use gt mpiexec n 2 nsim bar30_30_100 py 2 27 Example Parallel execution MPI 115 NMAG User Manual Documentation Release 0 2 1 To run the program again using 4 CPUs on the local machine gt mpiexec n 4 nsim bar30_30_100 py Note that mpich2 and mpich1 will spawn more processes than there are CPUs if necessary Le if you are working on some Intel Dual Core processor with 2 CPUs and one core each but request to run your program with 4 via the n 4 switch given to mpiexec than you will have 4 processes running on the 2 CPUs If you want to stop the mpd
179. ield data see Saving spatially resolved data The first and second line in the data file are headers that explain by column the physical quantities and their dimensions The ncol tool allows to extract particular columns easily so that these can be plotted later useful for hysteresis loop studies In this example we have only one timestep there only is one row of data in this file We will therefore discuss this in more detail in a subsequent example Extracting arbitrary data from the running program The line H_demag sim probe_subfield_siv H_demag x 0 0 obtains the demagnetisation field see Fields and Subfields in Nmag at position x 0 0 The suffix _siv to this function means that both positions and return values will be given as SI values The for loop in the program which iterates x in the range from 10 le 9 to 10 1e 9 in steps of le 9 produces the following output x le 08 H_demag None x 9e 09 H_demag 329655 76203912671 130 62999726469423 194 84338557811344 x 8e 09 H_demag 329781 46587966662 66 963624669268853 137 47161381890737 x 7e 09 H_demag 329838 57852402801 181 46249265908259 160 61298054099865 x 6e 09 H_demag 329899 63327447395 131 06488858715838 71 383139326493094 x 5e 09 H_demag 329967 79622912291 82 209856975234786 16 893046828024836 x de 09 H_demag 329994 67306536058 61 622521557150371 34 433041910642359 x
180. ified version of the script used for part I Here is the full listing of stt py We model a bar 100 nm x 100 nm x 10 nm where a vortex sits in the center This is part II we load the vortex from file and apply a spin polarised current import nmag from nmag import SI every at Define the material mat_Py nmag MagMaterial name Py Ms SI 0 8e6 A m exchange_coupling SI 13 0e 12 J m llg_gamma_G SI 0 2211le6 m A s lig_polarisation 1 0 lig_xi 0 05 lig_damping 0 1 Define the simulation object and load the mesh sim nmag Simulation sim load_mesh pyfilm nmesh h5 Py mat_Py unit_length SI le 9 m Set the initial magnetisation part II uses the one saved by part I sim load_m_from_h5file vortex_m h5 sim set_current_density lel2 0 0 unit SI A m 2 sim set_params stopping_dm_dt 0 0 WE x decide when the simulation should stop sim relax save fields at convergence very time SI 1 0e 9 s averages every time SI 0 05e 9 s at stage_end do exit at time SI 10e 9 s 1 We now discuss the script with particular emphasis on the differences with the first one One difference lies in the material definition Define the material mat_Py nmag MagMaterial name Py Ms SI 0 8e6 A m exchange_coupling SI 13 0e 12 J m 11g_gamma_G SI 0 2211e6 m A s lig_polarisation 1 0 lig_xi 0 05 l
181. ig_damping 0 1 Here we use two new arguments for the MagMaterial class The first is 1lg_polarisation which is used to specify the spin polarisation of the conduction electrons inside the given material The second 11g_xi is used to specify the degree of non adiabaticity Note that for the damping parameter 11g_damping we are now using a smaller value 0 1 these values are not realistic for Permalloy The script then continues by creating the simulation object and loading the mesh which is identical to the relax ation script shown in part I The initial magnetisation is read from the vortex_m h5 file Set the initial magnetisation part II uses the one saved by part I sim load_m_from_h5file vortex_m h5 Here we use the function load_m_from_h5file to load the magnetisation from the file vortex_m h5 which was created in part I by using the function save_restart_file We set the current density 2 21 Example Spin transfer torque Zhang Li model 85 NMAG User Manual Documentation Release 0 2 1 sim set_current_density le12 0 0 unit SI A m 2 The current density has norm 10712 A m 2 and is aligned in the x direction We then disable the convergence check sim set_params stopping_dm_dt 0 0 WE decide when the simulation should stop Here we decide that convergence should be reached when the magnetisation moves less than 0 0 degrees per nanosecond This cannot happen and hence convergence is never re
182. ile format which is called vtk A number of high level user interfaces exist to visualise data provided in such vtk files These include e MayaVi http mayavi sourceforge net e VisIt http www lInl gov visit e ParaView http www paraview org 9 2 MayaVi MayaVi is a free easy to use scientific data visualizer It is written in Python and uses the Visualization Toolkit VTK for graphical rendering MayaVi is free and distributed under the conditions of the BSD license It is also cross platform and should run on any platform where both Python and VTK are available which is almost any Unix Mac OSX or Windows The MayaVi web page is http mayavi sourceforge net MayaVi has been used to generate many of the plots in this manual Other tools are available for visualisation of vtk files see vtk 9 3 NumPy Numerical Python short numpy is an extension library to Python that provides fast array operations and is de signed for numerical work This Python extension and documentation can be found at http numpy scipy org 175 NMAG User Manual Documentation Release 0 2 1 176 Chapter 9 Useful tools CHAPTER TEN CONTACT The nmag developer team can be contacted at nmag soton ac uk Questions about the usage of nmag can also be send to the nmag users mailing list 177 NMAG User Manual Documentation Release 0 2 1 178 Chapter 10 Contact CHAPTER ELEVEN MINI TUTORIAL MIC
183. imental system Neither the University of Southampton nor the authors assume any responsibility whatsoever for its use by other parties and makes no guarantees expressed or implied about its quality reliability or any other characteristic 1 5 Support 5 NMAG User Manual Documentation Release 0 2 1 6 Chapter 1 Introduction CHAPTER TWO GUIDED TOUR We present a number of worked out examples that are explained in detail and should cover most of the usual applications You may also want to check the Frequently Asked Questions 2 1 Example Demag field in uniformly magnetised sphere This is the most basic example that computes the demagnetisation field in an uniformly magnetised sphere For this simple system the exact result is known analytically the demag field vector has to be equal to minus one third of the magnetisation vector everywhere When using finite element calculations a crucial and non trivial part of the work is the finite element mesh generation We provide a very small mesh for this example spherel1 nmesh h5 which was generated with Netgen from this geometry file This gives us a sphere of radius 10nm We can then use the following nmag script spherel py import nmag from nmag import SI create simulation object sim nmag Simulation define magnetic material Py nmag MagMaterial name Py Ms SI le6 A m exchange_coupling SI 13 0e 12 J m load mesh sim loa
184. iodic one 72 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 2 18 Example 2D periodicity This example is another application of the macro geometry feature where we now deal with a 2D thin film system The unit cell isa 30x10x10 nm 3 prism where we take 10 copies in x and 40 copies in y direction to create the macro geometry The script no_periodic py simulates behaviour of just the unit cell of size 30x10x10 nm 3 without any periodic copies import nmag from nmag import SI every at define magnetic material Py nmag MagMaterial name Py Ms SI 1le6 A nm exchange_coupling SI 13 0e 12 J m create simulation object sim nmag Simulation load mesh sim load_mesh prism nmesh h5 no periodic Py unit_length SI le 9 m set initial magnetisation sim set_m 1 1 1 loop over the applied field s SI 1 s sim relax save averages fields every time 5e 12x s at convergence and the relaxation curves are obtained via set term postscript enhanced color set out no_periodic ps set xlabel time s set ylabel M Ms plot plot_no_periodic dat u 1 2 ti Mx w lp plot_no_periodic dat u 1 3 ti My w lp plot_no_periodic dat u 1 4 ti which creates the following plot 2 18 Example 2D periodicity 73 NMAG User Manual Documentation Release 0 2 1 M Ms
185. ion load_m_from_h5file Arguments self filename x kwargs magnetisation stored in filename to set the magnetisation of the simulation If more than one magnetisation configurations have been saved in the file it will load the first one This can be used to retrieve the magnetisation saved in a restart file and to set the current magnetisation of the simulation object to this magnetisation This restart file could have been written explicitely using the save_restart_file method or implicitly by providing a restart action to the hysteresis relax commands 138 Chapter 4 Command reference NMAG User Manual Documentation Release 0 2 1 To simply continue a hysteresis relax simulation using the restart option there is no need to use this func tion It should only be used if lower level manipulation is required see for example Current driven motion of a vortex in a thin film 4 2 13 save restart file Module nmag Object Simulation save_restart_file Arguments self filename None fieldnames m all False rent magnetic configuration into file that can be used for restarting This function saves the current magnetisation the time and all what is needed to restart the simulation exactly from the point it was invoked Parameters filename string The file into which the restart file is written Defaults RUNID_restart h5 fieldnames list The fieldnames to be saved Defaults to m all boo
186. ion to a file using the function save_restart_file so that we can use this in part 2 as the initial configuration sim save_restart_file vortex_m h5 We can launch the script with the command nsim relaxation py The output files for this simulation will have the prefix relaxation in their names The script saves the magneti sation at the beginning before relaxation and at the end after relaxation The magnetisations can be extracted and saved into vtk files using the command nmagpp relaxation vtk m vtk as usual MayaVi can then be used to show the initial magnetisation as described by the initial_m function The magnetisation at the end of the relaxation process 2 21 Example Spin transfer torque Zhang Li model 83 NMAG User Manual Documentation Release 0 2 1 m_Py lt gt Z component 0 00 0 143 0 286 0 429 0 571 0 714 z component of magnetisation 0 571 0 00 0 143 0 286 0 429 0 714 0 857 1 00 0 857 1 00 84 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 The relaxed vortex is much smaller than the initial one The important thing to notice is that such a magnetisation configuration has now been saved into the file vortex_m h5 which will be used as the initial magnetisation for part II of this simulation where we study the current driven dynamics of the vortex 2 21 3 Part Il Current driven dynamics For part II we need to use a slightly mod
187. ional argument save This allows to carry out hysteresis loop computations and write the results to disk Technically we say that this function performs a multi stage simulation In our terminology a stage is a part of the simulation where the field does not change Therefore every value for the applied field specified in H_ext_list corresponds to a different stage Stages are numbered starting from 1 which corresponds to H_ext_list 0 In general during stage number i the applied field is H_ext_list i 1 Parameters H_ext_list list of values for the applied field It is something like H1 H2 H3 where Hi is the triple of components of the applied field i e SI objects having units of A m save list of pairs thing_to_save when thing_to_save is either a string or a function provided by the user and when is an instance of the class When i e an object which contains the specification of when the thing has to be saved Possible string values for thing_to_save are e averages to save the averages of all the fields together with other information such as the stage number the time reached etc This is done calling the method save_data Refer to its documentation for further details e fields to save all the fields The method save_data fields all is called for this purpose e restart to save the current magnetisation configuration and all the information needed to restart the simulation
188. ions required decreases the CPU time is increasing This is the first indication that at this tolerance level the system becomes difficult to treat efficiently by sundials it basically appears to be noisy and stochastic equations are hard to integrate In summary e to minimise the simulation time we need to choose a tolerance value as large as possible e The definition of possible will depend on the context A good way of obtaining a suitable tolerance value is to run the same simulation repeatedly with decreasing tolerance values Once the resulting curves converge as a function of decreasing tolerance settings a good tolerance level has been found This would be 1e 4 for the example shown here 2 26 Example Timestepper tolerances 113 NMAG User Manual Documentation Release 0 2 1 e Choosing the tolerance values to be too large can be counter productive and take much more CPU time than the lower accuracy level e The default value for the sundials tolerances is shown in the documentation of set_params A simulation can often be accelerated significantly by increasing this value e A change of the tolerances has to be considered together with the convergence criterion for hysterises loop calculations see next section Hysteris loop calculation not converging A word of warning 2 26 1 Hysteris loop calculation not converging A word of warning The hysteresis and the relax command need to have a crit
189. is contained in nanodot1 nmesh h5 which is created from the_nanodot geo with Netgen Z 0 100 1 00 1 00 To compute the hysteresis loop for the disc we use the script nanodot 1 py import nmag from nmag import SI at create simulation object sim nmag Simulation define magnetic material Py nmag MagMaterial name Py Ms SI 795774 A m exchange_coupling SI 13 0e 12 load mesh the mesh dimensions are scaled by 100nm sim load_mesh nanodotl nmesh h5 cylinder Py unit_length SI 100e 9 m set initial magnetisation sim set_m 1 0 0 Hs nmag vector_set direction 1 0 0 norm_list 1000 0 900 0 95 0 90 0 Liz L00 0 200 0 Iy J M 32 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 1000 0 900 0 95 07 9040 Ely 100 0 200 0 1000 0 units 1e3xS1I A m loop over the applied fields Hs sim hysteresis Hs save averages fields restart at convergence We assume that the previous example have been sufficiently instructive to explain the basic steps such as importing nmag creating a simulation object defining the material and leading the mesh Here we focus on the hysteresis command We would like to apply fields ranging from 1e6 0 0 A mto 100e3 0 0 A minsteps of 100e3 A m Then from 95e3 0 0 A mto 95e3 0 0 A mwe would like to use a smaller step
190. is to make the mesh coarser If we were to use second or higher order base functions then we have more sites than nodes In a second order basis function calculation we identify sites by a tuple of node id 3 7 Sl object We are using a special SI object to express physical entities see also S7 Let us first clarify some terminology physical entity A pair a b where a is a number for example 10 and b is a product of powers of dimensions for example m 1s 1 which we need to express a physical quantity in this example 10 m s dimension SI dimensions meters m seconds s Ampere A kilogram kg Kelvin K Mol mol candela cd These can be obtained using the units attribute of the SZ object SI value for a given physical entity a b where a is the numerical value and b are the SI dimensions this is just the numerical value a and can be obtained with the value attribute of the SZ object Simulation Units The dimensionless number that expressed an entity within the simulation core This is irrele vant to the user except in highly exotic situations There are several reasons for using SI objects 3 5 Mesh 125 NMAG User Manual Documentation Release 0 2 1 e In the context of the micromagnetic simulations the use of SI objects avoids ambiguity as the user has to specify the right dimensions and where possible the code will complain if these are unexpected units such as in the definition of material par
191. kly very big Column 2 contains the current value of max dM dt Il Column 3 contains the stopping value of dM dt Convergence is reached when column 2 lt column 3 for at least two times If the simulations is going well then you should see that column 2 contains numbers which are not oscillating rapidly and are rather decreasing or increasing smoothly This is what typically should happen even if it can be that your simulation has really a bizarre dynamics which really oscillates in a frenetic way so one should be careful when analysing the data The fourth column contains an evaluation of the quality of the convergence according to what we just said This number should be close to one when the convergence is smooth and close to zero when it is oscillating dramatically 8 14 What to do in case of convergence problems If your simulation has really a convergence problem you can do two things e improve the tolerances ts_abs_err and ts_rel_err decrease these numbers by using the method set_params of the Simulation object 8 13 How to check the convergence of a simulation 169 NMAG User Manual Documentation Release 0 2 1 e use a do next_stage at stage_time SI x s as an argument to the hysteresis method This way you impose a maximum time x to spend in the computation of a stage you should make sure this makes sense in your case 8 15 How to visualise the difference between two fields defined over the
192. l If true then all fields will be saved This function is used by the hysteresis and relax commands to save a magnetic configuration from which a run can be continued using restart Example A common usecase for this function maybe to write the magnetic configuration that comes from a relaxation process to a file And to load that configuration as the initial configuration for a subsequent series of simulation s In this case one may want to provide the filename explicitely For example sim save_restart_file filename relaxed_configuration h5 One can then use the load_m_from_h5file to read this file relaxed_configuration h5 and to use it to set the magnetisation up in the subsequent simulation 4 2 14 relax Module nmag Object Simulation relax Arguments self H_applied None save averages fields at stage_end True do convergence_check every 5 step This method carries out the time integration of the LLG until the system reaches a metastable equilibrium Internally this uses the hysteresis loop command Parameters H_applied list of SI objects For a 3 d simulation the SI objects Hx Hy and Hz would be specified as Hx Hy Hz Default value is None resulting in the currently applied external field H_ext being used save Schedule object Allows to define what data to save at what events See documentation on the hysteresis method and on the Schedule object converg
193. l you would like to change the defaults please contact the nmag team so we can take your requirements into account in the next release 2 one solver for the system of algebraic equations that results from the time integrator s implicit integration scheme We need to document the default settings and how to modify this 3 the ODE integrator Setting of the tolerances for the ODE integrator can be done with set_params An example of this is shown in section Example Timestepper tolerances 3 8 Terms 127 NMAG User Manual Documentation Release 0 2 1 We expect that for most users the tolerances of the ODE integrator are most important see Example Timestepper tolerances as this greatly affects the performance of the simulation 3 10 The equation of motion the Landau Lifshitz Gilbert equation The magnetisation evolution as computed by the advance_time or the hysteresis methods of the Simulation class is determined by the following equation of motion dM dt llg_gamma_G M x H llg_damping M x dM dt which is the Landau Lifshitz Gilbert equation we often use the abbreviation LLG a vector equation where M H and dM dt are three dimensional vectors and x represent the vector product This equation is used to dermine the evolution of each component of the magnetisation For example if the system has two materials with name ml and m2 then the magnetisation has two components M_m1 and M_m2 and the equations
194. ld_sites from_h5dfile Module nmag Object get_subfield_sites_from_h5file 4 3 get_subfield_from_hb5file 143 NMAG User Manual Documentation Release 0 2 1 Arguments filename subfieldname Analogous to get_subfield_sites which returns the site ids of nodes for a subfield of a simulation object but will retrieve data from saved _dat h5 file Parameters filename string The full name of the _dat h5 data file subfieldname string The name of the subfield to be retrieved Returns numpy array The ids are returned as si values 4 6 HMatrixSetup Module nmag Object HMatrixSetup Class constructor information self algorithm HCA2 kwargs ass collecting the parameters needed in order to set up an HMatrix with HLib within Nmag The optional argument algorithm is by default set to HCA2 At present no other values are supported The user can then specify a number of parameters in order to fine tune the setup of the HMatrix kwargs stands for one or more of the following parameters see Hlib documentation for detailed descriptions of the parameers Parameters of HCA II eps_aca float A heuristic parameter which influences the accuracy of HCA II By default this parameter is set to le 7 poly_order int A second parameter which influences the accuracy of the HCA II Its default setting is 4 Parameter for recompression algorithm eps float This parameter determines the accuracy of the r
195. le of 180 degrees would mean that they point in exactly opposite directions How much variation is acceptable i e how big is the spin angle allowed to be It depends on the accuracy required Some general guidelines from M Donahue in email to H Fangohr on 26 March 2002 referring to OOMMF which we fully endorse 180 Chapter 11 Mini tutorial micromagnetic modelling NMAG User Manual Documentation Release 0 2 1 Begin quote M Donahue if the spin angle is approaching 180 degrees then the results are completely bogus over 90 degrees the results are highly questionable Under 30 degrees the results are probably reliable end quote It is absolutely vital that the spin angle does not become excessive if the simulation results are to be trusted It is probably the most common error in micromagnetics one would like to simulate a large geometry thus one has to choose the discretisation length large to get any results within reasonable time However the results are often completely useless if the spin angle becomes too large Because this is such an important issue OOMMF for example provides Max Spin Ang data in its odt data table file for the current configuration the last stage and the overall run Nmag has a columns maxangle_m_xX in the Data files ndt file that provide this information where X is the name of the magnetic material You will probably find that often a discretisation length of half
196. le we are using a different approach to define the anisotropy First we define the function my_anisotropy which returns the energy density for the magnetic anisotropy Here we define a function which returns the energy for a uniaxial anisotropy of order 4 K1 SI 43e3 J m 3 K2 SI 21e3 J m 3 axis 0 0 1 The normalised axis def my_anisotropy m a scalar_product axis m return Kl xa 2 K2 axx4 Note that the function returns a SI object with units J m 3 energy density The reader may have recognised the familiar expression for the uniaxial anisotropy in fact the two code snippets we just presented are defining exactly the same anisotropy they are just doing it in different ways The function scalar_product which we have used in the second code snippet just returns the scalar product of two three dimensional vectors a and b and is defined in the line above 2 12 Example Arbitrary Anisotropy 55 NMAG User Manual Documentation Release 0 2 1 def scalar_product a b return a 0 b 0 a 1 xb 1 a 2 xb 2 The function my_anisotropy has to be specified in the material definition instead of passing anisotropy nmag uniaxial_anisotropy we just pass anisotropy my_anisotropy to the material constructor my_material nmag MagMaterial name MyMat Ms SI le6 A m exchange_coupling SI 10e 12 J m anisotropy my_anisotropy anisotropy_order 4 An important point to notice is t
197. lements This depends on what you want to simulate Here are some points to consider e Finite difference simulations are best when the geometry you simulate is of rectangular shape i e a cube a beam a geometry composed of such objects a T profile etc In these situations the finite element discretisation of the geometry will not yield any advantage Assuming that the finite difference grid is aligned with the edges in the geometry Finite difference simulations need generally less computer memory RAM This is in particular the case if you simulate geometries with a big surface such as thin films See Memory requirements of boundary element matrix for a description of the memory requirements of the hybrid finite element boundary element simulations both Nmag and Magpar are in this category If this turns out to be a problem for you we suggest to read the section Compression of the Boundary Element Matrix using HLib Finite element simulations are best suited to describe geometries with some amount of curvature or angles other than 90 degrees For such simulations there is an error associated with the staircase discretisation that finite difference approaches have to use This error is very much reduced when using finite elements We state for completeness that there are techniques to reduce the staircase effect in finite difference simu lations but these are currently not available in open source micromagnetic simulation code
198. llel execution MPI Nmag s numerical core which is part of the nsim multi physics library has been designed to carry out numerical computation on several CPUs simultaneously The protocol that we are using for this is the wide spread Message Passing Interface MPI There are a number of MPI implementations the best known ones are probably MPICH1 MPICH2 and LAM MPI Currently we support MPICH1 and MPICH2 Which mpi version to use Whether you want to use mpich1 or mpich2 will depend on your installation currently the installation from source provides mpich2 which is also used in the virtual machines whereas the Debian package relies on mpich1 no Debian package is provided after release 0 1 6163 2 27 1 Using mpich2 Before the actual simulation is started a multi purpose daemon must be started when using MPICH2 The mpd conf file MPICH will look for a configuration file with name mpd conf in the user s home directory If this is missing an attempt to start the multi purpose daemon will result in an error message like this gt mpd configuration file Users fangohr mpd conf not found A file named mpd conf file must be present in the user s home directory etc mpd conf if root with read and write access only for the user and must contain at least a line with MPD_SECRETWORD lt secretword gt 114 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 One way to saf
199. lly providing more and more flexibility in an ad hoc manner through adding configuration parameters slowly evolving into an extensive specialized programming language Nmag starts out as an extension to a widely used programming language Python from which it gains all its flexibility and evolves towards more specialized notions to conveniently define and study the properties of very specific physical systems The main advantage of this approach is two fold first we do not gradually evolve another ad hoc and potentially badly implemented special purpose programming language Second by drawing upon the capabilities of a well supported existing framework for flexibility we get a lot of additional power for free the user can employ readily available and well supported Python libraries for tasks such as data post processing and analysis e g generating images for web pages etc In addition to this some users may benefit from the capability to use Nmag interactively from a command prompt which can be very helpful during the development phase of an involved simulation script 5 The disadvantage is of course that a novice user may be confronted with much more freedom than he can handle We try to cope with this issue by providing a collection of example scripts in the Guided Tour for the most common applications that only need very slight modification for basic use e g changing of the mesh filename or material parameters At present Nmag is
200. machinel mydomain machine2 mydomain machine3 mydomain We then need to pass the name of this file to the mpi run command to run a mpi enabled executable with mpich mpirun machinefile machines txt np 3 usr bin nsim bar30_30_100 py For further details please refer to the MPICH1 documentation 2 27 3 Visualising the partition of the mesh We use Metis to partition the mesh Partitioning means to allocate certain mesh nodes to certain CPUs Generally 1t is good if nodes that are spatially close to each other are assigned to the same CPU Here we demonstrate how the chosen partition can be visualised As an example we use the Example demag field in uniformly magnetised sphere We are Using mpich2 gt mpd amp gt mpiexec l n 3 nsim spherel py The program starts and prints the chose partition to stdout nfem ocaml 2008 05 28 15 11 07 757 INFO Calling ParMETIS to partition the me sh among 3 processors nfem ocaml 2008 05 28 15 11 07 765 INFO Processor 0 177 nodes nfem ocaml 2008 05 28 15 11 07 765 INFO Processor 1 185 nodes nfem ocaml 2008 05 28 15 11 07 766 INFO Processor 2 178 nodes If you can t find the information on the screen stdout then have a look in spherel1_1log log which contains a copy of the log messages that have been printed to stdout If we save any fields spatially resolved as with the sim save_data fields all command then nmag will create a file with name in this case spherel1l
201. mag we only use the HCA II algorithm which seems to be the most reliable amongst the commonly used algorithms being still very efficient see for example Knittel et al 105 07D542 2009 postprint pdf The performance and accuracy of the HCA II algorithm can be tuned by providing a number of parameters which are collected inside a HMatrixSetup object A default HMatrixSetup object is provided where a reasonable choice of these parameters is made The default parameters can be overriden by users We point the reader to the documentation of the HMatrixSetup class for a list and description of all avaliable parameters The next example shows how to use HLib with the default values for the setup of the BEM matrix Using HLib with default parameters The Nmag script sphere_hlib py shows how Nmag can be used in order to compute the demagnetisation field within a sphere with a radius of 50 nm import nmag import time from nmag import SI When creating the simulation object specify that the BEM hmatrix should be set up by using the default parameters sim nmag Simulation phi_BEM nmag default_hmatrix_setup Specify magnetic material parameters chosen as in example 1 Py nmag MagMaterial name Py Ms SI le6 A m exchange_coupling SI 13 0e 12 J m Load the mesh sim load_mesh sphere nmesh h5 sphere Py unit_length SI le 9 m Set the initial magnetisation sim set_m 1 0 0 Save the demag
202. magnetic studies 2 22 Example Current driven magnetisation precession in nanopillars This is the second example we provide in order to illustrate the usage of the Zhang Li extension to model spin transfer torque in Nmag While in the Current driven motion of a vortex in a thin film example we tried to present two scripts one for initial relaxation and one for the spin torque transfer simulation sacrificing usability for the sake of clarity here we ll try to present a real life script using the power of the Python programming language as much as it is needed to achieve our goal We consider a ferromagnetic nanopillar in the shape of a cylinder We assume that the magnetisation in the nanopillar is pinned in the two faces of the cylinder along opposite directions on the right face the magnetisation points to the right while on the left face it points to the left The magnetisation is then forced to develop a domain 6 Massoud Najafi Benjamin Kruger Stellan Bohlens Matteo Franchin Hans Fangohr Antoine Vanhaverbeke Rolf Allenspach Markus Bolte Ulrich Merkt Daniela Pfannkuche Dietmar P F Moller and Guido Meier Proposal for a Standard Problem for Micromagnetic Simulations Including Spin Transfer Torque Journal of Applied Physics in print 2009 preprint available at http www soton ac uk fangohr publications preprint Najafi_etal_2009 pdf 86 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1
203. mmand allows us to extract the data and we redirect it to a text file with name nmag dat ncol nanodot H_ext_0 m_Py_0 gt nmag dat Plotting the data with Gnuplot gnuplot make_comparison_plot gnu which uses the script in make_comparison_plot gnu set term postscript eps enhanced color set out nanodot_evo eps set xlabel Applied field kA m set ylabel M M_s plot 250 50 1 2 1 2 magpar dat u 2 3 ti magpar w lp 4 nmag dat u 1 1000 2 ti m The resulting graph is shown here magpar Ce SE Ee 2 250 200 150 100 50 0 50 Applied field kA m and we can see that the results from nsim match those from magpar The magnetisation configurations during the switching process are shown in the following snapshots 2 6 Example Vortex formation and propagation in disk 37 NMAG User Manual Documentation Release 0 2 1 m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 2 1 Magnetisation configuration for a decreasing applied field of 20 kA m The x axis is increasing from left to right for this and the subsequent plots m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 2 2 Magnetisation configuration for a decreasing applied field of 15 kA m 38 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00
204. n object This will contain and provide information about our physical system sim nmag Simulation 2 1 3 Defining magnetic materials After importing the nmag module into Python s workspace and creating the simulation object sim we need to define a material using nmag MagMaterial We give it a name as a Python string which in this case we choose to be Py a common abbreviation for PermAlloy and we assign a saturation magnetisation and an exchange coupling strength Py nmag MagMaterial name Py Ms SI le6 A m exchange_coupling S1I 13 0e 12 J m The name of the material is important as we may want to simulate systems made up of multiple different materials and the material name will be used as a postfix to the name of some Fields and subfields The output files will also use that name to label output data Names must be alphanumeric 1 e formed exclusively out of the characters in the set 0 91 _a zA Z here 8 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 Rather than representing dimensionful physical quantities as numbers nmag uses a special object class the SI object The underlying rationale is that this allows automated detection of mismatches of physical dimensions If some physical parameter is given to nmag in a dimension different from the expected one nmag will detect this and report an error Also any nmag output e g a three dimensional VTK visualisati
205. n reached 66 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 2 16 Example Larmor precession This example shows how to derive the period of the Larmor precession for the magnetisation and compare the result from simulation to the analytical solution It is inspired by an example from the magpar documentation http magnet atp tuwien ac at scholz magpar doc html examples html sphere_larmor We us the larmor py script import nmag from nmag import SI every at si fcreate simulation object and switch off the computation of the demagnetising field sim nmag Simulation do_demag False define magnetic material so that Js mu0 Ms 1 T Py nmag MagMaterial name Py Ms 1 0 si Tesla si mu0 exchange_coupling SI 13 0e 12 J m llg_damping SI 0 0 load mesh sim load_mesh spherel nmesh h5 sphere Py unit_length SI le 9 m set initial magnetisation sim set_m 1 1 1 set external field Hs nmag vector_set direction 0 0 1 norm_list 1 0 units le6 SI A m ps SI le 12 s ps corresponds to one picosecond let the magnetisation precess around the direction of the applied field sim hysteresis Hs save averages every time 0 1xps do exit at time 300xps We turn off computation of the demagnetising field sim nmag Simulation do_demag False and set the damping term in the LLG equ
206. n the effect of cell size on vortex mobility e M J Donahue and R D McMichael Physica B 233 272 278 1997 e M J Donahue and D G Porter Physica B 343 177 183 2004 and one which included a section on discretisation induced Neel wall collapse e M J Donahue Journal of Applied Physics 83 6491 6493 1998 11 4 Micromagnetic packages The following micromagnetic simulation packages are freely available on the internet e OOMMEF finite differences e Magpar finite elements e nmag finite elements These are general purpose packages Some other and partly closed source commercial packages are listed at http math nist gov oommf otherlinks html 11 5 Summary The most important points in short e choose a small discretisation length so that the spin angle stays well below 30 degrees e if you want to simulate thin films or other geometries with a lot of surface nodes with finite elements consider how much memory you would need for the boundary element matrix best to do this before you start creating the mesh 182 Chapter 11 Mini tutorial micromagnetic modelling CHAPTER TWELVE ACKNOWLEDGEMENTS This work has been financially supported by the Engineering and Physical Science Research Council EPSRC GR T09156 01 EP E0400631 1 in the United Kingdom through funding from the European Community s Sev enth Framework Programme FP7 2007 2013 under Grant Agreement no 233552 and by the University of Sou
207. n the following plot 8e 05 6e 05 4e 05 Magnetisation A m 2e 05 0 2e 10 4e 10 6e 10 8e 10 time s 1 The time integrator here Sundials CVODE would have to do an extra step to get to the requested time If the current time is very close to the requested time it will simply report this value 2 2 Example 2 Computing the time development of a system 23 NMAG User Manual Documentation Release 0 2 1 In summary the relax function is useful to obtain a meta stable configuration of the system In particular it will carry out the time integration until the remaining torque at any point in the system has dropped below a certain threshold 2 2 6 Relaxing the system faster If we are only interested in the final meta stable configuration of a run we can switch off the precession term in the Laundau Lifshitz and Gilbert equation The MagMaterial definition in the following example shows how to do this import nmag from nmag import SI every at mat_Py nmag MagMaterial name Py Ms SI 0 86e6 A m exchange_coupling SI 13 0e 12 J m 11g_damping 0 5 do_precession False sim nmag Simulation bar_relax2 sim load_mesh bar30_30_100 nmesh h5 Py mat_Py unit_length SI le 9 m sim set_m 1 0 1 ps SI le 12 s sim relax save sl averages every time 5xps fields at convergence The new option is do_precession Fal
208. n through hierarchical matrices a sep arate nsim script file thinfilm20_full py thinfilm40_full py thinfilm60_full py thinfilm20_hlib py etc has been written It is important to start every simulation as a single process by calling nsim thinfilm20_full py clean etc so that there are no overlaps in the memory ac cess of different simulations From every script a routine run_simulation which is imported from a local nsim module simtools py starts a simulation specified by its arguments name of the simulation name of the mesh file name of hlib object in case hierarchical matrices are used and the tolerance for the time integrator 100 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 and returns the number of nodes of the mesh the simulation s memory consumption and the setup and relaxation times These values are then written to a file timings_hlib dat ortimings_full dat respectively Beside extracting the information on the performance it is also important to check whether simulations using the full boundary element matrix and a hierarchical matrix approximation actually do the same and that the simulated behaviour is physically correct Looking at the spatially averaged magnetisation we find a very good agreement between both simulation types example given for the film with an edge length of 100nm l 0 8 0 6 0 2 0 4 0 6 0 8 0 5e 10 le 09 1 5e 09 2e 09 2 5e 09 3e 09 3 5e
209. netisation field sim save_data fields H_demag Probe the demagnetisation field at ten points within the sphere for i in range 5 6 x ixle 9 Hdemag sim probe_subfield_siv H_demag x 0 0 print x x H_demag Hdemag In this first example we use default parameters for setting up the BEM matrix by passing the object nmag default_hmatrix_setup to the Simulation object sim nmag Simulation phi_BEM nmag default_hmatrix_setup This command specifies that the BEM matrix should be set up using the default parameters in nmag default_hmatrix_setup The actual values of the parameters can be visualised on the screen by simply printing the object with import nmag print nmag default_hmatrix_setup When running the simulation sphere_hlib py using the usual command nsim sphere_hlib py clean it should print out the demagnetisation field at ten points along the line x 0 0 98 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 x 5be 09 H_demag x le 09 H_demag x 3e 09 H_demag x 2e 09 H_demag 333060 61988567741 16 426569556599606 63 649046900628299 333061 67213255615 17 81158234138228 65 112039406898973 333062 69422596297 19 401486521725044 66 015626464953897 333062 72991753434 20 940683675745074 66 988296036794026 x le 09 H_demag 333061 60282647074 22 420106762492924 68 042400926888646 x 0 0 H_d
210. ng name of the subfield Example ave_M sim get_subfield_average_siv M Py will obtain the average magnetisation of the subfield M_Py of field M for example ave_M 100000 00 0 0 4 2 7 probe_subfield Module nmag Object Simulation probe_subfield Arguments self subfieldname pos unit None ven subfield name and position SI object return data as SI object Note that get_subfield_siv has the same functionality but takes a list of floats for the position instead of an SI object and returns a list of float s which is just the S value of that physical entity If the subfield is not defined at that part of space None is returned If the subfield does generally not exist then a KeyError exception is thrown Parameters subfieldname string The name of the subfield pos SI object The position for which the data should be returned unit SI object If you request the value for a subfield of a field that is part of nmag i e fields M m H_demag etc then you do not need to provide this object If you request data of any other multi physics fields then this function needs to know the SI dimensions of that field for the correct conversion from simulation units to SI units If incorrect dimensions are provided the returned data is likely to be wrongly scaled Returns data list of list of SI objects The returned object is an SI object for scalar subfields a list of SI objects for vector fi
211. normalised KI SI Object Second order phenomenological anisotropy constant as used in the equation above K2 SI Object Fourth order phenomenological anisotropy constant as used in the equation above Default value is 0 4 1 2 cubic_anisotropy Module nmag Object cubic_anisotropy Arguments axisl axis2 Kl K2 0 K3 0 Returns a predefined anisotropy modelling a cubic anisotropy energy density term E anis Kl lt axisl m gt 2 lt axis2 m gt 2 lt axisl m gt 2 lt axis3 m gt 2 lt axis2 m gt 2 lt axis3 m gt 2 K2 x lt axisl m gt 2 lt axis2 m gt 2 lt axis3 m gt 2 K3 x lt axisl m gt 4 lt axis2 m gt 4 lt axisl m gt 4 lt axis3 m gt 4 lt axis2 m gt 4 lt axis3 m gt 4 where m is the normalised magnetisation 130 Chapter 4 Command reference NMAG User Manual Documentation Release 0 2 1 Parameters axis vector list First cubic anisotropy axis will be normalised axis2 vector list Second cubic anisotropy axis will be orthonormalised with regards to axisl KI SI Object Fourth order phenomenological anisotropy constant as used in the equation above K2 SI Object Sixth order phenomenological anisotropy constant as used in the equation above Default value is O K3 SI Object Eigth order phenomenological anisotropy constant as used in the equation above Default value is 0 4 2 Simulation Module nmag Object Simula
212. nsim ellipsoid py If you have run the simulation before we need to use the clean switch to enforce overriding of existing data files nsim ellipsoid py clean The simulation should take only a few minutes for example 3 minutes on an Athlon64 3800 and needs about 75MB of RAM If the simulation has been interrupted it can be continued using nsim ellipsoid py restart 2 3 3 Obtaining the hysteresis loop data Once the calculation has finished we can plot the graph of the magnetisation projected along the direction of the applied field as a function of the applied field We use the ncol command to extract the data into a text file named plot dat ncol ellipsoid H_ext_0 m_Py_0 gt plot dat 2 3 4 Plotting the hysteresis loop with Gnuplot In this example rather than using xmgrace we show how to plot data using Gnuplot gnuplot make_plot gnu The contents of the gnuplot script make_plot gnu are set term postscript eps enhanced color set out hysteresis eps set xlabel Applied field H_x A m set ylabel M_x M_s set xrange 1050000 1050000 set yrange 1 2 1 2 plot plot dat u 1 2 ti ellipsoid example w lp 3 which generates the following hysteresis loop graph 2 3 Example Simple hysteresis loop 27 NMAG User Manual Documentation Release 0 2 1 ellipsoid example x K WW W E E E TE TE TE E ETE EEE 1e 06 500000 0 500000 1e 06 Applied field H A m
213. nts self subfieldname This function provides the node indices of the sites for data obtained with get_subfield Parameters subfieldname string The name of the subfield for example m_Py or H_demag Returns data numpy array Array containing a list of integers for every site The integers within each list are node indices of the mesh There will be only one integer per site in first order basis function calculations which is the usual case in micromagnetics 4 2 5 get_subfield_average Module nmag Object Simulation get_subfield_average Arguments self field_name subfield_name None the average of the subfield subfield_name of the field fieldname as an SI object or a list of list of list of SI objects in the field is a vector 2nd rank tensor etc Parameters field_name string name of the field subfield_name string name of the subfield See also get_subfield_average_siv 4 2 6 get_subfield_average_siv Module nmag Object Simulation get_subfield_average_siv Arguments self field_name subfield_name None the average of the subfield subfield_name of the field fieldname as a single floating point number or a list if it is a vector or a list of list for matrices etc The number is expressed in SI units hence the suffix _siv which stands for si value Parameters field_name string name of the field 4 2 Simulation 133 NMAG User Manual Documentation Release 0 2 1 subfield_name stri
214. o the nmesh format that can be read by nmag The nmeshimport tool can convert Netgen Gambit and Gmsh files into nmesh files The general usage is nmeshimport OPTIONS INPUTFILE NMESHFILE The OPTION to import from Netgen is netgen The contributed code for importing from a Gambit mesh file is gambit The OPTION to import from Gmsh is gmsh Usage example assuming we have a file mymesh neutral created with Netgen and would like to convert it to mymesh nmesh h5 we could use this command nmeshimport netgen mymesh neutral mymesh nmesh h5 Use nmeshimport help to see all available features 6 6 nsim This is the main executable It superficially appears to be a Python interpreter but has extended functionality In particular it has support for parallel execution using MPI and contains extensions accessible in the additional built in ocaml module which provides the additional functionality of the nsim multiphysics system Nmag is a Python library on top of nsim which itself is implemented in Objective Caml 6 7 nsimversion A script that provides some information about the version of the software If you need to report a bug problem please include the output of this program From release 0 2 onwards please use 6 5 nmeshimport 161 NMAG User Manual Documentation Release 0 2 1 nsim version instead 162 Chapter 6 Executables CHAPTER SEVEN FILES AND FILE NAMES
215. oarseness of the tree structure a too fine tree structure would result in a higher amount of memory required for the storage of the tree itself a parameter nmin has been introduced It is the minimal number of lines or rows a submatrix within a leave can have and is by default set to 30 144 Chapter 4 Command reference NMAG User Manual Documentation Release 0 2 1 Parameter for the numerical quadrature quadorder int The order of the Gaussian quadrature used to compute matrix entries for the low rank matrix blocks For the matrix blocks which are not approximated an analytical expression instead of numerical integration is used By default quadorder is set to 3 4 7 Sl Module nmag Object SI Class constructor information self value dimensions Physical quantity in the SI units system This class allows to associate SI dimensions such as meter kilogram Ampere seconds candela and mol with a floating point number The resulting object supports addition subtraction which fails if the dimensions of the objects in a sum or difference disagree multiplication and division There are different ways to create objects 1 The most fundamental approach is to provide a value and a list of pairs where each pair is a character identifying the SI base unit and an integer that provides its power Examples a v SI 10 m 1 s 1 is the code to create an SI object v that represents 10 m s b B
216. odified the data files on the disk Example nsim X py clean loglevel this switch determines the amount of information that is being send to stdout usually the screen and also to the file X_1o0g log The available levels are in increasing order of detail error print no messages apart from errors warning print warnings info print a moderate amount of information default info2 print slightly more information debug print a lot of information typically for developer and debugging use Example nsim X py loglevel info2 or nsim X py loglevel debug slavelog Log message from slave nodes when running under MPI are usually supressed This switch activates them Printing these messages will reduce the MPI performance somewhat as the messages are printed to stdout on each slave and then have to be transferred through the network to the master process Note that any log messages from the nodes will only go to stdout whereas log messages from the master will also go into the log file see File names for log files Messages from slave nodes are preceeded by SOX where X is the rank of the node Le log messages from slave node with rank 2 would start with S02 Example nsim X py slavelog restart If a calculation of a hysteresis loop is interrupted power cut computer crash exceeding allocated run time on cluster etc then the calculation can be carried out starting from the moment when the last restart file w
217. on Release 0 2 1 tol 1e 1 tol 1e 2 _ 8 55e 05 tol 10 3 tol 1e 4 tol 1e 5 tol 1e 6 aa 8 54e 05 gt AA 4 8 53e 05 8 52e 05 4 1 8e 10 2e 10 2 2e 10 2 4e 10 2 6e 10 2 8e 10 3e 10 time s M_Py A m We conclude that we should use a tolerance of at most le 3 for this simulation better 1e 4 or smaller In simulation work we are of course interested to get the most accurate simulation results However in reality this is conflicting with the increased run time that is associated with more accurate simulations In this example we have written some performance data into resultssummary txt Reformatted postprocessed and the rows re ordered this is the data complete with table headings tol steps CPU time s CPU time per step s 0 000001 740 120 81 0 163 0 000010 356 62 37 0 175 0 000100 182 46 10 0 253 0 001000 119 66 36 0 558 0 010000 114 92 08 0 808 0 100000 88 94 69 1 076 The accuracy of the simulation results decreases from the top of the table downwards We know from the graphs above that we should use a tolerance setting of 1e 4 or smaller to obtain fairly accurate results assuming that the le 6 curve is used as a reference The number of iterations required increases from the tolerance le 4 to tolerance le 6 by a factor of 4 while the total CPU time increases by a factor of 2 6 Looking at the greater tolerances le 3 and 0 01 we see that while the number of iterat
218. on data in the 1 1 0 direction because the applied field was acting in this direction We obtain this hysteresis loop 30 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 Stoner Wohlfarth M Ms 1000 500 0 500 1000 Applied field kA m The coercive field which is located somewhere between 165 and 170 kA m can now be compared with the analytically known result for this particular system To compute it we need the demagnetizing factors Nx Ny Nz of the particle along the main axes Since we deal with a prolate ellipsoid where two of the axes have the same dimension y and z in this case it is sufficient to compute the factor along the longest axis x axis The other two are easily derived from the relation Nx Ny Nz 1 The expression to compute Nx is N 1 m in 7 ym 1 1 z 1 m1 2 m2 1 where we call the length of the x semi axis a the length of the y or z semi axis c and take m to be the ratio m a c Here the value of Nx is therefore 0 1087 so we have Ny Nz 0 4456 With these values the shape anisotropy is easily computed according to the expression m ym 1 Ha Ms AN M Nz Nz This gives Ha 337 kA m in the case of Ms 1000 kA m The final step is to compute the coercive field hc using this analytical Stoner Wohlfarth result He he ca sin fo cos fo Here theta_0 is the angle between the easy axis of
219. on file will provide a sufficient amount of contextual information to clarify the physical meaning i e dimensions of numerical data We thus express the saturation magnetisation in Ampere per meter Ms SI 1le6 A m and the ex change coupling constant often called A in micromagnetism in Joules per meter exchange_coupling SI 13 0e 12 J m Note that these are not the true physical parameters of PermAlloy but have been chosen ad hoc for the sake of providing a simple example 2 1 4 Loading the mesh The next step is to load the mesh sim load_mesh spherel nmesh h5 sphere Py unit_length SI le 9 m The first argument is the file name sphere1 nmesh h5 The second argument is a list of tuples which describe the domains also called regions within the mesh In this example we have a one element list containing the 2 tuple sphere Py The left element of this pair sphere is a string of the user s choice and this is the name given to mesh region 1 i e the space occupied by all simplices that have the region id 1 in the mesh file This information is currently only used for debugging purposes such as when printing the simulation object The second part of the tuple is the MagMaterial object that has been created in Defining magnetic materials and bound to the variable Py This object determines the material properties of the material in this domain in this example we have specified the
220. on in this example can be manipulated as explained in the NumPy documentation because itis oftype numpy array Numpy provides a powerful matrix processing environment 2 21 Example Spin transfer torque Zhang Li model Nmag provides support for the Zhang Li extension to the Landau Lifshitz Gilbert LLG equation in order to model the interaction between a uniform electric current density and a spatially varying magnetisation The extened LLG equation reads aM a gt OM v yMxH M x nl Ma OF MB sat v Msat M x M x j VM Mxj VM where the first two terms on the right hand side are the normal LLG equation and the extra terms come from the Zhang Li model and M Simulation setm is the magnetisation H Simulation set H_ext is the effective magnetic field Msat Ms is the saturation magnetisation y 1lg_gamma_G is the gyromagnetic ratio a 11g damping is the damping parameter j V derivative along 3 the direction of the current The central column shows the method which can be used to set the field Simulation set_m or Simulation set_H_ext or the name of the corresponding parameter in the material definition for example mat MagMaterial Ms SI 0 8e6 A m The current density appears only throughout the quantity v which we define as P j uB e Mesat 1 gt yY with j Simulation set current density is the norm of the current density p llg polarisation is the degree of polarization
221. one E ext E_ext_Py E_ext_Co energy density of Py due to external field H_anis H_anis_Py H_anis_Co crystal anisotropy field E_anis E_anis_Py E_anis_Co crystal anisotropy energy density H_exch H_exch_Py H_exch_Co exchange field E_exch E_exch_Py E_exch_Co exchange energy H_demag H_demag demagnetisation field only one E_demag E_demag Py E demag_Co demagnetisation field energy density phi phi scalar potential for H_demag tho tho magnetic charge density div M H_total H_total_Py H_total_Co total effective field 3 4 3 Obtaining and setting subfield data Data contained in subfields can be written to files using save_data can be probed at particular points in space probe_subfield probe_subfield_siv or can be obtained from all sites simultaneously get_subfield Some data can also be set in particular the applied field H_ext using set_H_ext and all the subfields belonging to the field m using set_m 3 4 4 Primary and secondary fields There are two different types of fields in nmag primary and secondary fields Primary fields are those that the user can set arbitrarily Currently these are the normalised magnetisation m and the external field H_ext which can be modified with set_m and set_H_ext Secondary fields which could also be called dependent fields can not be set directly from the user but are com puted from the primary fields 124 Chapter 3 Background NMAG User Manual Documentation R
222. oop of an ellipsoidal magnetic object We use an ellipsoid whose x y z semi axes have lengths 30 nm 10 nm and 10 nm respectively The mesh is contained in ellipsoid nmesh h5 and produced with Netgen from ellipsoid geo 10 0 2999 x 9 9930 0 This picture has been obtained by converting the mesh to a v k file using nmeshpp vtk ellipsoid nmesh h5 mesh vtk and subsequent visualisation with MayaVi mayavi d mesh vtk m SurfaceMap We have further added the axes within MayaVi Visualize gt Modules gt Axes and changed the display color from blue to red Double click on SurfaceMap in the selected Modules list then uncheck the Scalar Coloring box click on Change Object Color and select a suitable color We provide the mayavi file mesh mv that shows the visulisation as in the figure above If you want to load this file into MayaVi just use mayavi mesh mv but make sure that mesh vtk is in the same directory as mayavi will need to read this 2 3 1 Hysteresis simulation script To compute the hysteresis loop for the ellipsoid we use the script ellipsoid py import nmag from nmag import SI at create simulation object 2 3 Example Simple hysteresis loop 25 NMAG User Manual Documentation Release 0 2 1 sim nmag Simulation define magnetic material Py nmag MagMaterial name Py Ms SI 1le6 A m exchange_coupling SI 13 0e 12 J m load mesh the mesh dimensions are scaled by 0
223. ositron_charge SI 1 6021765314e 19 c electron_charge positron_charge boltzmann_constant SI 1 3806504e 23 J K plank_constant 6 6260689633e 34 Joulexsecond reduced_plank_constant plank_constant 2 math pi To express the magnetisation in A m equivalent to the polaration of 1 Tesla we could thus use from nmag import si myM 1 5 si Tesla si mu0 The command reference for S provides some more details on the behaviour of SI objects 126 Chapter 3 Background NMAG User Manual Documentation Release 0 2 1 3 8 Terms 3 8 1 Stage Step iteration time etc We use the same terminology for hysteresis loops as OOMME stage step iteration time and extend this slightly step A step is the smallest possible change of the fields This corresponds usually to carrying out a time integration of the system over a small amount of time dt Step is an integer starting from 0 If we minimise energy rather than computing the time development exactly then a step may not necessarily refer to progressing the simulation through real time iteration Another term for Step deprecated stage An integer to identify all the calculations carried out at one constant applied magnetic field as in OOMMEF time The time that has been simulated typically of the order of pico or nanoseconds id This is an integer starting from 0 that uniquely identifies saved data 7 e whenever data is saved this number will increase
224. ou could in principle convert any data into the nmesh hdf5 format but it is expected that it is easier to convert the mesh into a nmesh ascii file and then use nmeshpp with option convert to convert the mesh fram nmesh ascii to nmesh hdf5 We describe the structure of the ascii nmesh file format using the following example Amesh file fora sphere with radius 1 with Netgen and this geometry file sphere geo The mesh file looks as follows PYFEM mesh file version 1 0 dim 3 nodes 79 simplices 174 surfaces 148 periodic 0 79 0 000000000000 0 000000000000 0 000000000000 1 000000000000 0 000000000000 0 000000000000 0 911922000000 0 410365000000 0 000000000000 0 941662000000 0 159249000000 0 296499000000 lt snip gt 0 038305000000 0 552912000000 0 107777000000 0 533150000000 0 052091000000 0 084880000000 174 58 0 62 78 33 78 36 50 19 77 0 17 1 67 75 78 72 lt snip gt 58 0 53 62 77 51 32 39 78 67 63 72 78 49 63 50 148 L 1 45 51 59 I I 5 12 13 La 25 37 39 lt snip gt L 1 19 30 34 LoL 42 44 54 l 1 32 45 51 We have removed a significant number of lines for the purpose of abbreviation in the places marked with lt snip gt We discuss the different parts of this file in more detail e The file starts with two lines starting with The first line contains a file format version string which needs to have exactly this form The second line contains a summary of the data i e 150
225. ould untar the HLib tarball it should patch it HLib needs to be patched in order to be usable by Nmag and it should install it in the right location with respect to the Nmag libraries If all goes well you should get an installation of Nmag which is capable of using HLib for the compression of the BEM matrix As you see the only additional step which is required with respect to the normal procedure for compiling Nmag from source is to put the HLib tarball inside the directory nnag 0 1 hlib pkg The current nmag release requires Hlib version 1 3p19 to support HLib matrix compression 2 24 3 Testing the HLib BEM Matrix compression There is a test target make checkhlib which tests whether a demag field can be computed using the HLib and compares this with the result of the same calculation using a full BEM If the deviations become large the test will fail To run the test do me mymachine nmag 0 1 make checkhlib The test should take less than 5 minutes If it passes then it appears that the hlib is used and produces quantita tively appropriate approximations of the true solution 2 24 Compression of the Boundary Element Matrix using HLib 97 NMAG User Manual Documentation Release 0 2 1 2 24 4 Using HLib example 1 Demagnetisation Field of a Sphere The properties of a hierarchical matrix depend much on the settings of different parameters and on the particular algorithm used to create the low rank approximations In N
226. ow to run a simulation given some parameters such as the initial magnetisation the damping the current density etc The function is defined starting with the line def run_simulation sim_name initial_m damping stopping_dm_dt j P 0 0 save do do_demag True The arguments of the function the names inside the parenthesis are those parameters which must be choosen differently in part I and part II For example we decided to make the current density j an argument for the function run_simulation because in part I j must be set to zero while in part II it must be set to some value greater than zero On the other hand the saturation magnetisation does not appear in the argument list of the function since it has the same value both in part I and part II A remark about the Python syntax arguments such as sim_name must be specified explicitly when using the function run_simulation while arguments such as P 0 have a default value 0 0 in this case and the user may omit them meaning that Python will then use the default values We skip the explanation of the body of the function and focus on the code which follows it We ll return later on the implementation of run_simulation For now the user should keep in mind that run_simulation just runs one distinct micromagnetic simulation every time it is called and what simulation this is will depend on the parameters given to the function The function returns the simulation object whic
227. p arxiv org abs arXiv 0907 1587 122 Chapter 3 Background NMAG User Manual Documentation Release 0 2 1 3 3 Fields and subfields 3 3 1 Field The Field is the central entity within the The nsim library It represents physical fields such as e magnetisation usually a 3d vector field e the magnetic exchange field usually a 3d vector field or e magnetic exchange energy a scalar field A field may contain degrees of freedom of different type which belong to different parts of a simulated object For example the magnetisation field may contain the effective magnetisation density for more than one type of magnetic atoms which may make up different parts of the object studied In order to deal with this we introduce the concept of Subfields A Nmag nsim field can be regarded as a collection of subfields Most often there only is one subfield in a field but when it makes sense to group together multiple conceptually independent fields such as the effective magnetisation of the iron atoms in a multilayer structure and that of some other magnetic metal also present in the structure a field may contain more than one subfield In particular the magnetisation field M may contain subfields M_Fe and M_Co The question what subfields to group together is partly a question of design For Nmag the relevant choices have been made by the Nmag developers so the user should not have to worry about this 3 3 2 Subfield Each field
228. p 1 We could visualise the magnetisation and all other fields as described in Example Demag field in uniformly magnetised sphere and would obtain the same figures as shown in section Saving spatially resolved data In step 2 we probe the demag field at positions along a line going from 10 0 0 nm to 10 0 0 nm and then print the values This produces the following output x le 08 H_demag None x 9e 09 H_demag 329656 18892701436 131 69946810517845 197 13873034397167 x 8e 09 H_demag 329783 31649797881 68 617197264295427 140 00328871543459 x 7e 09 H_demag 329842 17628131888 183 37401011699876 163 01612229436262 x 6e 09 H_demag 329904 84956877632 133 62473797637142 74 090532749764847 x 5be 09 H_demag 329974 43178624194 85 517390832982983 13 956465964930704 x 4e 09 H_demag 330002 69224229571 64 187663119270084 30 832135394870004 x 3e 09 H_demag 330006 79488959321 25 479055440690821 61 958073893954818 x 2e 09 H_demag 330020 18327401817 11 70722487517595 58 143562276077219 x le 09 H_demag 330025 52325345919 5 7120648683347452 52 237341988696294 x 0 0 H_demag 330028 67095553532 25 707310077918752 46 346108473560378 x le 09 H_demag 330058 98559210222 37 699378078580203 41 167364094137213 x 2e 09 H_demag 330089 30022866925 49 691446079241658 35 988619714714041 x 3e 09 H_demag 330145 36618529289 63 8
229. probe import Fields from nmag import float_set First we probe the field in the required points handler Fields sys argv 1 field handler set_field_data m Py 0 xs float_set 150 0 145 0 15 0 12 5 15 0 20 0 50 0 angles float_set 0 20 2 math pi R R2 4 9 5 1 rs vs for x in xs for angle in angles r x R math cos angle R math sin angle rs append x R2 math cos angle R2 math sin angle vs append ocaml probe_field field m_Py r 0 1 Now we output the values to a VIK file grid pyvtk UnstructuredGrid rs data pyvtk PointData pyvtk Vectors vs v pyvtk VtkData grid data v tofile sys argv 2 8 17 Notes on using GMSH to create a family of related meshes If you want to create many meshes using Gmsh you may first generate a mesh manually Then you can create a Python script which uses this mesh as a template to quickly create a mesh for a different set of parameters Below is such a script which shows how to do so The mesh file geo has been enclosed between quotes and some 8 17 Notes on using GMSH to create a family of related meshes 171 NMAG User Manual Documentation Release 0 2 1 of the values for the points coordinates have been substituted with strings that the Python script substitutes with real values Note that we use Mesh CharacteristicLengthFactor 5 0 to control the discretisation of the mesh We also us
230. rovide the geometrical volume of the regions By convention the vacuum has volume 0 In this example the bar volume is meant to be 30x30x100 90000 The deviation from this due to limited numerical precision and of the order of le 10 The boundary points are the number of nodes located at the surface of the bar This number is important if using the hybrid finite element boundary element method to compute the demagnetisation field as the boundary element matrix size will be proportional to the square of the number of boundary points The size of the boundary element matrix is given as well see Memory requirements of boundary element matrix The periodic points are the number of points that have mirage images in the mesh There will always be zero periodic points and thus zero mirage images unless we are dealing with a periodic mesh see nmeshmirror and Example Spin waves in periodic system Finally we are given some information about the statistics of the edge lengths a0 in the mesh the average value the standard deviation the maximum and minimum value This is important as in micromagnetics the angle of the magnetisation must not vary strongly from one node to the next In practice the edge length a0 should therefore 158 Chapter 6 Executables NMAG User Manual Documentation Release 0 2 1 be significantly smaller than the exchange length see What size of the cells FD and tetrahedra FE should I choose 6 3 2 Memory r
231. rt nm SI le 9 m define nm as nanometre ps SI le 12 s define ps as picosecond m0_filename m0 h5 the file containing the equilibrium magnetisation A function which sets up the simulation with given name and damping def simulate_nanowire name None damping 0 5 permalloy MagMaterial Py Ms SI 0 86e6 A m 104 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 exchange_coupling SI 13e 12 J m lig_damping damping s Simulation name s load_mesh cylinder nmesh h5 nanopillar permalloy unit_length nm return s The file defines a few entities which are used in both the two parts of the simulations nm is just an abbreviation for nanometer and similarly ps is an abbreviation for picosecond mO_filename is the name of the file where the re laxed magnetisation will be saved in part I and loaded in part II Finally the function simulate_nanowire deals with the portion of the setup which is common to both part I and part II In particular it defines a new mate rial permalloy creates a new simulation object s load the mesh and associates to it the material permalloy Such setup procedure is very similar to what has been encountered so far in the manual the only element of nov elty is that here we do it inside a function and return the created simulation object as a result of the function The file defined here is not supposed to be run by itself but r
232. ry first node has index 0 e The next section contains the data for the surface elements The first line contains the number of surface elements 148 The next 148 lines contain each the following information The first two integers are the region identifiers between which the surface is sandwiched If there is no simplex on one side of the surface then the outside region identifier of 1 will be used It is possible to use other negative numbers to discern between different parts of the outer boundary This 1s occasionally important in nsim to specify Dirichlet and von Neumann boundary conditions along different parts of a boundary The following integers are the node ids of the nodes that define the surface In this example we have three nodes as the surface elements are triangles Note that this last section is only contained in the file to make the users life easier for say plotting of the mesh This section on surface elements can be omitted and nmesh will read and process the mesh even if the surface elements are not specified they can be computed from the node and simplex data provided in the other sections e The next section contains data about periodic points The first line again is the number of data lines to follow Each data line gives the node indices belonging to one set of points that are treated as copies of the same point Le Nmag will know that field degrees of freedom associated to points from such
233. s for this in detail We assume you downloaded the HLib tarball and the Nmag tarball in your home directory but any other subdirectory will work fine Then if you issue a 1s command you get something like me mymachine ls HLib 1 3p19 tar gz nmag 0 1l all tar gz You can now untar the nmag tarball and enter the newly created directory me mymachine tar xzvf nmag 0 1 all tar gz me mymachine cd nmag 0 1 Note that in this particular example we assume the Nmag version to be 0 1 For later versions you ll have to change the tarball name and the paths accordingly e g nmag X Y Z for version X Y Z Inside the directory nmag 0 1 there is a directory called hlib pkg and we need to copy or move the HLib tarball into this directory me mymachine nmag 0 1 cp HLib 1 3p19 tar gz hlib pkg You can now compile Nmag with HLib support in the usual way me mymachine nmag 0 1 make The build system should recognise that the hl ib pkg directory contains a tarball and should prompt you asking what to do me mymachine nmag 0 1 make bash patches hlib hlib untar sh hlib pkg HLib 1 3p19 tar gz amp amp rm f deps_hlib_patch amp amp make deps_hlib_install true It seems you want to compile Nmag with HLib support I ll need your confirmation in order to proceed I found hlib pkg HLib 1 3p19 tar gz Is this the HLib tarball you want to use yes no yes Type yes and ENTER The build system sh
234. s would be a list of three integers for example 0 1 0 to mirror the input mesh on the xz plane that limits the mesh in the y direction e newfile is the name of the ASCII file with the new periodic mesh e remove is an optional argument which takes the values O and 1 and removes the periodic points from the final mesh when is set to 1 The default value is 0 Calling orig nmesh the ASCII file of a 3D non periodic mesh an example of the use of nmeshmirror is the following where the mesh is mirrored along the positive x axis and the negative z axis nmeshmirror orig nmesh le 6 le 6 1 0 1 periodic nmesh resulting in a periodic mesh along the same axes 160 Chapter 6 Executables NMAG User Manual Documentation Release 0 2 1 6 4 2 nmeshsort The nmeshsort script sorts the nodes of a mesh along a given axis not recommended when using parmetis with multiple object meshes We expect this to be most relevant to developers The general usage is nmeshsort meshfile axis newfile where e meshfile is the original ASCII nmesh file e axis is the axis over which the sorting takes place e newfile is the name of the ASCII file with the new periodic mesh Calling orig nmesh the ASCII file of a 3D mesh an example of the use of nmeshsort is the following where the mesh is sorted along the z axis nmeshsort orig nmesh 2 sorted nmesh 6 5 nmeshimport The nmeshimport command can be used to read other mesh formats and write them int
235. se in the constructor of the PermAlloy material mat_Py As a result there will be no precession term in the equation of motion 8e 05 6e 05 4e 05 Magnetisation A m 2e 05 0 2e 10 4e 10 6e 10 8e 10 time s While the time development of the system happens at the same time scale as for the system with the precession term see Relaxing the system the computation of the system without the precession is significantly faster for this example we needed about 3500 iterations with the precession term and 1500 without it and the computation time scales similarly 24 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 Note that the dynamics shown here are of course artificial and only used to obtain a meta stable physical configuration more efficiently 2 2 7 Decreasing execution time Note that the execution time can generally be reduced significantly by decreasing the tolerances for the time integrator In short one has to use the set_params function after set_m has been called Decreasing the requested accuracy will of course make the simulation results less accurate but this is often acceptable An example of how to use the se _m function and detailed discussion of the micromagnetic example shown in this section for a variety of tolerance values is given in the section Example timestepper tolerances 2 3 Example Simple hysteresis loop This example computes the hysteresis l
236. set ylabel M z millions of A m Mz x 1400e3 cos pi 2 atan sinh x 252e 9 sqrt 30e 12 520e3 plot 220 280 1 5 1 5 14 ow l 0 lt 1e4 t row i Or N bar_mag_x dat u 1 le 9 4 le6 t nmag w lp 2 commf bar_mag_x txt u 1 1e 9 4 1e6 t oommf w lp 1 Mz x le 9 le6 ti analytical w 1 3 which generates the following plot showing good agreement of both systems 1 5 nmag gt oommf analytical M z millions of A m 220 230 240 250 260 270 280 x nm The plot shows also the known analytical solution Mz x Ms cos pi 2 atan sinh x x_wall sqrt A K1 The plot shows only a restricted region located at the center of the bar thus allowing an easier comparison between the three sets of data 52 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 2 11 Example Cubic Anisotropy In this example we will study the behaviour of a 10 x 10 x 10 nm iron cube with cubic_anisotropy in an external field 2 11 1 Cubic anisotropy simulation script import nmag from nmag import SI si Create the simulation object sim nmag Simulation Define the magnetic material data from OOMMF materials file Fe nmag MagMaterial name Fe Ms S1 1700e3 A m exchange_coupling SI 2le 12 J m anisotropy nmag cubic_anisotropy axisl 1l 0 0 axis2 0 1 0 K1 SI 48e3 J m 3 Load the mesh sim load_mesh cube nm
237. such a cell could be a cube of dimensions 3nm by 3nm by 3nm Let s assume we would like to simulate a sphere The following picture shows an approximation of the shape of the sphere by cubes This is the finite difference approach For clarity we have chosen rather large cubes to resolve the sphere in an actual simulation one would typically use a much smaller cell size in order to resolve geometry better On the other hand the finite element method typically subdivides space into many small tetrahedra The tetra hedra are sometimes referred to as the finite element mesh elements Typically the geometry of these tetrahedra does vary throughout the simulated region This allows to combine the tetrahedra to approximate complicated geometries Using tetrahedra the a discretised sphere looks like this 179 NMAG User Manual Documentation Release 0 2 1 The spherical shape is approximated better than with the finite differences The first step in setting up a micromagnetic simulation is to describe the geometry In the case of finite difference calculations it will depend on the package you use currently there is only OOMMF freely available how to tell the package what geometry you would like to use and how small your simulation cells should be In the case of finite element calculations you need to create a finite element mesh see Finite element mesh generation 11 2 What is better finite differences or finite e
238. t use the step as a unique identifier last_step_dt is the length of the last time step carried out by the timestepper This is a useful indicator to learn about the stiffness of the system the time step is adjusted automatically to achieve a certain accuracy and thus the size of the time step reflects how hard it is to integrate the equations of motion The fields starting with E_total_Py down to H_exch_Py_ 2 are all nsim subfields see fields and the data stored for these are spatially averaged numbers For example the subfield M_Py_0 is the x component of the Magnetisation of the material Py averaged over all the space where this material is defined The maxangle_m_Py is the maximum angle in degree of the change of the magnetisation from one node in the mesh to the next It is important that this number is small the equations on which the micromagnetic theory is based assume that the magnetisation changes slowly as a function of space In the discretised solvers this applies to nmag as it applies to OOMMF Magpar and other codes this means that the maximum angle between neighbouring sites should be kept small How small is good enough This is hard to say in general We provide some subjective guidance Values of 180 degrees or 180 degrees quite clearly indicate that the results of the calculations must not be trusted i e they are wrong Values around 90 degrees make the results highly questionable Values of below 30 degrees indi
239. terial Co to this region If there was a region 3 in the mesh file we would add a third list entry for example cylinder Co for a Co cylinder Note that at this stage of nmag the region name such as cubel cube2 etc are not used in the simulation apart from diagnostic purposes in progress messages Physically what happens in this system is that the magnetisation of the Cobalt cube aligns rather fast with the anisotropy direction and then slowly forces the magnetisation of the PermAlloy cube into the opposite direction through the action of the stray field to minimise total energy of the configuration The Initial magnetisation is taken to point in x direction As this is an unstable equilibrium direction for the mag netisation anisotropy of the Cobalt cube we slightly distort the initial magnetisation by adding a tiny component in z direction It is instructive to compare the Fields and Subfields for this particular example with the list of fields and subfields for a single material simulation In effect all the fields that are related to the properties of some particular magnetic component carry multiple subfields In particular there is only one H_ext field as the externally applied field is experienced in the same way by all materials but the Mx H energy density associated with H_ext has a dependency on the magnetic component through M so we have two subfields E_ext_Py and E_ext_Co in the field E_ext The situ
240. thampton We thank Thomas Schrefl Wyn Williams Michael Donahue Richard Boardman and Jiirgen Zimmermann for useful discussion that have supported the development of this tool Further acknowledgements go to the Magpar software and its main author Werner Scholz Magpar has provided a finite element implementation of micromagnetics that has proved very useful in the development of nmag Special thanks to Werner Scholz who has discussed various numerical problems with the nmag team in great depth We further thank the beta users for their helpful feedback in particular Michael Martens David Vokoun Niels Wiese Gabriel David Chaves O Flynn and David Gonzales at the very early stages of the project 183
241. the base name of the vtk file that is to be generated In this manual we use MayaVi as the visualisation tool for vtk files but there are others available see vk Starting MayaVi with the command mayavi d spherel 000000 vtk will load our simulation data Us ing the pull down menu Visualize gt Modules gt VelocityVector will then tell MayaVi to display the magnetisation vector field Likewise we can use Visualize gt Modules gt Axes to add a 3d coor dinate system to the visualization 2 1 Example Demag field in uniformly magnetised sphere 11 NMAG User Manual Documentation Release 0 2 1 9 96 The magnetisation is pointing in positive x direction because we initialised the magnetisation in this orientation by issuing the command sim set_m 1 0 0 The Configure Data button in the DataVizManager section of MayaVi s user interface allows to select e a vector field and e a scalar field which provide the data that is used for subsequent visualisation modules Above we have used the m_Py vector field The demagnetisation field should point in the opposite direction of the magnetisation However let s first create a colour coded plot of the scalar magnetic potential phi from which the demag field is computed by taking its negative gradient 12 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 9 93 2939 phi lt A gt 0 00328 0 00234 Y 00140 0 000458 0 000482 0
242. the cell size is reduced even further One should therefore treat the suggestions made above as advise on good practice but never solely rely on this Critical examination of the validity of simulation results is a fundamental part of any simulation work In summary it is vital to keep the maximum spin angle small to obtain accurate results One should always check the value of the spin angle in the data files One should also carry out a series of simulations where the spin angle is reduced from one simulation to the next while keeping all other parameters and the geometry the same This should reveal any changes in the results that depend on the discretisation length 11 3 1 Exchange length There is sometimes confusion about what equation should be used to compute the exchange length In this doc ument we refer to this equation for soft materials where the demagnetisation energy is driving domain wall formation e 24 No M2 11 3 What size of the cells FD and tetrahedra FE should choose 181 NMAG User Manual Documentation Release 0 2 1 and this equation for hard materials with uniaxial pinning where the crystal anisotropy governs domain wall lengths A 2 K If in doubt which of the two equations is the right one compute both 1 and l2 and choose the minimum length as the relevant exchange length for this system 11 3 2 Further reading Micheal Donahue and co workers have published a couple of papers o
243. the corresponding OOMMF curves as spheres together with nmag s results The Magpar curve which is not shown here follows the nmag data very closely 8e 05 D y o a 4e 05 Magnetisation A m 2e 05 time s Spatially resolved fields The command sim save_data fields all saves all fields into the file bar_dat h5 as explained the filename is composed of the name of the simulation here bar and the extension _dat h5 The code bar30_30_100 py above calls the save_data command every 10 iterations As every dt corresponds to 0 5 picoseconds the data hence is saved every 5 picoseconds We can confirm this by using the nmagpp command nmagpp idlist bar which produces the following output id stage step time fields Q gt 1 0 0 E_anis E_demag E_exch E_ext E_total H_anis H_demag phi 10 gt 1 312 5e 11 E_anis E_demag E_exch E_ext E_total H_anis H_demag phi 20 gt 1 495 le 10 E_anis E_demag E_exch E_ext E_total H_anis H_demag phi 30 gt L 603 5e 10 E_anis E_demag E_exch E_ext E_total H_anis H_demag phi 40 gt 1 678 2e 10 E_anis E_demag E_exch E_ext total H_anis H_demag phi 50 gt 1 726 5e 10 E_anis E_demag E_exch E_ext total H_anis H_demag phi 60 gt T 762 3e 10 E_anis E_demag E_exch E xt total H_anis H_demag phi The first column is a unique identifier id for a confi
244. the particle x axis in our case and the direction of the applied field Substituting theta_0 45 degrees in the formula we obtain hc 0 5 that is Hc 0 5 Ha 168 kA m As we have seen before the simulated hysteresis loop gives a value between 165 and 170 kA m which is in agreement with the analytical solution Note that this simulation is relatively slow due to a number of constraints to get good Stoner Wolfarth behaviour we need to describe the shape of the ellipsoid well and thus need a small edgelength when we generate the mesh We further need uniform behaviour of the magnetisation which limits the overall size of the ellipsoid A general property of micromagnetic simulations is that the associated differential equations get stiffer if the edge lengths or more generally distances between neighbouring degrees of freedom become smaller Stiffer systems of differential equations are harder to intergrate and thus take more time 2 4 Example Hysteresis loop for Stoner Wohlfarth particle 31 NMAG User Manual Documentation Release 0 2 1 2 5 Example Hysteresis loop for thin disk This example computes the hysteresis loop of a flat disc magnetised along a direction orthogonal to the main axis In comparison to the previous Example Hysteresis loop for Stoner Wohlfarth particle it demonstrates the use of a more complex sequence of applied fields We use a disc 20 nm thick and 200 nm in diameter for this example the mesh
245. the sphere The x component is approximately a third of the magnetisation and the y and z components are close to zero as would be expected for a perfectly round sphere We mention for completeness that most fields such as magnetisation exchange field anisotropy field etc are only defined within the region s occupied by magnetic material However there is a special function probe_H_demag_siv to probe the demagnetisation field anywhere in space Saving spatially resolved data The command sim save_data fields all will save full spatially resolved data on all fields see Fields and subfields for the current configuration into a file with name spherel_dat h5 It will also save the spatially averaged values as described in Saving averaged data Whenever the save_data function is called it will write the averaged field values into the Data files ndt file This name is by default based on the name of the simulation script but can be overridden with an optional argument to the Simulation constructor The data in this file are kept in some compressed binary format built on the hdf5 standard and can be extracted and converted later using the nmagpp tool For example we can extract the magnetisation field from this file with the command nmagpp dump spherel However here we are interested in creating a v k from the saved data file for visualisation We use nmagpp vtk spherel vtk spherel where spherel vtk is
246. ticular the file real space dat will be filled with the values of the y component of dm t x y Z along the selected lattice That will be a text file which can be inspected with a text editor and used within plotting programs such as Gnuplot e ft axes 0 1 specifies that the selected data should be Fourier transformed along the axis 0 time and 1 x space This can also be written as ft axes t x e ft out norm induces nmagprobe to compute the norm of the complex numbers coming from the Fourier transform These are the values which are finally saved to file ft out rec space dat specifies the output file for the Fourier transformed data The command creates two files real space dat containing the y component of the magnetisation variation as a function of time and space and rec space dat containing the Fourier transform of such a quantity To plot the data in the two files we use the Gnuplot script plot gnp set term png set pm3d map set out real space png set title y component of magnetisation variation set xlabel position in axis nm set ylabel time ps splot 0 0 001 0 001 real space dat u 2 1 1le 12 5 t set out rec space png set title Fourier transform set xlabel k 1 nm set ylabel omega GHz splot 0 0 1 7e 8 rec space dat u 2 1 2x pix1le9 5 t Here is the result after running the script with Gnuplot 2 26 Example
247. tion Class constructor information self name None phi_BEM None periodic_bc None do_demag True do_anisotropy_jacobian False temperature None thermal_delta_t None user_seed_T 0 timestepper_max_order 2 timestepper_krylov_max 300 ksp_tolerances adjust_tolerances False use_pvode True lam_debugfile None Parameters name string Name of the simulation object this is used e g for prefixing filenames created by nmag Default value is the name of the current script sans extension do_demag bool Pass False to disable the demagnetisation field do_anisotropy_jacobian bool Pass True to enable the inclusion of derivatives from the anisotropy into the Jacobian Complicated anisotropy terms may blow up memory re quirements for the Jacobian Default value is True temperature SI Object Simulated temperature unless equal to None stochastic thermal fluc tuations will be enabled Currently not supported since July 2008 thermal_delta_t SI Object Time step to use when stochastic thermal fluctuations are enabled Currently not supported since July 2008 timestepper_max_order int Maximum order for the time integrator we use the BDF method Default value is 2 timestepper_krylov_max int Maximum dimension of the Krylov subspace to be used in the time integrator Default recommended value is 300 ksp_tolerances dictionary Keys to this dictionary are DBC rtol DBC atol DBC dtol DBC ma
248. to 30 in order to help Gnuplot fit the curve Such fit on T gives the value 28 4293 this value corresponds to 0 0284293 ns when rescaled by the 10e12 factor used for the plotting and shows a difference starting from the 5th digit when compared to the analytical solution of 0 0284284 ns 2 17 Example 1D periodicity 2 17 1 Introduction periodic boundary conditions macro geometry Concerning the simulation of periodic magnetic structures there are a few somewhat subtle issues to be taken into account both with respect to the demagnetising and the exchange field The issue with the exchange field is that we may encounter situations where the magnetic material crosses the boundary of an elementary cell a periodic array of non touching spheres in a cubic lattice is fundamentally different from its complement a cubic lattice made of spherical holes insofar as that in the latter case it is impossible to do a simulation using periodic boundary conditions without identifying degrees of freedom that live on boundaries of the simulation cell Nmag can deal with this automatically provided the mesh file contains periodicity information i e data on how to identify nodes on exterior faces As for the demagnetising field the most important problem is that one cannot ignore the effect of the faraway boundaries of the system a 100 nm x 100 nm x 100 nm cell made of magnetic material in the center of a large three dimensional periodic array will e
249. tor For this reason we have the unique identifier id 8 10 How to generate a mesh with more than one region using GMSH To assign different material properties to different objects the mesher needs to assign different region number to different simplices of the mesh The manual shows how to do this for netgen see two_cubes geo file in example Example two different magnetic materials How does one define different regions using GMSH User Xu Shu Wuhan China kindly provides this solution Within GMSH one has to firstly add physical groups and choose the two detached volumes sepa rately to add them into different groups then choose edit to redefine the number of the two groups thus you can get two physical objects as you want 8 11 Can run more than one simulation in one directory If you want to run two or more simulations in the same directory then this is fine as well as long as they have different simulation names The simulation name is either the string given to the constructor of the simulation object or if no name is defined explicitly the name of the python file that contains the simulation script without the py extension See File names for data files for a detailed example for this Data and log files will all start with the simulation name followed by some specific appended string and specific file extensions It is thus safe to run simulations with different names in the same directory
250. two_cubes py we can analyse the results For example we can plot the magnetisation of the two materials against time 64 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 0 20 10 4e 10 6e 10 8e 10 e 09 1 2e 09 1 4e 09 t s The blue lines represent the soft permalloy and the black lines show the hard cobalt Each thick line denotes the z component of the corresponding material This plot has been created with the following command ncol two_cubes 0 m_Co_0 m_Co_1 m_Co_2 m_Py_0 m_Py_1 m_Py_2 xmgrace nxy We can further convert the field data into vtk files nmagpp vtk two_cubes vtk two_cubes_dat h5 and visualise their content We start with the initial configuration Permalloy in blue on the left Cobalt in black on the right only 10 percent of the actual magnetisation vectors on the mesh nodes are shown to improve the readability of the plots Time T 0 ps Time T 1e 10s 0 1ns Cobalt is already pointing up i e in the direction of the anisotropy axis while Permalloy has just started to rotate 2 15 Example two different magnetic materials 65 NMAG User Manual Documentation Release 0 2 1 Time T 0 3ns Cobalt has reached its final configuration pointing up and Permalloy is still rotating but already pointing down to minimise the interaction energy between the cubes to the demagnetisation stray fields 16 0 Time T 1 ns The final configuration has bee
251. uation where the step counter may not have changed from the last saved configuration is if the user is modifying the magnetisation or external field manually otherwise the call of the time integrator to advance or relax the system will automati cally increase the step counter 4 2 16 set_m Module nmag Object Simulation set_m Arguments self values subfieldname None Parameters values vector list function or numpy array The values to be set See more detailed expla nation below This method sets the normalised magnetisation 1 e the m field to a particular value or pattern It can be used in three different ways 1 Providing a constant vector If given a vector this function sets the m field to uniformly point in the given direction everywhere For example to have the magnetisation point in x direction we could call the function like this sim set_m 1 0 0 To point in a 45 degree direction between the x and y axis we could use sim set_m 1 1 0 The magnetisation will automatically be normalised 140 Chapter 4 Command reference NMAG User Manual Documentation Release 0 2 1 2 Providing a function If the magnetisation is meant to vary spatially then a function can be given to the set_m method as in this example def my_magnetisation x y zZ get access to pi cos and sin import math change angle of Mx and My by 10 degree when x varies by inm angle xx 1e9 x 10 360x2 mat
252. ulation What to do in case of convergence problems How to visualise the difference between two fields defined over the same mesh How to re sample data from a saved h5 file Notes on using GMSH to create a family of related meshes 8 1 What is the difference between the OOMMF and nmag ap proach There are several aspects One important point is the calculation of the demagnetisation field as this is a computa tionally very expensive step OOMME is based on discretising space into small cuboids often called finite differences One advantage of this method is that the demag field can be computed very efficiently via fast Fourier transformation techniques One disadvantage is that this methods works less well i e less accurately if the geometry shape does not align with a cartesian grid as the boundary then is represented as a staircase pattern nmag s finite elements discretise space into many small tetrahedra The corresponding approach towards the com putation of the demagnetisation field which is the same as Magpar s method is based on the Fredkin and Koehler Hybrid Finite Element Boundary Element method The advantage of this method over OOMMP s approach is that curved and spherical geometries can be spatially resolved much more accurately However this method of calculating the demagnetisation field is less efficient than OOMMP s approach for thin films In particular mem ory requirements for the boundary element met
253. ulation script import nmag from nmag import SI every at from numpy import array import math Create simulation object no demag field sim nmag Simulation do_demag False Define magnetic material data from OOMMF materials file Co nmag MagMaterial name Co Ms SI 1400e3 A m 2 10 Example Uniaxial anisotropy 49 NMAG User Manual Documentation Release 0 2 1 exchange_coupling SI 30e 12 J m anisotropy nmag uniaxial_anisotropy axis 0 0 1 K1 SI 520e3 J m 3 Load the mesh sim load_mesh bar nmesh h5 bar Co unit_length SI le 9 m Our bar is subdivided into 3 regions region A for x lt offset region B for x between offset and offset length region C for x gt offset length The magnetisation is defined over all the three regions but is pinned in region A and C offset 2e 9 m meters length 500e 9 m Set initial magnetisation def sample_m0 x y 2 relative position goes linearly from 1 to 1 in region B relative_position 2x x offset length 1 mz min 1 0 max 1 0 relative_position return 0 math sqrt 1 mzxmz mz sim set_m sample_m0 Pin magnetisation outside region B def sample_pinning x Y Z return x gt offset and x lt offset length sim set_pinning sample_pinning Save the magnetisation along the x axis def save_magnetisation_along_x sim f open bar_mag_x dat w for
254. uld therefore be written as probe_H_demag_siv 0 0 1 pos_unit SI le 9 m epsilon float This parameter is used internally to compute the demag field via central differ ences from the magnetic potential if the observer point is in the exterior vacuum region It is the distance between the two points at which each of the field components is being computed because the field is the negative gradient of the potential The default value of le 7 should be sensible if normal simulation units are used i e the mesh was provided with coordinates in the range 1 1000 Typically this parameter should be ignored Note that this number is measured in simulation units Returns A list of floats containing the demag field in SI units i e A m at the specified position 4 2 10 hysteresis Module nmag Object Simulation hysteresis Arguments 4 2 Simulation 135 NMAG User Manual Documentation Release 0 2 1 self H_ext_list save averages fields at stage_end do convergence_check every step 5 This method executes a simulation where the applied field is set in sequence to the values specified in H_ext_list The time integration proceeds with the same applied field until convergence is reached At this point the field is changed to the next one in H_ext_list and the method reinitialise is called to proceed with the simulation The user can specify when to save data using the opt
255. umentation Release 0 2 1 10 sim save_data fields all else sim save_data if i In each iteration we first call sim advance_time i dt which instructs nmag to carry on time integration up to the time ixdt The call to save_data will save the average data into the bar_dat ndt file The last four lines contain an if statement which is used to save spatially resolved data every ten time steps only and averaged data every time step The percent operator computes i modulo 10 This will be 0 when i takes values 0 10 20 30 In this case we call sim save_data fields all which will save the spatial averages of all fields going into the bar_dat ndt file and the spatially resolved data for all fields that are saved to bar_dat h5 If i is not an integer multiple of 10 then the command sim save_data is called which only saves spatially averaged data 2 2 3 Analysing the data Time dependent averages We first plot the average magnetisation vector against time To see what data is available we call ncol with just the name of the simulation which here is bar ncol bar O time lt s gt 0 1 id lt gt E Za step lt gt 0 3 stage_time lt s gt 0 4 stage_step lt gt 0 5 stage lt gt 0 6 E_total_Py lt kg ms 2 gt 0 2603465789714 ws phi lt A gt 0 0002507410390772 8 E_ext_Py lt kg ms 2 gt 0 9 H_demag_0 lt A m gt 263661 6680783 10 H_demag_1
256. variety of ways Remember that all field values are shown in SI units by default see nmagpp and positions are as provided in the mesh file In this case positions are expressed in nanometers this comes from the unit_length SI 1e 9 m expression in the sim load_mesh command This is the initial configuration with magnetisation pointing in the 1 0 1 direction 30 0 The final configuration shows that the magnetisation aligns along the z direction The coloured surface shows the x component of the magnetisation and the colorbar provides the scale It can be seen that the magnetisation at position z 100 nm goes into a flower state to minimise the overall energy Note that strictly speaking this system is not yet in a meta stable state after 300 ps but already quite close 20 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 30 0 M_Py lt A m gt X component 2 15e 05 1 44e 05 7 20 04 311 7 14e 04 1 43e 05 2 15e 05 2 86e 05 Because we have saved all fields not just the magnetisation we can also study other properties For example the following image shows the demagnetisation field as vectors and the legend refers to the magnitude of the vectors as well as the magnetic scalar potential as a stack of isosurfaces Because the demagnetisation field is the negative gradient of the scalar potential the vectors are perpendicular on the isosurfaces 30 0 1080 0
257. where the parameter gamma called gyromagnetic ratio is taken to have the following value see ge Me 1 7588 x 10 T 1s 1 Y so that f_Larmor 35 176 GHz and the period T 1 f_Larmor 0 0284284 ns We save the average magnetisation every 0 1 ps in order to have a sufficient number of points to compute the period T We execute the script as usual nsim larmor py and extract the spatially averaged magnetisation data for all save time steps ncol larmor time m_Py_0 m_Py_1 m_Py_2 gt data txt Using Gnuplot we extract the value of the Larmor period T from the x component of the magnetisation gnuplot and the following command plots the x component of the magnetisation as a function of the simulation time together with a fit for a function f x where x represents time gnuplot gt f x Axsin 2xpix x B C D gnuplot gt B 30 gnuplot gt fit f x data txt u 1 le 12 2 via A B C D gnuplot gt plot data txt u 1 1e 12 2 f x The result is the following image 2 See the OOMMF manual and in Werner Scholz thesis after 3 7 llg_gamma_G 2 210173e5 m As 68 Chapter 2 Guided Tour NMAG User Manual Documentation Release 0 2 1 data txt u 1 1e 12 2 f x o N x component of normalised magnetisation 1 1 1 1 1 1 o 50 100 150 200 250 300 Simulation time The values for B in the fit which corresponds to the unknown period T is initially set
258. will be expressed in multiplies of this unit_quantity Returns float This is the number that multiplied by the unit_quantitity will provide the SI quan tity of the object itself 4 7 4 is_compatible_with Module nmag Object SI is_compatible_with Arguments self physical_quantity Returns True when the given physical quantity is compatible with the object itself Example gt gt gt from nsim si_units import SI gt gt gt m_per_sec SI 1 m SI 1 s gt gt gt km_per_hour S1I 1000 m SI 3600 s gt gt gt Newton SI 1 kg x xSI 1 m SI 1 s xx2 gt gt gt m_per_sec is_compatible_with Newton False gt gt gt m_per_sec is_compatible_with km_per_hour True 4 8 ipython Module nmag Object ipython Arguments globals None locals None Interactive python prompt see Example IPython 4 9 Command line options Nmag supports a number of command line options to configure its behaviour Suppose the simulation script is called X py then these OPTIONS can be specified like this nsim X py OPTIONS X py needs to contain at least the line import nmag as this will process the command line options The available options are 4 8 ipython 147 NMAG User Manual Documentation Release 0 2 1 clean to override any existing _dat h5 and _dat ndt files If this option is not provided and the data files exist already then nmag will interrupt the execution without having m
259. x gt offset length 502 nm of the bar note that the pinning function may also just return a python truth value rather than the number 0 0 or 1 0 def sample_pinning x Y Z return x gt offset and x lt offset length sim set_pinning sample_pinning Finally we relax the system to find the equilibrium magnetisation configuration which is saved to the file bar_mag_x dat in a format understandable by Gnuplot 2 10 2 Visualization We can then use the following Gnuplot script to visualize the equilibrium magnetisation set term png giant size 800 600 set out bar_mag_x png set xlabel x nm set ylabel M z millions of A m plot 0 504 1 5 1 5 144 E y 10 1 4t wl bar_mag_x dat u 1 le 9 0 4 1e6 t nmag w 1 2 The resulting plot clearly shows that a Bloch type domain wall has developed 1 5 M z millions of A m 0 5 1 5 o 100 200 300 400 500 x nm The figure shows also that the Bloch domain wall is well localized at the center of the bar in the region where x goes from 200 to 300 nm 2 10 Example Uniaxial anisotropy 51 NMAG User Manual Documentation Release 0 2 1 2 10 3 Comparison After simulating the same scenario with OOMMF see oommf bar mi f we can compare results using another Gnuplot script set term postscript enhanced eps color set term png giant size 800 600 set out bar_mag_x_compared png set xlabel x nm
260. xits NBC rtol NBC atol NBC dtol NBC maxits 4 2 Simulation 131 NMAG User Manual Documentation Release 0 2 1 Values are the petsc KSP solver tolerances for the Dirichlet and von Neumann Laplace solvers used internally to compute the magnetic scalar potential from magnetic charge den sity 4 2 1 advance time Module nmag Object Simulation advance_time Arguments self target_time max_it 1 exact_tstop None This method carries out the time integration of the Landau Lifshitz and Gilbert equation Parameters target_time SI Object The simulation will run until this time is reached If the target_time is zero this will simply update all fields max_it integer The maximum number of iterations steps to be carried out in this time inte gration call If set to 1 then there is no limit exact_tstop boolean When exact_tstop is True the time integration is advanced exactly up to the given target_time When False the time integration ends close to the target_time The latter option can result in better performance since the time integrator is free to choose time steps which are as wide as possible When exact_tstop is not given or is None the default value for this option will be used The default value can be set using the method set_params which should hence be used to control the behaviour of the hysteresis and relax methods 4 2 2 get_subfield Module nmag Object Simulation get_subfield Arguments
261. xle 9 position in metres H_exch_Py sim probe_subfield_siv H_exch_Py x 0 0 print x x H_exch_Py H_exch_Py Now modify the magnetisation at position 0 0 0 this happens to be node 0 in the mesh in steps 4 to 6 Step 4 request a vector with the magnetisation of all sites in the mesh 2 7 Example Manipulating magnetisation 41 NMAG User Manual Documentation Release 0 2 1 myM sim get_subfield m_Py Step 5 We modify the first entry myM 0 0 1 0 Step 6 Set the magnetisation to the new modified values sim set_m myM Step 7 saving the fields again so that we can later plot the demag and exchange field sim save_data fields all Step 8 sample demag field through sphere as step 2 for i in range 10 11 x ixle 9 position in metres H_demag sim probe_subfield_siv H_demag x 0 0 print x x H_demag H_demag Step 9 sample exchange field through sphere as step 3 for i in range 10 11 x ixle 9 position in metres H_exch_Py sim probe_subfield_siv H_exch_Py x 0 0 print x x H_exch_Py H_exch_Py To execute this script we have to give its name to the nsim executable for example on linux nsim sphere_manipulate py After having created the simulation object defined the material loaded the mesh set the initial magnetisation and the external field we save the data the first time Ste
262. xperience very different demagnetising fields depending on the shape of the outer boundaries of this array Assuming spatially constant magnetisation if these cells form a macroscopic tree dimensional sphere H_demag will be 1 3 M while for a flat box H_demag may be very close to M Nmag takes these macro geometry effects into account by allowing the user to provide a geometrical layout for a finite number say 100 1000 of cells that approximates the shape of the faraway outer boundary of the system The macro geometry approach is described in which may serve as a more detailed instruction to the concept 3 Hans Fangohr Giuliano Bordignon Matteo Franchin Andreas Knittel Peter A J de Groot Thomas Fischbacher A new approach to quasi periodic boundary conditions in micromagnetics the macro geometry Journal of Applied Physics 105 07D529 2009 Online at 2 17 Example 1D periodicity 69 NMAG User Manual Documentation Release 0 2 1 2 17 2 1d example In this example we simulate a single cell in the middle of a long one dimensional periodic array where for the purpose of computing the demagnetising field we take three extra copies of this cell to the left and three copies to the right along the x axis For real applications one would use more copies The only effect of additional copies are to increase the setup time needed to compute an internal boundary boundary interaction matrix The next Example 2D
263. y unit_length SI le 9 m Set initial magnetisation sim set_m 1 0 0 Activate interactive python session nmag ipython print Back in main code 2 8 Example IPython 45 NMAG User Manual Documentation Release 0 2 1 To execute this script we have to give its name to the nsim executable for example on linux nsim sphere_ipython py The new command appearing here is nmag ipython This calls an interactive python interpreter this is like the standard ipython interpreter called from the command prompt Once we are inside this ipython interpreter we can interactively work with the simulation object We demon strate this with the transcript of such a session nsim sphere_ipython py lt snip gt In 1 sim get_subfield H_demag Out 1 array 3 30028671e 05 2 57073101e 01 4 63461085e 01 3 30518650e 05 2 65364907e 01 2 12323921e 02 3 30380750e 05 1 34382835e 02 1 94635283e 01 3 30063839e 05 4 56312711e 01 1 31204248e 02 3 30056243e 05 3 23341645e 01 2 26732582e 02 3 29950815e 05 4 44150291e 01 5 41700794e 01 1 In 2 sim set_m 0 0 1 In 3 sim get_subfield H_demag array 6 86773473e 01 4 44496808e 01 3 30084368e 05 2 83792944e 02 1 78935681e 02 3 30268314e 05 2 04396266e 02 2 48374212e 02 3 30180923e 05 1 02055030e 02 9 53215211e 01 3 30239401e 05 1 94875407e 02 1 22757584e 02 3
264. ynamics is analysed by saving periodically the data the magnetisation the other fields and their averages Here we use two separate simulation scripts to carry out part I and part II subsequentely This is the approach that is easiest to understand Once the basic ideas have become clear it is often a good idea to write only one simulation script that carries out both part I and part II Indeed many of the parameters such as the saturation magnetisation or the exchange coupling need to be specified in each of the two scripts leading to possible errors for example if one decides to investigate a different material and changes the parameters just in one file and forgets the other etc In the next section Example Current driven magnetisation precession in nanopillars we present a more robust approach where both part I and part II are executed by just one script 2 21 2 Part 1 Relaxation The first script carries out a normal micromagnetic simulation i e no spin transfer torque and determines the relaxed magnetisation configuration for a given geometry material and initial configuration It saves the final magnetisation to disk Here is the full listing of relaxation py We model a bar 100 nm x 100 nm x 10 nm where a vortex sits in the center This is part I we just do a relaxation to obtain the shape of the vortex import math nmag from nmag import SI at from nsim si_units si import degrees_per_ns Define the material m
265. you may have to create it first with something like the_dir mydir import os if not os path exists the_dir os mkdir the_dir 8 13 How to check the convergence of a simulation How long it takes to run a simulation This depends very much on what you are simulating and under what conditions applied field current etc Sometimes however your simulation may not be ending as quickly as you expected and you may want to check what is happening It may be indeed that the simulation is not converging which means that it may actually never end One thing you can do in such a case is to take a look at the file _progress txt where stands for the simulation name given to the Simulation class when creating the simulation oject For example if you created your simulation object with a line such as s nmag Simulation one Then you may be looking for a file with name one_progress txt If you used simply s nmag Simulation and your file is named two py then you should look for a file with name two_progress txt This file contains statistics about the time integrator You ll first get the current time step number etc Then you ll get a list of rows each containing four columns such as 123 0 456 0 123 None Column 1 is the step reached an integer number which always increases The file shows convergence statistics for the last few steps it doesn t contain statistics for all the steps since this would make it quic

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