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NMAG User Manual (Incomplete DRAFT)

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1. 8e 09 H_exch_Py 1 1231714572170603e 08 0 0 0 0 9e 09 H_exch_Py 7 3643182171284044e 09 0 0 0 0 1e 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 demonstrate how the magnetisation can be modified and to see that this is reflected in the dependant fields such as demag and exchange immediately 2 7 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 nmag4 as nmag from nmag4 import SI create simulation object sim nmag Simulation define magnetic material Py nmag MagMaterial name Py Ms SI 1e6 A m 39 exchange_coupling SI 13 0e 12 J m load mesh sim load_mesh sphere1 nmesh h5 sphere Py unit_length SI 1e 9 m set initial magnetisation sim set_m 1 0 0 nmag ipython To execute this script we have to give its name to the nsim executable for example on linux user host user gt nsim sphere_ipython py The new command appearing here is nmag ipython in the last line This
2. 10 0 10 0 phi lt A gt 0 00328 0 00234 Y 00 140 0 000458 0 000482 0 00142 0 00236 0 00330 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 units of the potential phi are Ampere this is the lt A gt Unless the user specifies a particular request for the units of data the following rules apply for vtk files e position are given in the same coordinates as the mesh coordinates that is why 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 10 H_demag lt A m gt 3 33e 05 9 93 2 86e 05 19 0 2 38e 05 10 8 1 90e 05 1 43e 05 9 52e 04 2939 4 76e 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 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 colorbar on the left refers to the magnitude of the demagnetisation field which is expressed in Ampere per metre as can be seen from the label lt A m gt 2 2 Example 2 Computing the time development of a system This example computes the time development of the magnetisation in a bar with dimensions 30nm in the x and y
3. By providing the h5 extension we write a compressed mesh file which is significantly smaller than an ascii file see mesh file size The generated mesh is shown here hs We can examine the mesh using nmeshpp to find out about the mesh quality the statistical distribution of edge lengths and the overall number of points and elements etc 2 2 2 The simulation Having obtained the mesh file bar30_30_100 nmesh h5 we can use the following program with name 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 1llg_damping SI 0 5 sim nmag Simulation bar sim load_mesh bar30_30_100 nmesh h5 Py mat_Py unit_length SI 1e 9 m sim set_m 1 0 1 dt SI 5e 12 s for i in range O 61 12 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 otherwise just save averages As in Example demag field in uniformly magnetised sphere we import nmag and create the the material object import nmag from nmag import SI mat_Py nmag MagMaterial name Py Ms S1 0 86e6 A m exchange_coupling SI 13 0e 12 J m 1lg_damping SI 0 5 We set the 1lg_damping parameter to 0 5 To be consistent with the other input parameters for the materia
4. 4 2 3 get_subfield_positions Module nmag Object Simulation get_subfield_positions Arguments self subfieldname pos_units SI 1 m 1 This function provides the positions of the sites for data obtained with get_subfield Parameters subfieldname string The name of the subfield for example m_Py or H_demag pos_units SI Object How should the positions be expressed Default is SI 1 m The default means that the site positions are expressed in metres If you would like to see them in simulation units then use ST 1 If you would like to see node positions in nano meters then use SI 1e 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 Arguments 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 integer 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 probe_subfield Module nmag Object Simulation probe_subfield Arguments self subfieldname pos unit None for a given subfield name and position SI obje
5. set ylabel M Ms plot 0 2e3 0 2e3 1 2 1 2 nmag dat u 2 1000 3 ti nmag w lp 3 mag par dat u 3 4 ti magpar w lp 4 is shown here nmag x mag ar 3 DWASE HSE ENERGIES EEE E E Ea M Ms K FEHR HSE ESERIES SE NEHER AIA 200 150 100 50 0 50 100 150 200 Applied field A m Here we can see the different switching point between nmag and magpar probably due to different tolerances in the estimation of the convergence for the time integrator in the two cases 2 5 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 a flat the same geometry as in the Hysteresis loop for thin disk example cylinder 10 nm thick and 200 nm in diameter the mesh is contained in nanodot nmesh h5 29 Z 0 100 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 S1 795774 A m exchange_coupling SI 13 0e 12 J m load mesh the mesh dimensions are scaled by 100nm sim load_mesh nanodot_comparison nanodot 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_l
6. 1 0 01 0 500 0 600 42 0 22 0 600 0 700 364 1 95 0 700 0 800 2420 12 96 eR RRR 0 800 0 900 8252 44 20 FAC RRR OO K Kk kk kk kk kk kk kk 0 900 1 000 7592 40 66 FC KK AK KK kkk 6 4 3 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 interval counts probability 1 954 2 329 234 0 63 2 329 2 705 1424 3 81 xk 78 2 705 3 080 7921 21 17 FA kkk k kkk kkk kkk k kkk kkk 3 080 3 456 8790 23 50 FRR k k kkk kkk k kkk kkk kkk kkk 3 456 3 831 7573 20 24 CR RK kkk 3 831 4 207 5884 15 73 eR kkk kkk 4 207 4 582 3769 10 08 RRR RRR kkk kkk k 4 582 4 957 1385 3 70 4 957 5 333 365 0 98 5 333 5 708 63 0 17 average a0 lt a0 gt 3 543451 stand dev a0 lt a0 2 gt 0 581220 2 min and max 1 953689 5 708395 6 4 4 nmeshimport The nmeshimport tool can convert Netgen and Gambit neutral files into nmesh files Usage example assuming you have created a file mymesh neutral in Netgen and you would like to convert it to mymesh nmesh h5 you would use this command nmeshimport netgen mymesh neutral mymesh nmesh h5 7 Files and file names 7 1 mesh file nmesh nmesh h5 File that contain the finite element mesh See Nmesh file format 7 2 Simulation scripts py File that contains the simulation p
7. 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 very first node has index 0 e The next section contains the data for the surface elements The first line contains the number of surface elments 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 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 75 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 ommitted and nmesh will read and process the mesh even if the surface elements are not specified they can be computed from the nodes and simplices data in the other sections e The next section contains data about periodic points The first line contains the number of lines to follow The remaining lines refer to one set of identical points each I
8. 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 1v 1 which we need to express a physical quantity in this example 10 m s dimension Sl dimensions meters m seconds s Ampere A kilogramm kg Kelvin K Mol mol candela cd These can be obtaining using the units attribute of the SI object Sl number for a given physical entity a b where a is the numerical value and b are the dimensions this is just the numerical value and can be obtained with the value attribute of the SI object Simulation Units The dimensionless number that expressed an entity within the simulation core This is irrelevant to the user There are several reasons for using SI objects 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 parameters e The specification of units is more important when the micromagnetism is extended with other physical phenom ena moving towards multi physics calculations for which in principle the software cannot predict what units these will have 3 7 Terms 3 7 1 Stage Step iteration time We use the same terminology for hysteresis loops as OOMMEF stage step iteration time and extend this slightly step A step is the smallest possible
9. user host user gt gnuplot make_plot gnu which uses the script in make_plot gnu set term postscript enhanced color set out hysteresis ps set xlabel Applied field kA m set ylabel M Ms versor_x 0 707106781186548 versor_y 0 707106781186548 versor_z 0 0 scalar_prod x1 x2 x3 x1l versor_x x2 versor_y x3 versor_z magnit x1 x2 x3 sqrt x1 x1 x2 x2 x3 x3 plot 1050 1050 1 2 1 2 plot dat u scalar_prod 1 2 3 1000 scalar_prod 4 5 6 ti Stoner Wohlfahrt w lp 4 and provides the following hysteresis loop Stoner Wohlfahrt 8 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 an analytical solution of the problem To compute it we need the demagnetizing factors Nx Ny Nz of the particle along the main 24 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 and the other two are easily derived from the relation Nx Ny Nz 1 The expression to compute the Nx is the following eS e l m m m 1 2 m 1 2 m 1 3 m m 1 3 where calling a the length of the particle semi axis along the x direction and c the length of the semi axis along the y or z direction mis defined as m a c The value of Nx is therefore 0 108
10. we then plot the z component of magnetisation against time for all three temper atures 50 set term png giant size 800 600 set out thermal_mag_z png set xlabel t s set ylabel M z A m plot thermal_Ok_mag_z txt ti 0 K w 1 1 ther mal_4k_mag_z txt ti 4 K w 1 2 thermal_8k_mag_z txt ti 8 K wl 3 resulting in the following image 1 5e 06 T T T T T T T T T 1e 06 500000 M z A m 500000 1e 06 1 5e 06 o 1e 11 2e 11 3e 11 4e 11 5e 11 Ge 11 7e 11 8e 11 9e 11 1e 10 t s Clearly in the case of 4 K and 8 K thermal effects allowed to overcome the energy barrier introduced by anisotropy and hence to switch magnetisation to z direction the direction of the applied field We further note that larger noise amplitudes at 8 K resulted in reduced switching time as one would expect 2 12 Example Larmor precession This example shows how to derive the period of the Larmor precession for the magnetization and compare the result from simulation to the analytical solution In the file larmor py import nmag4 as nmag from nmag4 import SI every at create simulation object and switch off the computation of the demagnetiz ing field sim nmag Simulation do_demag False define magnetic material so that Js 1 T Py nmag MagMaterial name Py Ms S1 795774 71 A m exchange_coupling SI 13 0e 12 J m 51 llg_damping SI 0
11. x x H_demag H_demag Step 3 sample exchange field through sphere for i in range 10 11 x i 1e 9 position in metres H_exch_Py sim probe_subfield_f 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 Step 4 request a vector with the magnetisation of all sites in the mesh 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 for i in range 10 11 x ixle 9 position in metres H_demag sim probe_subfield_f H_demag x 0 0 print x x H_demag H_demag Step 9 sample exchange field through sphere for i in range 10 11 x i 1e 9 position in metres H_exch_Py sim probe_subfield_f 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 user host user gt nsim sphere_manipulate py Let us discuss the sphere_manipulate py script step by step After having created the simulation object defined the material loaded the mesh set the initial magnetisation and the external field we save
12. 0 load mesh sim load_mesh spherel nmesh h5 sphere Py unit_length SI 1e 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 1e6 SI A m s SI 1 s get SI dimensions for seconds let the magnetization precess around the direction of the applied field sim hysteresis Hs save averages every time 0 1e 12 s C fields every time 0 1e 12 s restart at time 300e 12 s we use a Sphere as the magnetic object and starting from a uniform magnetic configuration along the 1 1 1 direction apply a static field along the positive z axis These condition are defined with the lines sim set_m 1 1 1 and Hs nmag vector_set direction 0 0 1 norm_list 1 0 units 1e6 SI A m We set the magnetization evolution to be independent from the demagnetizing field and the damping term in the LLG equation with the lines sim nmag Simulation do_demag False and llg_damping SI 0 0 and to make the calculation easier the saturation magnetisation is chosen such that Js 1 T The dynamics of the magnetisation is driven only by the Zeeman effect with a torque on each of the magnetization dipoles m which is orthogonal to both M and H and makes the magnetization precess around the applied field direction The frequency of the precession called f_Larmor i
13. 0 995 0 990 0 1000 0 units 1e3 SI A m loop over the applied fields Hs sim hysteresis Hs save averages at convergence fields at convergence To execute this script we call the nsim executable for example on linux user host user gt nsim ellipsoid 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 as well as the external field 2 3 2 Hysteresis loop computation Assume wed like to apply magnetic fields with a strength of 1e6 A m down to 1e6 A m in the 110 direction i e 45 degrees between the x and the y axis in steps of 5e3 A m To convey this information efficiently to nmag we use 1 adirection for the applied field here just 1 1 0 2 a list of magnitudes of the field this is H_norms that will be multiplied with the direction vector 3 another multiplier that defines the strength of the applied fields here 1e3 SI A m Putting all this together we obtain this command Hs nmag vector_set direction 1 1 0 norm_list 1000 0 995 0 1000 0 995 0 990 0 1000 0 units 1e3 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 will
14. 001 m gt gt gt gt print a b lt SI 0 001 m2 gt gt gt gt print a b gt gt gt lt SI 1000 gt Note that this is dimensionless because we devided meters by meters 4 3 1 value Module nmag Object SI value Property 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 72 4 3 2 units Module nmag Object SI units Property information None Read only attribute to obtain units of Physical Object returned as list of pairs of dimension name and power 4 3 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 S1 10 m gt gt gt inch SI 2 54e 3 m gt gt gt d in_units_of inch 3937 0078740157478 Another example 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
15. 07 x nm 2 10 Example Cubic Anisotropy In this example we will study the relationship between the magnitude of an external field and the magnetisation of a 10 x 10 x 10 nm iron cube exhibiting cubic anisotropy 2 10 1 Cubit anisotropy simulation script import nmag from nmag import SI every at si from math import sin cos pi sqrt create simulation object sim nmag Simulation define magnetic material data from OOMMF materials file Fe nmag MagMaterial name Fe Ms S1 1700e3 A m exchange_coupling SI 21e 12 J m anisotropy nmag cubic_anisotropy axis1 1 0 0 axis2 0 1 0 K1i SI 48e3 J m load mesh sim load_mesh cube nmesh cube Fe unit_length SI 1e 9 m set initial magnetisation sim set_m 0 0 1 apply fields Hs nmag vector_set direction 1 0 0 0 0001 norm_list range 0 191 10 range 191 211 range 210 501 10 47 units 0 1 0 001 si T 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 S1I 1700e3 A m exchange_coupling SI 21e 12 J m anisotropy nmag cubic_anisotropy axis1 1 0 0 axis2 0 1 0 K1i SI 48e3 J m We the 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 a
16. 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 it s power Examples A v SI 10 m 1 s 1 is the code to create an SI object v that represents 10 m s 71 B B SI 0 6 kg 1 s 2 A 1 is the code to create an SI object T that represents 0 6 kg s 2 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 m s A m SI 1 m s SI 1 s A SI 1 A and then to use these SI objects to create more complex expressions v 10 m s B 0 6 kg s 2 A Of course short hand notations can be defined such as T kg s 2 A B 0 6 T 3 Finally there is another convenient but not generic as yet way The SI object knows about some typical units that are being used in magnetism such as A m N for Newton J for Joule and J m for Joule per metre This can be used such as f SI 100 N However be warned that at the moment there is just a list of hard coded strings that provide this functionality and that list is very short A very basic demonstration of the SI object in use gt gt gt a SI 1 m gt gt gt b SI 1e 3 m gt gt gt print atb lt SI 1
17. 250904652583e 15 13 dmdt_Py_1 lt A ms gt 2 333344983225e 16 14 dmdt_Py_2 lt A ms gt 8 250904652583e 15 15 H_anis_Py_0 lt A m gt 0 16 H_anis_Py_1 lt A m gt 0 17 H_anis_Py_2 lt A m gt 0 18 m_Py_0O lt gt 0 7071067811865 19 m_Py_1 lt gt 0 20 m_Py_2 lt gt 0 7071067811865 21 M_Py_0O 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 25 E_exch_Py lt kg ms 2 gt 5 046530179037e 17 26 rho lt A m 2 gt 0 03469702141876 27 H_ext_0O lt A m gt 0 28 H_ext_1 lt A m gt 0 29 H_ext_2 lt A m gt 0 30 H_total_Py_0 lt A m gt 263661 6680783 31 H_total_Py_1 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 14 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 number of the left row is e O for the time e 21 for M_Py_O 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 t
18. below a certain threshold Matteo XXXX what is this value and where do we set it 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 Lifschitz and Gilbert equation This is done when we define the Material in the following example 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 llg_damping S1 0 5 do_precession False sim nmag Simulation bar_relax2 sim load_mesh bar30_30_100 nmesh h5 Py mat_Py unit_length SI 1e 9 m sim set_m 1 0 1 s SI s get SI dimensions for seconds sim relax save averages every time 5e 12 s fields at convergence 2 The integrator here Sundials would have to do an extra step to get to the requested time and if the current time is close to the requested time it will simply report this value 20 The new command is do_precession False in the constructor of the Permalloy variable mat_Py As a result there will be no precession in the equation of motion 8e 05 E 6e 05 lt Cc 2 amp 4e 05 D e gt 2e 05 0 I l f f I 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 sys
19. calls an interactive python interpreter this is like the standard ipython interpreter called from the command prompt Once we are inside this interpreter we can interactively work with the simulation object We demonstrate this with the transcript of such a session user host user gt 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 In 2 sim set_m 0 0 1 In 3 sim get_subfield H_demag Out 3 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 29771010e 05 6 16259262e 01 1 66071597e 02 3 29848851e 05 mman Note that within ipython one can just press the TAB key to autocomplete object names funtions and commands You can leave the ipython enviroment by pressing CTRL D For the script shown here this will stop the execution 2 8 Example Pinning Magnetisation In this example we show how to pin i e fix magnetisation in certain parts
20. 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 alist of magnitudes of the field this is the norm_list that will be interpreted and then multiplied with the direction vector As in the Stoner Wohlfarth example the input provided here is interpreted For example the expression 1000 0 900 0 D 95 0 means that we start with a magnitude of 1000 the next magnitude is 900 The empty brackets 1 indicate that this sequence should be continued i e 800 700 600 500 400 300 200 100 until the next value given is reached 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 1 95 0 90 0 D 100 0 200 0 O 1000 0 900 0 95 0 90 0 D 100 0 200 0 1000 0 units 1e6 SI A m which computes a list of vectors Hs The hysteresis command takes this list of applied fields Hs as one input parame ter and will compute the hysteresis loop for these fields sim hysteresis Hs save averages at convergence fields at convergence 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 fi
21. field of 30 kA m m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 5 Magnetisation configuration for a decreasing applied field of 95 kA m 34 m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0 429 0 714 1 00 Figure 6 Magnetisation configuration for a decreasing applied field of 100 kA m position and it is eventually expelled when the magnetisation aligns with the field direction over all the disc 2 6 Example Manipulating magnetisation The basics of this file are as in Example Demag field in uniformly magnetised sphere a ferromagnetic sphere is stud ied and initially configured to have homogeneous magnetisation Here is the source code of sohere_manipulate py import nmag4 as nmag from nmag4 import SI create simulation object sim nmag Simulation define magnetic material Py nmag MagMaterial name Py Ms SI 1e6 A m exchange_coupling SI 13 0e 12 J m load mesh sim load_mesh sphere1l nmesh h5 sphere Py unit_length SI 1e 9 m set initial magnetisation sim set_m 1 0 0 set external field sim set_H_ext 0 0 0 SI 1 A m Save and display data in a variety of ways Step 1 save all fields spatially resolved 35 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_f H_demag x 0 0 print
22. 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 i e non material specific On the other hand anisotropy depends on the atomic species so this is HLanis_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 Data contained in subfields can be written to files using save_data can be probed at particular points in space get_subfield get_subfield_f_ or can be obtained from all sites simulatenously Some data can also be set in particular the applied field H_ext and all the subfields belonging to the field m 3 4 Mesh In finite element calculations we need a mesh to define the geometry of the system For development and debugging purposes nsim includes some 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 XXX T F Done up to here XXX 3 4 1 Node Roughly speaking a mesh consists of mesh nodes which are connected with their n
23. gt f x 0 M O M 1 M 2 tal ll simulate dt SI 1e 9 s for i in range 0 11 sim advance_time i dt save_magnetisation_along_x bar_mag_x_ 02ins txt i 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 Co material modelling cobalt exhibiting uniaxial anisotropy in z direction with phenomenological anisotropy constant K1 SI 520e3 J m73 Co nmag MagMaterial name Co Ms S1 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 z if x lt 2 return 0 0 1 if x gt 502 44 return 0 0 1 z 2 x 2 0 500 1 return 0 sqrt 1 z z z We further pin magnetisation at the very left and right of the bar pin lhs rhs magnetisation def sample_pinning x y z return x gt 2 and x lt 502 sim set_pinning sample_pinning Finally we compute the system s time development for 10 nanoseconds saving magnetisation spatially resolved along the x axis in a form
24. magnetisation in Ampere per metre Ms SI 1e6 A m and the exchange coupling constant often called A in micromagnetism in Joules per metre exchange_coupling SI 13 0e 12 J m 2 1 4 Loading the mesh The next step is to load the mesh sim load_mesh sphere1 nmesh h5 sphere Py unit_length SI 1e 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 list with one tuple sphere Py The first element of the tuple 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 properties of PermAlloy The third argument to load_mesh is an SI object which defines what real distance should be associated with the length 1 0 as given in the mesh file In this example the mesh has been created in nanometres i e the distance 1 0 in the mesh file should correspond to 1 nanometre in the real world We
25. 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 visualize it by showing an isosurface of the pinning field Shown as blue 9 96 10 0 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 coinciding with the 4nm sphere the shape of the blue region is not particularly spherical We further show 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 42 The next figure shows the same data is the last one but in addition a ScalarCutPlane in MayaVi terminology has been introduced which is coloured according to the x component of the magnetisation Red corresponds to 1 0 and blue corresponds to 0 73 we have not shown the legend
26. or numpy array See set_m for an explanation of possible values unit S Object An SI Object that is used as a multiplier for the values The units have to come down to Amper per metre We provide an example where the applied field is homogenous and always point in the x direction i e the y and z components are zero sim set_H_ext 1e6 0 0 SI 1 A m is equivalent to sim set_H_ext 1 0 0 SI 1e6 A m However we could also define the field in Oersted from nmag si import Oe sim set_H_ext 100 0 0 0e or in Tesla mu0 from nmag si import T mu0 sim set_H_ext 1 0 0 T mu0 4 2 13 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 3 Sl Module nmag Object SI Class constructor information self value dimensions Physical quantity in the SI units system This class allows to associate Sl dimensions such as metre kilograme Ampere seconds candela and mol with a floating point number The resulting object support addition which fails if the dimensions of the objects disagree multiplication and division Different ways of creating this SI objects
27. snip gt 1 58 0 53 62 1 77 51 32 39 1 78 67 63 72 1 78 49 63 50 148 A 45 51 59 17t 5 12 13 Ld 25 37 39 lt snip gt Lot 19 30 34 1 1 42 44 54 1 1 32 45 51 We have removed significant parts of the file where it says 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 version string which needs to be provided like this The second line contains a summary of the data i e dim the dimensionality of the space in which the mesh is defined usually 3 for 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 tetrahe dron surfaces the number of surface elements here 148 In 3d the surface elements are triangles periodic the number of points that are periodic e The next section contains the data for all the nodes The first line of this section contains again the total number of nodes 79 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 174 The next 174 lines contain the following information each
28. the nmagpp tool to access the data 7 5 File names for data files The filenames for the ndt and h5 data files are the 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 which starts 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 i e the simulation name will be mybar Let s assume for the remainder of the 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 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 name of the log file starts with the name of the simulation script without the py extension and ends with _log 1og For example a simulation script with name mybar py will have an associated log file with name mybar_log 1log Another three files will be created automat
29. thus use an SI object of 1nm 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 normalised magnetisation whereas the field M contains the magnetisation with its proper magnitude i e M is the saturation magnetisation whereas m 1 0 For this simulation we provide a unit vector pointing in the x direction to indicate that we would like the initial magnetisation to point in the positive x direction We could provide a vector with non normalised magnitude which would be normalised automatically This is convenient for say magnetisation pointing 45 degrees between x and y axis 1 1 0 2 1 6 Setting the external field We could set the external field using the set_H_ext command sim set_H_ext 0 0 0 SI A m In contrast to set_m this method takes two arguments The first defines numerical values for the direction and magnitude of the external field The second determines the meaning of these numerical values using an SI ob ject Suppose we would like an external field of 1e6 A m acting in the y direction then the 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 1e6 A m The default value for the external field is 0 0 0 A m so for this example we could have ommitted the set_H_ext command altogether 2 1 7 Extracting and saving data We have three different ways of ext
30. to compute the demagnetisation field as the boundary element matrix size will be proportional to the square of the number of boundary points 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 should therefore be significantly smaller than the exchange length 6 4 2 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 don t want the tetrahedra to be flat nmeshpp uses the ratio of the radius of the insphere the sphere that can just fit into a tetrahedron so that it touches the sides to radius of the cirumsphere the sphere defined by the 4 corners multiplied by the number of dimensions This numer is 1 0 for a perfect tetrahedran with identical edge lengths and 0 for a completely 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 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
31. 0 0 0 0 0 x 5e 09 H_exch_Py 1 6323042074911775e 09 0 0 0 0 x 4e 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 1e 09 H_exch_Py 3 0929969691649876e 09 0 0 0 0 x 0 0 Hiexch_Py 9 2633407053741312e 10 0 0 0 0 x 1e 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 1e 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 the is only one demag field that is experienced by all materials 2 6 1 Modifying the magnetisation In step 4 we use the get_subfield command This will return a numpy array that contains one 3d vec
32. 011463311 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 le 08 H_exch_Py None 9e 09 H_exch_Py 1 264324643856989e 09 0 0 0 0 8e 09 H_exch_Py 2 0419540595507732e 10 0 0 0 0 7e 09 H_exch_Py 1 4334754136843496e 09 0 0 0 0 6e 09 H_exch_Py 2 7214181426130964e 10 0 0 0 0 5e 09 H_exch_Py 1 6323042074911775e 09 0 0 0 0 4e 09 H_exch_Py 153858 81305452777 153858 81305452611 0 0 3e 09 H_exch_Py 972420 67935341748 972420 67935341166 0 0 2e 09 H_exch_Py 2445371 8369108676 2445371 8369108611 0 0 1e 09 H_exch_Py 5283169 701234119 5283169 7012341227 0 0 0 0 Hiexch_Py 15888993 991894867 15888993 991894867 0 0 1le 09 H_exch_Py 8434471 7912872285 8434471 7912872266 0 0 2e 09 H_exch_Py 979949 59067958547 979949 59067958279 0 0 3e 09 H_exch_Py 1112837 3087986181 1112837 3087986207 0 0 4e 09 H_exch_Py 193877 66176242317 193877 6617624248 0 0 5e 09 H_exch_Py 1 6602158583197139e 09 0 0 0 0 6e 09 H_exch_Py 1 8844573960991853e 09 0 0 0 0 i i S a E o S a O a S a S o A a S a S a R a S a S a R o S a M a a M a i 7e 09 H_exch_Py 6 2460015649740799e 09 0 0 0 0
33. 1 6e 09 1 8e 09 2e 09 time s where we notice that the final configuration is now with the magnetization aligned along the negative y axis and not along the x axis as before Understood why Because now the system has a total size of 300 09 nm 30nmx10copies plus spacings along the x direction times 400 39 nm 10nmx40copies plus spacings along the y direction times 10nm no periodic copies along the z direction so that now the longest side is along the y direction 2 15 Restart example To be written 2 16 Timestepper parameter example To be written 2 17 Periodic boundary conditions to be documented 2 18 Parallel execution to be documented 59 3 Background In this section we list some background information on the simulation package some explanation of the philosophy behind it which may explain some of the user interface choices that have been made and explanation of some terms that are relevant 3 1 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 3 2 Fields and subfields 3 2 1 Field The Field is the central entity within nsim 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 scala
34. 29 14 090609104026118 6e 09 H_demag 330380 1392610991 115 83746059068679 37 072085708324757 7e 09 H_demag 330418 85831447819 122 47512022500726 62 379121138009992 8e 09 H_demag 330476 40747455234 110 84257225592108 108 06217226524763 9e 09 H_demag 330500 20126762061 68 175725285038382 162 46166752217249 1e 08 H_demag 330517 86675206106 24 351273685146875 214 40344001233677 Ca a a a i i a a S a S a R a D a S a R o S a M a a a a iT At position 1e 8 there is no field defined this is just outside the mesh and therefore the value None is returned We can see how the demagnetisation field varies slightly throughout 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 occupied by the magnetisation However there is a special function to probe the demag netisation field anywhere in space XXX to be documented Ticket 19 2 1 7 3 Saving spatially resolved data The command sim save_data fields all will save all fields see Fields and subfields spatially resolved for the current configuration into a file with name sphere1_dat h5 It will also save the spatially average values as described in Saving averaged data Whenev
35. 6618529289 63 819285767062581 22 213920341440794 4e 09 H_demag 330220 13307247689 76 54950394725968 5 0509172407556262 5e 09 H_demag 330298 69089200837 90 534514175273259 13 57279800234617 6e 09 H_demag 330375 34327985492 117 01128011426778 35 262477275758371 7e 09 H_demag 330415 38940687838 123 68558207391983 60 580352625726341 8e 09 H_demag 330474 37719032855 112 22952205433305 106 13032196062491 9e 09 H_demag 330499 64039893239 69 97070465326442 160 41688110297264 1e 08 H_demag 330518 649930441 26 536490670368085 212 32392103651733 The data is approximately 1 3 Ms 333333 in the direction of the magnetisation and approximately zero in the other directions as we would expect in a homogenously 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 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 ra a S a D o O e A o S e E o S o E a i tal ll x 1e 08 H_exch_Py None x 9e 09 H_exch_Py 1 264324643856989e 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 1
36. 7 while the others are Ny Nz 0 4456 from the equation Nx Ny Nz 1 With these values the shape anisotropy is easily computed according to the expression H a A a AN A il g Nz Nx which gives Ha 337 kA m in the case of Ms 1000 kA m The final step is to compute the coercive field hc using the following analytical result Stoner Wohlfahrt model He he s n Oo COS bo a where theta_0 is the angle between the easy axis of 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 2 4 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 Stoner Wohlfarth example it shows use a more complex sequence of applied fields We use a disc 10 nm thick and 200 nm in diameter for this example the mesh is contained in nanodot nmesh h5 which is created from nanodot1 geo with Netgen 25 Z 0 100 1 00 1 00 To compute the hysteresis loop for the disc we use the following script nanodot1 py import nmag from nmag import SI at create simulation object sim nmag Simulation define magnetic material Py nmag M
37. 8540342884 532 73877752122235 6e 09 H_demag 339506 72150998382 5316 1506383768137 969 36630578549921 5e 09 H_demag 344177 83909963415 8732 9787600552572 1610 433091871927 4e 09 H_demag 344725 75257842313 16708 164927667149 5224 2484897904633 3e 09 H_demag 337963 49070659198 24567 078937669514 3321 016613832679 2e 09 H_demag 321612 85117992124 30613 873989917105 1385 6383061516099 le 09 H_demag 298312 3363571504 41265 117003123923 636 60703829516081 0 0 H demag 273449 78240732534 52534 176864875568 2793 5027588779139 P PA i bi bd bio bd bi pio bio P 38 1e 09 H_demag 293644 21931918303 39844 049389551074 4310 6449471266505 2e 09 H_demag 313838 65623104072 27153 921914226579 5827 7871353753881 3e 09 H_demag 330296 09687372146 21814 293451835449 5525 7290665358933 4e 09 H_demag 343611 94111195666 18185 932406317523 4931 5464761658959 5e 09 H_demag 348062 40814087034 11029 603829202088 3781 8263522408147 6e 09 H_demag 342272 36888512014 6604 210117819096 50 151907623841332 7e 09 H_demag 338716 66400897497 3860 7761876767272 485 90273674867018 8e 09 H_demag 335656 89887674141 2610 0345208853882 586 74812908870092 9e 09 H_demag 334985 59512328985 2169 9546280837162 542 76746044672041 1e 08 H_demag 334441 59096545313 1634 8337299563193 627 17874
38. Imagine now to introduce the periodic copies of the unit cell This time let us assume to put our unit cell on the 1 1 0 point of the lattice as shown in periodic2 py and let the system relax import nmag from nmag import SI import nsim sets as sets define magnetic material Py nmag MagMaterial name Py Ms SI 1e6 A m exchange_coupling S1I 13 0e 12 J m 57 lattice spacings along the main axes the value must be zero for no periodic copies larger than the body dimension otherwise x_lattice 30 01 the spacing is 0 01 y_lattice 10 01 the spacing is 0 01 z_lattice 0 0 list to store the lattice points where the periodic copies will be placed lattice_points for xi in range 4 6 for yi in range 19 21 lattice_points append xi x_lattice yi y_lattice 0 0 z_lattice copies of the system on the lattice points pbc nmag SetLatticePoints vectorlist lattice_points scalefactor SI 1e 9 m create simulation object sim nmag Simulation periodic_bc pbc structure load mesh sim load_mesh prism nmesh h5 repeated prism 2D Py unit_length SI 1e 9 m set initial magnetisation sim set_m 1 1 1 loop over the applied field s SI 1 s from nsim when import every at sim relax save averages every time 5e 12 s at convergence Jy fields every time 5e 12 s at convergence As in the previous example le
39. M Ms A TTEELCELETTETETELLELEETTELE 250 200 150 100 50 0 50 Applied field A m and we can see that the results from nsim match those from magpar The magnetization configuration during the switching process are shown in the following snapshots m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 1 Magnetisation configuration for a decreasing applied field of 20 kA m We see that during magnetisation reversal a vortex nucleates on the boundary of the disc when the field is sufficiently 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 32 SAN yen sata i eS te ieee rag ri sp SG e E ANNA PEE A Arae ES NS A PEERAA an m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 2 Magnetisation configuration for a decreasing applied field of 15 kA m m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 3 Magnetisation configuration for a decreasing applied field of 10 kA m 33 m_Py lt gt X component 1 00 0 714 0 429 0 143 0 143 0429 0 714 1 00 Figure 4 Magnetisation configuration for a decreasing applied
40. NMAG User Manual Incomplete DRAFT Author Hans Fangohr Author Thomas Fischbacher Author Matteo Franchin Author Giuliano Bordignon Author Michael Walter Author Jacek Generowicz Licence GNU General Public License GPL Version manual txt 4253 2007 10 04 12 03 44Z fangohr SVN Version 4249 4253 This document compiled 2007 10 04 at 12 58 Outline of document 1 Introduction 1 1 Ie 2 Guid 2 1 22 2 3 Nmag Philosophy How to read this document ed Tour Example Demag field in uniformly magnetised sphere 2 1 1 Importing nmag 2 1 2 Creating the simulation object 2 1 3 Defining magnetic materials 2 1 4 Loading the mesh 2 1 5 Setting the initial magnetisation 2 1 6 Setting the external field 2 1 7 Extracting and saving data 2 1 7 1 Saving averaged data 2 1 7 2 Extracting arbitrary data from the running programme 2 1 7 3 Saving spatially resolved data Example 2 Computing the time development of a system 2 2 1 Mesh generation 2 2 2 The simulation 2 2 3 Analysing the data 2 2 3 1 Time dependent averages 2 2 3 2 Spatially resolved fields 2 2 4 these are the basics 2 2 5 Relaxing the system 2 2 6 Relaxing the system faster Example Hysteresis loop for Stoner Wohlfarth particle 2 3 1 Hysteresis simulation script ining the hy eresis loop data p with Gnuplot o for thin disk 11 2 Simulating therr 2 11 3 Comparison of runs at different temperatures 2 12 Example Larmor pre
41. OSX or Windows http mayavi sourceforge net We have used MayaVi to display and study data from the vtk files for this manual Other tools are available for visualtion of vtk files see vtk 9 3 NumPy Numerical Python short numpy is an extension to Python that provides fast array operations and is designed for numerical work This Python extension and documentation can be found at http numpy scipy org 10 Acknowledgements This work has been financially supported by the Engineering and Physical Science Research Council EPSRC in the United Kingdom and by the University of Southampton We thank Thomas Schrefl Wyn Williams Werner Scholz and Michael Donahue for useful discussion that have helped the development of this tool 81 Generated on 2007 10 04 Generated by Docutils from reStructuredText source 82
42. agMaterial name Py Ms S1 795774 A m exchange_coupling SI 13 0e 12 J m load mesh the mesh dimensions are scaled by 100nm sim load_mesh example_hysteresis cylinderi 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 1 95 0 90 0 D 100 0 200 0 1000 0 900 0 95 0 90 0 D 100 0 200 0 1000 0 units 1e3 SI A m 26 loop over the applied fields Hs sim hysteresis Hs save averages at convergence C fields at convergence restart at convergence not working yet 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 We focus on the hysteresis command We d like to apply fields ranging from 1e6 0 0 A mto 100e3 0 O A min steps of 100e3 A m Then from 95e3 0 0 A mto 95e3 0 0 A mwe would like to use a smaller step 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 symmetric 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 1e6 0 0 A m At this point we would like to reverse the whole sequency to sweep the
43. agnetisation field is less efficient than OOMMF s approach for thin films In particular memory requirements for the boundary element method grow as the square of the number of surface points 8 2 Why do you have your own Python interpreter nsim Due to ability to run code in a distributed environment using MPI we cannot use the standard Python executable It so happens that by providing our own Python executable which is called nsim we have easier access to the low level library of nsim which is written in Objective Caml 9 Useful tools 9 1 vtk The Visualisation ToolKit vtk has this homepage 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 file 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 Vislt http www llnl 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 amazing Visualization Toolkit VTK for the graphics It provides a GUI written using Tkinter 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
44. ame 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 and because every dt corresponds to 0 5 pico seconds the data is saved every 5 pico seconds We can confirm this by using the nmagpp executable with this command nmagpp timesteplist bar which produces the following output Available time steps for field m are row time lt s gt step stage 0 0 0 1 1 5e 11 307 1 2 1e 10 562 1 3 1 5e 10 1002 1 4 2e 10 1471 1 5 2 5e 10 1584 1 6 3e 10 1668 1 The column row is simply a counter for the stored entries for this field We used to select which of the data to process further The time is shown in seconds lt s gt and we can see the 5 pico second interval between the different rows The step is the iteration counter for the calculation It can be used as a unique identifier of a time step in the run The stage is only relevant for calculations of hysterises curves see hysteresis example We convert the first saved time step into a vtk file bar_initial vtk using nmagpp range 0 vtk bar_initial vtk bar and we also convert the last saved time step at 300 pico seconds to avtk file with name bar_final vtk using nmagpp range 6 vtk bar_final vtk bar Using MayaVi we can display this data in a variety of ways Remember that all field values are shown in SI units by default see nmagpp and positions are as provided in the
45. at understandable by Gnuplot 2 9 2 Visualization We can then use Gnuplot to visualize magnetisation after 10 nanoseconds using the following script set term png giant size 800 600 set out bar_mag_x_10ns png set xlabel x nm set ylabel M z A m plot 0e 9 502e 9 1400e3 1400e3 bar_mag_x_10ns txt u 1 4 ti nmag w 1 2 The resulting plot clearly shows that a Bloch type domain wall has developed T T T T T 1e 06 500000 M z A m 500000 1e 06 ce 1e 07 2e 07 3e 07 4e 07 5e 07 x nm 2 9 3 Comparison After simulating the same scenario with OOMMF see example_uniaxial_anis oommf bar mif we can compare results using another Gnuplot script 45 set term png giant size 800 600 set out bar_mag_x_10ns_vs_oommf png set xlabel x nm set ylabel M z A m plot 0e 9 502e 9 1400e3 1400e3 bar_mag_x_10ns txt u 1 4 ti nmag w 1 2 oommf bar_mag_x txt u 1 4 ti oommf w 1 which generates the following plot showing good agreement of both systems T T T T T 1e 06 500000 M z A m 500000 1e 06 fe 1e 07 2e 07 3e 07 4e 07 5e 07 x nm We also remark that the nmag result almost perfectly matches the analytical solution given by cos atan sinh x x_wall sqrt A K1 pi 2 Ms 46 nmag analytical 1e 06 500000 M z A m 500000 1e 06 ce 1e 07 2e 07 3e 07 4e 07 Se
46. ation and used to progress the configuration of the system through time In principle this is all one needs to know to compute hysteresis loops and carry out the common micromagnetic calculations The following sections and subsequent examples introduce some higher level functions that make computing a hysterises loop easier and provide further functionality 2 2 5 Relaxing the system The relax command is a function of the simulation that takes the current magnetisation configuration and computes the time development until the torque on each mesh site is smaller than a certain threshhold This is useful for the example of our bar as in general we don t know for how long we need to integrate the system until it stops in a local energy minimum configuration Here is the source code changed to use the relax command import nmag4 as nmag from nmag4 import SI every at mat_Py nmag MagMaterial name Py Ms SI 0 86e6 A m exchange_coupling SI 13 0e 12 J m 1llg_damping SI 0 5 sim nmag Simulation bar_relax sim load_mesh bar30_30_100 nmesh h5 Py mat_Py unit_length SI 1e 9 m sim set_m 1 0 1 18 s SI 1 s get SI dimensions for seconds sim relax save averages every time 5e 12 s fields at convergence We ll explain the relax command sim relax save averages every time 50e 12 s fields at convergence in m
47. cession iple 1D periodicity 2D periodicity t example imestepper parameter example lic boundary conditions 2 18 Parallel execution 3 Background 3 1 The nsim library subfields 3 6 SI eeu 3 7 Terms 5 Finite eleme 5 1 Nmesh fi 5 3 Conversion of mesh files into nmesh format 6 Executables 6 1 ncol 6 3 nsim 6 4 nmeshpp 6 4 1 General information info 6 4 2 g the quality of a mesh 5 4 3 Histogram of edge lengths import 7 3 Data files ndt 7 4 Data files h5 7 5 File names for data files 7 6 File names for log files 8 Frequently asked questions 8 1 What s the difference between OOMMF and nmag 8 2 Why do you have your own Python interpreter nsim 9 Useful tools 9 1 vtk 9 2 MayaVi 9 3 NumPy 10 Acknowledgements 1 Introduction Nmag is a flexible finite element based micromagnetic simulation package with an user interface based on the Python programming language 1 1 Nmag Philosophy The majority of specialized simulation codes used in research today consists of a highly specialized core application which was written initially to simulate the behaviour of some very specific system Usually 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 scrip
48. change of the fields This corresponds usually to carrying out a time integration of the system over a small about of time at If we minimise energy rather than computing the time development exactly then this may not nec essarily refer to real time We use the Step in the simulation to uniquely identify time steps during the run of a whole simulation iteration another term for Step deprecated stage All the calculations carried out at one constant applied magnetic field are called stage time The time that has been simulated typically of the order of pico or nano seconds id This is an integer starting from 0 that uniquely identifies saved data Je whenever data is saved this number will increase by 1 It is available in the h5 and the ndt5 files and thus allows to match data in the ndt files with the corresponding spatially resolved field data in the _dat 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 62 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 local_time but in a more computer fri
49. ched 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 all1 is called for this purpose The user can provide his own function to save data For example the following two lines def my_fun sim sim save_data_table sim hysteresis save my_fun every 10 step are equivalent to sim hysteresis save averages every 10 step 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 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 e stage_time the simulation time passed from the beginning of the current stage e stage the number of the current stage e convergence a boolean value which is True if the convergence criterion is satisfied Use in this way at convergence Remember that you can combine time specifications using the operator or and amp and every 2 stage amp at convergence gt at convergence of odd stages every 10 step at convergence Examples are sim hysteresis save averages every 10 step fields at convergence If save
50. compute the hysteresis loop for these fields sim hysteresis Hs save averages at convergence fields at convergence The second parameter save 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 In the example shown here we request that the averages of the fields should be saved at the point in time where we reach convergence We also request that the spatially resolved fields should be saved at convergence 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 during Hs The value for stopping_dm_dt which is used as the convergence criterion see Timestepper parameter example 23 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 The ncol command allows us to extract the data and we redirect it to a text file with name nsim dat ncol ellipsoid time H_ext_O H_ext_1 H_ext_2 m_Py_O m_Py_1 m_Py_2 gt plot dat 2 3 4 Plotting the hysteresis loop with Gnuplot Instead of xmgrace which we have used in Time dependent averages for plotting other applications can be used Here we use Gnuplot
51. 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 13 Example 1D periodicity This example shows how to use the macro geometry feature to simulate an array of periodic copies of our system First of all the definition periodic here is not completely correct as the lattice where the periodic copies are placed is not infinite but has a limited size defined by the macro geometry To understand what this means let us assume 1 see OOMMF manual and in Werner Scholz s thesis after 3 7 llg_gamma_G 2 210173e5 m As 53 to have a cube 15x15x15 nm 3 If now we want to build a prism which is 105x15x15 nm 3 using the cube as the unit cell we need 7 periodic copies of the cube along the x axis We take the original one as the first one and copy it 3 times along the positive x axis and 3 along the negative x axis The way to do this operation in nsim is quite straightforward and it is shown in the script periodic1 py import nmag from nmag import SI define magnetic material Py nmag MagMaterial name Py Ms SI 1e6 A m exchange_coupling SI 13 0e 12 J m lattice spacings along the main axes the value must be zero for no periodic copies larger than the body dimension otherwise x_lattice 15 01 the spacing is 0 01 y_lattice 0 0 z_lattice 0 0 list to s
52. ct return data as SI object Note that get_subfield_f 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 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 66 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 fields a list of list of SI objects for rank 2 tensor fields etc 4 2 6 probe _H demag Module nmag Object Simulation probe_H_demag Arguments self pos pos_unit SI 1 m 1 epsilon 9 9999999999999995e 08 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 th
53. d 3438 surface elements 2d 4086 points 1 simplex regions 1 2 point regions 1 1 2 region volumes 0 0 89999 999999999782 1721 boundary points a0 average 3 543451 std 0 581220 min 1 953689 max 5 708395 77 Starting from the top of the output we are given the information that this is a three dimonsional 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 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 The region volumes provide 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 1e 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
54. d 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 optional 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 out 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 67 Parameters H_ext_list list of values for the applied field Itis something like H1 H2 H3 where Hi is the triple of components of the applied field i e Sl 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 rea
55. direction m If you specify a custom anisotropy function you also need to pass the anisotropy_order pa rameter Default value is None that is no anisotropy term is used anisotropy_order int Specifies the maximal degree of the polynomial approximation which is internally generated by nmag from the given custom anisotropy function Default value is None do_precession True or False Boolean that can switch the precessional term in the LLG equation off This is useful to improve convergence speed when studying metastable configurations Example and default value True 63 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 Ki lt axis m gt 2 K2 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 normalised K1 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 axis1 axis2 K1 K2 0 K3 0 Returns a predefined anisotropy modelling a cubic anisotropy energy density term E_anis Ki lt axisi m gt 2 lt axis2 m gt 2 lt axis1 m gt 2 lt axi
56. directions and 100nm in z direction 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 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 show 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 the finite elements Such a subdivision of space is known as a mesh or grid We use Netgen to create this mesh Netgen reads a geometry file which tells it what geometry to mesh To create the mesh used here start Netgen and load the geometry file by using the menu File gt Load Geometry 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 click on the Generate Mesh button to generate the mesh Finally using File gt Export save the mesh as a neutral file this is the default under the name bar30_30_100 neutral We provide a gzipped version of this file for completeness here 2 This neutral file needs to be converted into a nmesh file We do this using 11 nmeshimport netgen bar30_30_100 neutral bar30_30_100 nmesh h5
57. e 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 3 Fields and Subfields in Nmag 3 3 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 60 Field Subfield Comment 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 rho rho magnetic charge density div M H_total H_total_Py total effective field 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
58. e 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 purely for numerical reasons Parameters pos list of floats The SI numbers described the position in metres A command like probe_H_demag 0 0 1e9 would thus probe the demag field one nanometre 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 could therefore be written as probe_H_demag 0 0 1 pos_unit SI 1e 9 m epsilon float This parameter is used internally to compute the demag field via central differences from the magnetic potential It is the distance between the two points at which each of the field compo nents is being computed because the field is the negative gradient of the potential The default value of 1e 7 should be sensible if normal simulation units are used Typically this parameter should be ignored Note that this number is measured in simulation units Returns A numpy python array containing the demag field in SI units i e A m at the specified position 4 2 7 hysteresis Module nmag Object Simulation hysteresis Arguments self H_ext_list save averages fields at convergence True convergence_check eve gt step This method executes a simulation where the applie
59. e_data fields all else sim save_data In each iteration we first call sim advance_time i dt which instructs nmag to carry out the integration up to a 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 and are used to save the data The percent operator computes i modulo 10 This will be 0 when i takes values 0 10 20 30 i e every 10 iterations 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 saves only the spatially averaged data 2 2 3 Analysing the data 2 2 3 1 Time dependent averages First we will 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 gt ncol bar 0 time lt s gt 0 1 id lt gt 1 2 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 7 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 lt A m gt 8 218106743355 11 H_demag_2 lt A m gt 77027 641984 12 dmdt_Py_0 lt A ms gt 8
60. earest neighbours nmag uses an unstructured mesh i e nodes that connect to fill the ferromagnetic geometry with tetrahedra in three dimensions 3 4 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 4 3 node position Each node has of course a position in 3d space i e just a 3d vector that defines where the node is located 61 3 5 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 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 base function calculation we identify sites by a tuple of node id comment XXX Here a plot of first order and second order triangles would be useful 3 6 SI object We are using a special SI object to express physical entities see also Sl Let s first clarify some terminology
61. elds should be saved at the point in time where we reach convergence We also request that the spatially resolved fields should be saved at convergence We further request that restart data is saven at convergence see restart example 27 2 4 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 The ncol command allows us to extract the data and we redirect it to a text file with name plot dat ncol nanodoti H_ext_0 m_Py_O gt plot dat which saves the file plot dat which starts as following 1000000 0 9999551243645 950000 0 9999541970431 900000 0 9999531184538 850000 0 9999519886171 800000 0 999950827041 We use Gnuplot to plot the hysteresis loop user host user gt gnuplot make_plot gnu which uses the script in make_plot gnu set term postscript enhanced color set out nanodot_hyst ps set xlabel Applied field A m set ylabel M Ms plot 1 2e6 1 2e6 1 2 1 2 nmag dat u 2 3 ti nmag with linespoints lw 3 pt 5 The resulting graph is shown here nmag 0 5 M Ms 0 5 1e 06 500000 0 500000 1e 06 Applied field A m and the comparison with the magpar data obtained with the script make_comparison_plot gnu set term postscript enhanced color set out nanodot_hyst ps set xlabel Applied field A m 28
62. endly way for computing differences 3 7 2 Some geek talk deciphered nmag uses some object orientation in the high level user interface prensented 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 4 Command reference 4 1 MagMaterial Module nmag Object MagMaterial Class constructor information self name Ms 11g_damping exchange_coupling anisotropy None anisotropy_order Parameters name string The name of the material This will be used in the names of material dependent fields and subfields Example Py Ms SI Object The saturation magnetisation of the material in Ampere per metre Example and default value SI 0 86e6 A m Ilg_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 OOMMF is 0 5 Example and default value SI 0 5 exchange_coupling SI Object The coupling strength for the exchange interaction in Joule per metre Example and default value SI 1 3e 11 J m 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 function a m returning anisotropy energy density given the normalised magnetisation
63. er the save_data function is called it will write the averaged field values into the 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 in compressed binary format build on the hdf5 standard and can be extracted and converted later using the nmagpp tool For example we can dump the magnetisation field to stdout which is typically the screen using nmagpp dump spherel However here we are interested in creating a vtk file for visualisation purposes from the saved data We use nmagpp vtk spherei vtk spherel where sphere1 vtk is the name of the vtk file that is to be generated Once this is executed we can visualise the data For this manual we use MayaVi as the visualisation tool for vtk files but there are others avialable see vik We start MayaVi and load the vtk data file with mayavi d spherei vtk Using MayaVi s menus we can add a VelocityVector module to display the magnetisation 9 96 The magnetisation is pointing in the x direction because we initialised the magnetisation in this orientation by issuing the command sim set_m 1 0 0 The demagnetisation field should point in the opposite direction of the magnetisation Let s first create a colour coded plot of the scalar magnetic potential phi from which the demag field is computed by taking the negative gradient 9 93
64. et_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 y y z z lt 4e 9 4e 9 return 0 0 else return 1 0 The function receives a 3 tuple x y z containing the three floating point variables x y and z provide the position coordinates in metres for which 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 The formula in the if statement simply evaluates the Cartesian magnitude of the vector x y z by squaring each component This number is then compared against 4nm 2 As a result all the nodes i e corners of tetrahedra that are located within a sphere with radius 4nm are pinned and all nodes that are located outside this sohere can change as usual Second we need to tell nmag that it should use this function to decide where the magnetisation should be pinned 41 sim set_pinning pin_at_center Note the slightly counterintuitive fact that value 1 means no pinning Finally we apply an external field of half a Tesla in y direction and use relax to compute the equilibrium configuration 2 8 3 Visualisation After running the example via nsim sphere py we convert the equilibrium data to VTK format
65. etc fileversion Array 1L data file type version mesh 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 gt 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 tetrahedra 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 belows Regions are coded by integer values with 0 being vacuum and 1 the area outised 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 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 written by Netgen in its format The second line just shows the file size of the same file compressed with gzip The third line shows the size of the mesh stored as an Ascii nmesh while the last line shows 76 the size of the mesh stored as a Hdf5 nmesh file 5 3 Conver
66. f we have periodic boundary conditions then some points for example on the far left and on the far right are effectively representing the same physics For each set of these identical points we use one line and write their indices in this line 5 1 2 Hdf5 nmesh In addition to the Ascii nmesh format there is another binary and compressed way of storing nmesh meshes To do this we use a library called hdf5 which is often abbreviated as h5 We recommend that you use this fileformat to store your meshes as it is a binary and a compressed file format and thus much more space efficient You can convert ascii nmesh files into hdf5 nmesh files using the nmeshpp tool using convert or the nmeshimport tool by specifying the target name of the nmesh file to end in h5 We recommened to use the extension nmesh h5 but h5 is sufficient to trigger saving in hdf5 format If you need to manually convert mesh files into the nmesh format via code you have to write we suggest that you write the ascii nmesh format and then convert this ascii nmesh file to h5 files For completeness we outline the nmesh h5 file format here You may find the following description more useful after having familiarised yourself with hdf5 or pytables The nmesh h65 file contains the following nodes this is output from pytables s ptdump program RootGroup gt etc Group Configuration and version data etc filetype Array 1L data file type
67. g the relaxation curves for Mx My and Mz using only the unit cell assuming to have an initial uniform magnetisation along the 1 1 1 direction The script is no_periodic py import nmag from nmag import SI import nsim sets as sets define magnetic material Py nmag MagMaterial name Py Ms SI 1e6 A m exchange_coupling S1I 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 1le 9 m set initial magnetisation sim set_m 1 1 1 loop over the applied field s SI 1 s 56 from nsim when import every at sim relax save averages every time 5e 12 s at convergence fields every time 5e 12 s at convergence and the relaxation curves are obtained using the commands gnuplot gt gt set term postscript enhanced color gt gt set out no_periodic ps gt gt set xlabel time s gt gt set ylabel M Ms gt gt plot plot_no_periodic dat u 1 2 ti Mx w lp gt plot_no_periodic dat u 1 3 ti My w lp gt plot_no_periodic dat u 1 4 ti so here is the figure M Ms E Aa a oe REO O nn HOE OOOI BE IK x 0 5e 11 1e 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
68. gt gt km 1000 m gt gt gt h 3600 s gt gt gt print velocity in_units_of km h 8 2 Parameters unit_quantity SI Object The SI object itself i e self 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 quantity of the object itself 4 3 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 73 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 SI 1000 m SI 3600 s gt gt gt Newton SI 1 kg SI 1 m SI 1 s 2 gt gt gt m_per_sec is_compatible_with Newton False gt gt gt m_per_sec is_compatible_with km_per_hour True 5 Finite element mesh generation Finite element mesh generation is a difficult business and one needs to get used to using at least one mesh gener ating software to be able to create meshes for the geometries that you want 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
69. he position is specified in SI units and the data returned are also expressed in SI units The for loop in the programme which iterates x in the range from 10 1e 9 to 10 1e 9 in steps of 1e 9 produces the following output le 08 H demag None 9e 09 H_demag 329655 76203912671 130 62999726469423 194 84338557811344 8e 09 H_demag 329781 46587966662 66 963624669268853 137 47161381890737 7e 09 H_demag 329838 57852402801 181 46249265908259 160 61298054099865 6e 09 H_demag 329899 63327447395 131 06488858715838 71 383139326493094 5e 09 H_demag 329967 79622912291 82 209856975234786 16 893046828024836 4e 09 H_demag 329994 67306536058 61 622521557150371 34 433041910642359 3e 09 H_demag 329997 62759666931 23 222244635691535 65 991127111463769 2e 09 H_demag 330013 90370482224 10 11035370824321 61 358763616681067 1e 09 H_demag 330023 50844056415 6 9714476825652287 54 900260456937708 0 0 H_demag 330030 98847923806 26 808832466764223 48 465748009067141 1e 09 H_demag 330062 38479507214 38 660812022013424 42 83439139610747 2e 09 H_demag 330093 78111090627 50 512791577262625 37 2030347831478 3e 09 H_demag 330150 72580001026 64 552170478617398 23 120555702674721 4e 09 H_demag 330226 19050178828 77 236085707456397 5 5373829923226916 5e 09 H_demag 330304 59300913941 90 5844138218132
70. his 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 i 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 The recommended way therefore is to directly specify the name of the columns that are to be extracted i e time M_Py_O M_Py_1 M_Py_2 ncol bar time M_Py_O M_Py_1 M_Py_2 gt data_M txt We use xmgrace to plot this data by calling it with xmgrace nxy data_M txt adding the legend and axis labels and create this plot 8e 05 D 0 oO oO 4e 05 Magnetisation A m 2e 05 n f fi 0 1e 10 2e 10 3e 10 time s We have carried out the same simulation with Magpar and OOMMF The following plot shows 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 g 86405 lt Cc S 4e 05 3 D Cc D i 2e 05 time s 2 2 3 2 Spatially resolved fields The command sim save_data fields a11 saves all Fields into the file bar_dat h5 in general the filen
71. ically which 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 e mybar_nmag conf Some variables used in the nmag code 8 Frequently asked questions 8 1 What s the difference between OOMMF and nmag 8 2 Why do you have your own Python interpreter nsim 80 8 1 What s the difference between OOMMF and nmag There are several aspects We address the calculation of the demagnetisation field here as this is the computationally most demanding part of the calculation OOMMF 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 One disadvantage is that this methods works less well i e less accurately if the geometry shape does not align with a cartesian grid because the boundary is represented as a Staircase pattern nmag s finite element discretises space into many small tetrahedra The corresponding approach to computing 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 OOMMF s approach is that curved and spherical geometries can be spatially resolved much more accurately However this method of calculating the dem
72. initially aligned along its easy axis and given an applied field opposite to initial magnetisation 2 11 1 Thermal effects simulation script import nmag4 as nmag from nmag import SI si every at import sys parse temperature given as command line argument if len sys argv lt 2 raise Exception Usage nsim thermal py lt TEMPERATURE IN KELVIN gt temperature SI float sys argv 1 K create simulation object ps SI 1e 12 s sim nmag Simulation temperature temperature thermal_delta_t 0 0025 ps define magnetic material data from Kronmueller NdFeB nmag MagMaterial name NdFeB Ms 1 6 si T si mu0 exchange_coupling SI 7 3e 12 J m anisotropy nmag uniaxial_anisotropy axis 0 0 1 K1 SI 4 3e6 J m 3 K2 load mesh 49 sim load_mesh sphere1 nmesh h5 sphere NdFeB unit_length SI 1e 9 m set initial magnetisation to z direction sim set_m 0 0 1 apply external field in z direction H_n 8 79 si T si mu0d sim set_H_ext 0 H_n 0 H_n 1 H_n relax num_steps 100 for n in range 0 num_stepst 1 print Step i i n num_steps sim advance_time n ps if n 5 0 sim save_data fields all else sim save_data We will now discuss the thermal py example step by step 2 11 2 Simulating thermal effects nmag supports the simulation of thermal effects by adding a stochastically fluctuating field with proper variance This feature is enabled b
73. is not given averages will be saved whenever convergence is reached this is the default behaviour 4 2 8 load_mesh Module nmag Object Simulation 1load_mesh Arguments self filename region_names_and_mag_mats unit_length do_reorder False 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 previously as nmag MagMaterial Having two Materials X and Y both defined in region A we would use region_A X Y unit_length SI object The SI object defines what a length of 1 0 in the mesh file corresponds to in reality If the length 1 0 in the mesh is a nano metre then the corresponding SI object would be SI 1e 9 m 68 Returns mesh mesh object 4 2 9 relax Module nmag Object Simulation relax Arguments self H_applied None save averages fields at convergence True convergence_check gt step This method carries out the time integration of the LLG until the system reaches a meta stable equilibrium It uses internally the hysteresis loop command Parameters H_applied list of SI objects For a 3 d simu
74. ist 12 0 7 0 200 0 units 1e3 SI A m loop over the applied fields Hs sim hysteresis Hs save averages at convergence C fields at convergence 30 restart at convergence not working yet We would like to compute the magnetisation behaviour in the applied fields ranging from 12e3 0 0 A mto 200e3 0 0 A m in 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 0 units 1e3 SI A m sim hysteresis Hs save averages at convergence fields at convergence Once the calculation has finished we can plot the evolution of the magnetisation i e the graph of the magnetisation computed along the direction of the applied field as a function of the applied field The ncol command allows us to extract the data and we redirect it to a text file with name nsim dat ncol nanodot time H_ext_O m_Py_O m_Py_1 m_Py_2 gt plot dat Plotting the data with Gnuplot user host user gt gnuplot make_plot gnu which uses the script in make_plot gnu set term postscript enhanced color set out nanodot_evo ps set xlabel Applied field A m set ylabel M Ms plot 250 50 1 2 1 2 nsim dat u 2 1000 3 ti nsim w lp 3 mag par dat u 1 gt 0 3 1 0 4 ti magpar w lp 4 The resulting graph is shown here 31
75. l this needs to be an SI object without units this is why we write SI 0 5 The next line creates the simulation object sim nmag Simulation bar Here we provide a name for the simulation object i e bar This will be used as the root 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 it 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 1e 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 SI 5e 12 s simply creates an SI object which represents this amount of time i e 5 pico seconds over which to carry out that integration 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 for i in range 0 61 sim advance_time dt i if i 10 0 sim sav
76. lation the Sl 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 convergence_check every object The default value every 5 step 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 10 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 oat 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 h5 files If a11 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 Note The list of fieldnames to save has to be the same list throughout a run This can be changed but requires some work Please let the nmag team know if you would consider this usef
77. lation object copies of the system along the x axis pbc nmag SetLatticePoints vectorlist lattice_points scalefactor SI 1le 9 m create simulation object sim nmag Simulation periodic_bc pbc structure The rest is simply the definition of a relaxation process as shown in Example 2 To note that for the symmetry of the system if the initial x component of the magnetisation is 0 there is no evolution towards the configuration with the magnetisation along the x axis Varying the number of periodic copies used in the system one can obtain an estimate of the number of copies needed to approximate an infinite prism along the periodic axis The curves of the demagnetising field as a function of the number of periodic copies for a uniform magnetisation along the periodic axis and along the orthogonal direction are the following 300000 250000 200000 zB E gt 450000 E oD a 100000 50000 0 10 20 30 40 50 60 70 80 90 copies 55 440000 420000 400000 380000 360000 Demag field 340000 320000 300000 280000 0 10 20 30 40 50 60 70 80 90 copies 2 14 Example 2D periodicity This example is another application of the macro geometry feature where now we deal with a 2D system In this case the unit cell is a 30x10x10 nm 3 prism and we want to copy it in the x and y directions for a total of 400 copies of the unit cell 10 in the x direction and 40 in the y Let us start computin
78. les together with more detailed explanation of their structure 2 1 Example Demag field in uniformly magnetised sphere This example computes the demagnetisation field in a uniformly magnetised sphere We know of course that the demag field has to have the opposite direction to the magnetisation and a magnitude of 1 3 of the magnetisation in this special case When using finite element calculations a crucial and non trivial part of the work is the finite element mesh gen eration We provide a very small mesh for this example sphere1 nmesh h5 which was generated with Netgen It describes a sphere of radius 10nm Using this we can write the following nmag script with name sphere1 py import nmag from nmag import SI create simulation object sim nmag Simulation define magnetic material Py nmag MagMaterial name Py Ms SI 1e6 A m exchange_coupling SI 13 0e 12 J m load mesh sim load_mesh sphere1 nmesh h5 C sphere Py unit_length SI 1e 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 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 i le 9 position in metres H_demag sim probe_subfield_f H_demag x 0 0 print x x H_de
79. mag H_demag To execute this script we have to give its name to the nsim executable for example on linux user host user gt nsim spherel py Let s discuss the sphere1 py script step by step 2 1 1 Importing nmag First we need to import nmag and any subpackages of nmag that we need this is just the SI object import nmag from nmag import SI 2 1 2 Creating the simulation object Next we need to create a simulation object sim nmag Simulation 2 1 3 Defining magnetic materials After having imported the nmag module into Python s workspace and after 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 is Py and we assign a saturaration magnetisation and an exchange coupling strength Py nmag MagMaterial name Py Ms SI 1e6 A m exchange_coupling SI 13 0e 12 J m The name of the material chosen here plays an important role as all the Fields and Subfields will automatically be given names which include this material name The output files will also use that name to label output data All data input and output within nmag is expressed in SI units by default To avoid ambiguity here but simultanouesly provide flexibility in the choice of input and output units an SI object is provided This has to be used when defining the material parameters and in some other places We thus express the saturation
80. mesh file In this case positions are expressed in nanometers this comes from the unit_length SI 1e 9 m expression in the sim 1load_mesh command The following image shows the initial magnetisation pointing in the 1 0 1 direction 30 0 10030 0 The final configuration show that the magnetisation aligns along the z direction The coloured surface show 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 stricly speaking this system is not in a meta stable state yet but a snap shot of a dynamical process 30 0 M_Py lt A m gt X component 2 15e 05 1 44e 05 7 20e 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 and the magnetic scalar potential is shown via 10 isosurfaces Because the demagnetisation field is the negative gradient of the scalar potential the vectors are perpendicular on the isosurfaces 30 0 10G30 0 H_demag lt A m gt 0 00 6 81le 04 1 36e 05 2 04e 05 2 72e 05 3 4le 05 4 09e 05 4 77e 05 2 2 4 these are the basics The examples above provide an overview of the fundamental commands used to setup a micromagnetic calcul
81. of a material 2 8 1 Pinning simulation script import nmag 40 from nmag import SI si create simulation object sim nmag Simulation define magnetic material PermAlloy Py nmag MagMaterial name Py Ms S1 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 1e 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 x x y y z z lt 4e 9 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 apply external field in y direction unit 0 5 si T si muO 500mT in A m sim set_H_ext O unit 1 unit O unit relax the magnetisation sim relax We will now discuss the sphere py example step by step We first define a material modelling Permalloy and apply it to a sphere with radius 10 nm Then we set initial magnetisation to point in x direction 2 8 2 Pinning magnetisation In order to allow the user to fix 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 now set the pinning field using set_pinning which is used like s
82. ommon applications that only need very slight modification e g changing of the mesh filename or material parameters for basic use At present Nmag is 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 As most of the underlying field theoretical foundations used by Nmag are derived from the low level nsim multiphysics simulator which is not closely tied to Python it would be possible to provide support for other scripting languages in the future should the need arise e g in case Python should become unpopular over the years 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 users who want to design sophisticated simulation scripts in Python 2 Guided Tour We present a number of examp
83. ore detail The argument save is telling the relax function that it should save data according to the following instructions There are two objects provided in the list between the square brackets and here The first one is this tuple C averages every time 50e 12 s and means that the averages should be saved every 50 pico seconds The syntax that is used breaks down in the following parts e averages is just the keyword a string to say that the average data should be saved e every is aspecial 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 50e 12 s which is the amount of time after which the data should be saved again This has to be a SI object and this is achieved in this example by multipyling a number 50e 12 with the SI object s which just represents one second and has been defined in our example program We can provide further keywords to the every object for example to save the data every n iter ation steps we can use every 10 step The relax command uses the hysteresis command internally so this can be used to look up more explanation The second object in the list is fields at convergence and 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 s
84. pply gradually stronger fields in x direction up to 50 mT s nmag vector_set direction 1 0 0 0 0001 norm_list range 0 191 10 range 191 211 range 210 501 10 units 0 1 0 001 si T 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 10 2 Analyzing the result First we extract magnitude of the applied field and the x component of magnetisation ncol cube H_ext_O M_Fe_0O gt cube_hext_vs_m txt Then we compare the result with OOMMF 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 oommf cube_hext_vs_m txt u 1 795 77471545947674 2 ti which gives the following result 48 1 8e 06 T T T T T T T nmag Pett tHE gomp H 1 6e 06 1 4e 06 1 2e 06 1e 06 800000 M x A m 600000 400000 200000 200000 e 5000 10000 15000 20000 25000 30000 35000 40000 H_ext x A m 2 11 Example Thermal Effects In this example we will analyze the relationship between simulation temperature and switching time of magnetisation of a NdFeB particle whose magnetisation is
85. r 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 2 2 Subfield Each field 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 hav
86. racting data from the simulation 1 saving averaged values of fields which can be analysed later 2 saving spatiallialy resolved fields which can be analysed later 3 extracting field values at arbitrary positions from within the running programme In the sphere1 example discussed here we use all three methods and will discuss these in more detail now 2 1 7 1 Saving averaged data sim save_data The save_data method writes averages of all fields see Fields and subfields into a text file This file is best analysed using the ncol tool but can also just be read with a text editor The format follows OOMMF s odt fileformat every row corresponds to one snap shot of the system see save_data The function can also be called with parameters to save spatially resolved field data see Saving spatially resolved data The first and second line in the file are headers that explain the entity and the units of the entity saved in the corresponding column The ncol tool allows to extract particular columns easily so that these can be plotted later useful for hysterises loop studies In this example where have only one timestep there is only one row of data in this file and we shall not explore this further here 2 1 7 2 Extracting arbitrary data from the running programme The line H_demag sim get_subfield_f H_demag x 0 0 obtains the demagnetisation field see Fields and subfields in nmag at position x 0 0 By default t
87. recommending any mesh generating software We have used Netgen to generate most of the meshes for this manual The Vienna 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 Export Filetype and ensure that Neutral Format is selected Then export the mesh with File gt Export Mesh e There is a contributed import module for Gambit Use at your own risk 5 1 Nmesh file format There are two nmesh file formats ascii nmesh and hdf5 nmesh 5 1 1 Ascii nmesh We describe the structure of the ascii nmesh file format using the following example A mesh file has been generated of a sphere with radius 1 with Netgen and this geometry file sohere geo The mesh file looks like this PYFEM mesh file version 1 0 dim 3 nodes 79 simplices 174 surfaces 148 periodic 0 79 0 000000000000 1 000000000000 0 911922000000 0 941662000000 lt snip gt O 000000000000 O 000000000000 0 410365000000 0 159249000000 74 O 000000000000 O 000000000000 O 000000000000 0 296499000000 0 038305000000 0 552912000000 0 107777000000 0 533150000000 0 052091000000 0 084880000000 174 1 58 0 62 78 1 33 78 36 50 1 19 TT 0 17 1 67 75 78 72 lt
88. rogram code The ending is by convention py which reflects that the programming 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 OOMMF 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 However often it is more convenient to use the ncol tool filter the data that matters and only to pass the filtered data to a plotting program Data is written into the ndt file whenever the save_data method of the simulation object is called 79 7 4 Data files 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
89. s given by Larmor pp He Heyt where the parameter gamma called gyromagnetic ratio is taken to have the following value see g ie es E a gjel 1 7588 x 10 T s 2 Me 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 To execute this script we have to give its name to the nsim executable for example on linux y 52 user host user gt nsim larmor py The data on the magnetization components at each time step 0 1 ps is extracted with the following command userGhost user gt ncol larmor 0 20 21 22 gt data txt and we use Gnuplot to extract the value of the Larmor period T Gnuplot is run with the command user host user gt gnuplot and the following command plots the x component of the magnetization as a function of the simulation time gnuplot gt f x A sin 2 pi x B C D gnuplot gt B 30 gnuplot gt fit f x data txt u 1 1e 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 1 T T T T T data txt u 17 1e 12 2 f x Magnetisation angle from initial position 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 to 30 in order to help Gnuplot fit the curve Such fit on T gives the value 28 4293 this value
90. s3 m gt 2 lt axis2 m gt 2 lt axis3 m gt 2 K2 lt axisi m gt 2 lt axis2 m gt 2 lt axis3 m gt 7 2 K3 lt axisi m gt 4 lt axis2 m gt 4 lt axisi m gt 4 lt axis3 m gt 4 lt axis2 m gt 4 lt axis3 m gt 7 4 where m is the normalised magnetisation Parameters axis vector list First cubic anisotropy axis will be normalised axis2 vector list Second cubic anisotropy axis will be orthonormalised with regards to axis7 K1 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 0 K3 SI Object Eigth order phenomenological anisotropy constant as used in the equation above Default value is 0 4 2 Simulation Module nmag Object Simulation Class constructor information self name None use_hlib False periodic_bc None do_demag True tem perature None thermal_delta_t None timestepper_max_order 2 timestepper_krylov_max 300 64 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 Default value is True temperature SI Object Simulated temperature unless equal to None stochastic thermal fluctuations will be enabled thermal_delta_
91. sion of mesh files into nmesh format The nmeshimport command can be used to import other mesh formats into nmesh 6 Executables 6 1 ncol ncol is a utility to conveniently analyse ndt files 6 2 nmagpp The nmagpp program is the NMAG data PostProcessor It can be used to e 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 3 nsim The main executable It appears to be a Python interpreter but has extendend functionality In particular it can be executed in parallel using MPI and provides access to a module with name ocam1 that provides the functionality of the nsim multiphysics library 6 4 nmeshpp The nmeshpp program is the NMESHPre Processer and NMESHPost Processor It provides quick access to some statistical information about nmesh meshes The basic usage is nmeshpp OPTIONS INPUTFILE OUTPUTFILE 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 6 4 1 General information info The command nmeshpp info bar30_30_100 nmesh h5 produces the following output 3 dimensional mesh 18671 volume elements 3
92. t SI Object Time step to use when stochastic thermal fluctuations are enabled timestepper_max_order int Maximum order for Adams method Default value is 2 timestepper_krylov_max int Maximum dimension of the Krylov subspace to be used Default value is 300 4 2 1 advance_time Module nmag Object Simulation advance_time Arguments self target_time max_it 1 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 integration call If set to 1 then there is no limit 4 2 2 get_subfield Module nmag Object Simulation get_subfield Arguments 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 we will lookup the correct SI dimensions for this subfield and use this If you would like to see simulation units in the output then use SI 1 In short if you ommit the second parameter you will obtain SI numbers Returns data numpy array 65
93. t first define the three unit vectors of the lattice again slightly larger than the dimension of the unit cell to avoid overlapping 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 1e 9 m The z direction is already done as we don t want any periodic copy there Along the x direction we want to place 4 copies along its negative orientation 5 along the positive and therefore the lattice points along such direction are those between 4 0 0 and 5 0 0 An analogous procedure is repeated for the y axis where we place 20 copies along the positive y axis and 19 along the negative one The next step is then to set the copies on the lattice 58 copies of the system on the lattice points pbc nmag SetLatticePoints vectorlist lattice_points scalefactor SI 1le 9 m and now let see how the system evolves when set in the same initial configuration as before with a uniform magneti sation along 1 1 1 and let it evolve towards the equilibrium The outcome is shown in the following figure 1 0 8 0 6 0 4 F 0 2 M Ms 0 2 0 4 0 6 0 8 0 2e 10 4e 10 6e 10 8e 10 1e 09 1 2e 09 1 4e 09
94. t 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 gradually 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 from which it gains all its flexibility and evolves towards more specialized notions to conveniently define the properties of very specific 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 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 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 for the most c
95. table 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 i e at the end of the simulation in this example After having run this programme we can use the ncol tool to look at the averages saved ncol bar_relax step time we get the following output only the beginning shown 0 0 82 5e 12 120 te 11 146 1 5e 11 176 2e 11 201 2 5e 11 227 3e 11 248 3 5e 11 which shows 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 pico seconds 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 7 5e 11 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 From the data saved we can obtain the following plot 8e 05 E 6e 05 E c S g 4e 05 v Cc D o 2e 05 0 2e 10 4e 10 6e 10 8e 10 time s In summary the relax function is useful to obtain a metastable 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
96. tem 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 Note that the dynamics shown here are of course artifical and only used to obtain a meta stable configuration more efficiently 2 3 Example Hysteresis loop for Stoner Wohlfarth particle This example computes the hysteresis loop of an ellipsoidal magnetic object and compares the results with the analytical solution given by the Stoner Wohlfahrt model We use an ellipsoid with semi axes dimensions of 3 nm 1 nm and 1 nm along the x y and z direction respectively the mesh is contained in ellipsoid nmesh h5 and produced with Netgen from ellipsoid geo 21 0 999 0 999 0 998 3 00 0 998 Y 2 3 1 Hysteresis simulation script To compute the hysteresis loop for the ellipsoid we use the following script ellipsoid py import nmag from nmag import SI at create simulation object sim nmag Simulation define magnetic material Py nmag MagMaterial name Py Ms SI 1e6 A m exchange_coupling SI 13 0e 12 J m load mesh the mesh dimensions are scaled by 100nm sim load_mesh ellipsoid nmesh h5 ellipsoid Py unit_length SI 0 5e 9 m set initial magnetisation sim set_m 1 1 0 22 Hs nmag vector_set direction 1 1 0 norm_list 1000 0 995 0 1000
97. the data the first time Step 1 We could visualise the magnetisation and all other fields as described in Example Demag field in uniformly magne tised 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 36 9e 09 H_demag 329656 18892701436 131 69946810517845 197 13873034397167 8e 09 H_demag 329783 31649797881 68 617197264295427 140 00328871543459 7e 09 H_demag 329842 17628131888 183 37401011699876 163 01612229436262 6e 09 H_demag 329904 84956877632 133 62473797637142 74 090532749764847 5e 09 H_demag 329974 43178624194 85 517390832982983 13 956465964930704 4e 09 H_demag 330002 69224229571 64 187663119270084 30 832135394870004 3e 09 H_demag 330006 79488959321 25 479055440690821 61 958073893954818 2e 09 H_demag 330020 18327401817 11 70722487517595 58 143562276077219 1e 09 H_demag 330025 52325345919 5 7120648683347452 52 237341988696294 0 0 H_demag 330028 67095553532 25 707310077918752 46 346108473560378 1e 09 H_demag 330058 98559210222 37 699378078580203 41 167364094137213 2e 09 H_demag 330089 30022866925 49 691446079241658 35 988619714714041 3e 09 H_demag 330145 3
98. to provide a larger main plot This demonstrates the gradual change from the pinned magnetisation in the centre to the outside bi A 7 La A 2 9 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 9 1 Unixaial anisotropy simulation script import nmag from nmag import SI every at from numpy import array from math import sin cos pi sqrt 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 43 Ms S1 1400e3 A m exchange_coupling SI 30e 12 J m anisotropy nmag uniaxial_anisotropy axis 0 0 1 K1 SI 520e3 J m 3 load mesh sim load_mesh bar nmesh h5 bar Co unit_length SI 1e 9 m set initial magnetisation def sample_m0 x y z if x lt 2e 9 return 0 0 1 if x gt 502e 9 return 0 0 1 z 2 x 2e 9 500e 9 1 return 0 sqrt 1 z z z sim set_m sample_m0 pin lhs rhs magnetisation def sample_pinning x y z return x gt 2e 9 and x lt 502e 9 sim set_pinning sample_pinning save magnetisation along x axis def save_magnetisation_along_x filename f open filename w for i in range 0 504 array it0 5 0 5 0 5 1e 9 M sim probe_subfield_f M_Co x print gt
99. tor for every site of the finite element mesh 37 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 we have obtained using get_subfield can be retrieved from get_subfield_sites Correspondly 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 m_Py lt gt X component 0 00 0 143 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 le 08 H_demag None 9e 09 H_demag 333816 99138074159 1884 643376396662 16 665519199152595 8e 09 H_demag 334670 87148225965 2293 608410913705 102 38526828192296 7e 09 H_demag 335258 77403632947 3061 170
100. tore 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 copies of the system along the x axis pbc nmag SetLatticePoints vectorlist lattice_points scalefactor SI 1le 9 m create simulation object sim nmag Simulation periodic_bc pbc structure load mesh sim load_mesh cube nmesh h5 repeated cube 1D Py unit_length SI 1e 9 m set initial magnetisation the component along x must be different from 0 sim set_m 0 1 1 1 loop over the applied field from nsim when import every at sim relax save averages at convergence fields at convergence The operation can be splitted in 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 overlapping between the cells and leave to zero the value for the directions where we don t want to have periodic copies of our magnetic object s 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 54 for xi in range 3 4 lattice_points append xi x_lattice 0 0 y_lattice 0 0 z_lattice and in the third step we define the object whose structure attribute will be used as the parameter in the definition of the simu
101. ul avoid_same_step bool If True then the data will only be saved if the current clock step counter is 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 situation where the step counter may not have changed from the last saved con figuration 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 automatically increase the step counter 69 4 2 11 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 explanation below This method sets the normalised magnetisation to a particular value or pattern The field that it will set is the m field therefore the name It can be used in three different ways 1 Providing a constant vector To set the magnetisation to point everywhere in the same direction this function accepts a list of 3 floats to represent this For example to have the magnetisation point in the x direction we could call the function like this assuming that sim is a simulation object sim set_m 1 0 0 To point in a 45 degree direction between the x and y a
102. xis we could use sim set_m 1 1 0 The magnetisation will automatically be normalised 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 z get access to pi cos and sin import math change angle of Mx and My by 10 degree when x varies by inm angle x 1e9 10 360 2 math 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 position in space This position x y z as given to the function is expressed in metres 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 because the magnetisation has three components If you are unsure about the required format use the Simulation get_subfield function to obtain exactly such a numpy array for the relevant subfield 70 4 2 12 set_H_ext Module nmag Object Simulation set_H_ext Arguments self values unit None Parameters values vector list function
103. y specifying a temperature when creating the Simulation object Since thermal noise renders nmag s standard time integrator unusable it is using a fixed time step integration method instead the actual timestep to be used is passed via the thermal_delta_t parameter In our particular case we have the user specify simulation temperature on the command line and we use a timestep of 0 0025 ps temperature SI float sys argv 1 K ps SI 1e 12 s sim nmag Simulation temperature temperature thermal_delta_t 0 0025 ps We then define a magnetic material modelling NdFeB and assign it to a spherical mesh of radius 10 nm Initial magnetisation is set to point to z direction which also is the material s easy axis and an external field of 8 79 T equal in magnitude to the nucleation field as determined using hysteresis is applied in z direction Finally we compute the system s time development for 100 ps saving field data spatially resolved every 5 ps and averages every 1 ps 2 11 3 Comparison of runs at different temperatures We run the simulation script for temperatures of 0 K 4 K and 8 K extracting time and average z component of magnetisation after each run nsim thermal py 0 0 ncol thermal time M_NdFeB_2 gt thermal_Ok_mag_z txt nsim thermal py 4 0 ncol thermal time M_NdFeB_2 gt thermal_4k_mag_z txt nsim thermal py 8 0 ncol thermal time M_NdFeB_2 gt thermal_8k_mag_z txt Using the following Gnuplot script

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