mammos_mumag quickstart

mammos_mumag can compute hysteresis loops of magnetic materials using finite elements.

Requirements:

• mammos and esys-escript

import mammos_entity as me
import mammos_units as u
import pandas as pd
from mammos_mumag import hysteresis

u.set_enabled_equivalencies(u.magnetic_flux_field())

<astropy.units.core._UnitContext at 0x7f7cf1139f10>

Hysteresis simulation

The hysteresis.run function computes a hysteresis loop for a homogeneous material with given parameters. We need to pass in a suitable mesh, mammos_mumag.mesh provides a sample mesh.

hysteresis_result = hysteresis.run(
    mesh="cube20_singlegrain_msize2",
    Ms=me.Ms(1280000, unit="A/m"),
    A=me.A(7.7e-12, unit="J/m"),
    K1=me.Ku(4300000, unit="J/m3"),
    theta=0,
    phi=0,
    h_start=(10 * u.T).to("A/m"),
    h_final=(-10 * u.T).to("A/m"),
    h_n_steps=20,
)

Hysteresis result object

The returned results_hysteresis object provides a plot method to visualize the computed data. mammos_mumag.hysteresis only computes half a hysteresis loop, going from hstart to hfinal. To show a full loop this function mirrors the computed data and plots it twice:

hysteresis_result.plot();

To only see the actual simulation, we can use the flag duplicate=False:

hysteresis_result.plot(duplicate=False);

The results object provides access to:

• the external field H

• the magnetization M in the direction of the applied field

• the components Mx, My, Mz of the magnetization

• the energy density

hysteresis_result.H

ExternalMagneticField(value=
[ 7957747.15026276  7161972.43523649  6366197.72021021  5570423.00518393
  4774648.29015766  3978873.57513138  3183098.86010511  2387324.14507883
  1591549.43005255   795774.71502628        0.          -795774.71502628
 -1591549.43005255 -2387324.14507883 -3183098.86010511 -3978873.57513138
 -4774648.29015766 -5570423.00518393 -6366197.72021021 -7161972.43523649
 -7957747.15026276],
 unit=A / m)

hysteresis_result.M

Magnetization(value=
[ 1279920.92569655  1279911.14633934  1279899.42963877  1279885.2268147
  1279867.77972873  1279846.01687668  1279818.38389404  1279782.55594664
  1279734.92828792  1279669.66402409  1279576.79658277  1279438.13222608
  1279217.45234696  1278833.60909754  1278070.51029595  1276161.36652649
  1267635.43145344 -1279885.22584968 -1279899.42846665 -1279911.1452972
 -1279920.92579483],
 unit=A / m)

hysteresis_result.Mx

Magnetization(value=
[ -23.54037126  -25.0451965   -26.7560345   -28.71848504  -30.99269791
  -33.65924931  -36.82966917  -40.66202659  -45.38837715  -51.36375841
  -59.15966038  -69.76275253  -85.0222662  -108.88273736 -151.57027633
 -250.75175893 -861.56501265   28.53876135   26.72983079   25.0250458
   23.51679169],
 unit=A / m)

hysteresis_result.My

Magnetization(value=
[  -48.9635178    -52.0457853    -55.54281008   -59.54464247
   -64.16984798   -69.57549466   -75.97863179   -83.68435754
   -93.13691972  -105.00949446  -120.37511784  -141.05920632
  -170.42606819  -215.51717585  -294.12895559  -469.64559154
 -1433.18253466    59.01421681    55.28635356    51.8495188
    48.99411012],
 unit=A / m)

hysteresis_result.Mz

Magnetization(value=
[ 1279920.92569655  1279911.14633934  1279899.42963877  1279885.2268147
  1279867.77972873  1279846.01687668  1279818.38389404  1279782.55594664
  1279734.92828792  1279669.66402409  1279576.79658277  1279438.13222608
  1279217.45234696  1278833.60909754  1278070.51029595  1276161.36652649
  1267635.43145344 -1279885.22584968 -1279899.42846665 -1279911.1452972
 -1279920.92579483],
 unit=A / m)

hysteresis_result.energy_density

EnergyDensity(value=
[-16794046.39939273 -15514130.21974726 -14234224.74917092
 -12954332.18513003 -11674455.37178373 -10394598.05726379
  -9114765.28465126  -7834964.0056009   -6555204.08037736
  -5275499.98242484  -3995873.86585082  -2716361.46928677
  -1437024.49582884   -157979.70553049   1120520.7665673
   2397803.50265979   3671036.31564498 -12954332.18511862
 -14234224.74916488 -15514130.2197436  -16794046.39939053],
 unit=J / m3)

The attribute configuration_type contains a list of indices that refer to saved magnetization field configurations. We will use this information later.

hysteresis_result.configuration_type

array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2])

We can also get the hysteresis data as a pandas dataframe in SI units:

hysteresis_result.dataframe

	configuration_type	H	M	Mx	My	Mz	energy_density
0	1	7.957747e+06	1.279921e+06	-23.540371	-48.963518	1.279921e+06	-1.679405e+07
1	1	7.161972e+06	1.279911e+06	-25.045197	-52.045785	1.279911e+06	-1.551413e+07
2	1	6.366198e+06	1.279899e+06	-26.756035	-55.542810	1.279899e+06	-1.423422e+07
3	1	5.570423e+06	1.279885e+06	-28.718485	-59.544642	1.279885e+06	-1.295433e+07
4	1	4.774648e+06	1.279868e+06	-30.992698	-64.169848	1.279868e+06	-1.167446e+07
5	1	3.978874e+06	1.279846e+06	-33.659249	-69.575495	1.279846e+06	-1.039460e+07
6	1	3.183099e+06	1.279818e+06	-36.829669	-75.978632	1.279818e+06	-9.114765e+06
7	1	2.387324e+06	1.279783e+06	-40.662027	-83.684358	1.279783e+06	-7.834964e+06
8	1	1.591549e+06	1.279735e+06	-45.388377	-93.136920	1.279735e+06	-6.555204e+06
9	1	7.957747e+05	1.279670e+06	-51.363758	-105.009494	1.279670e+06	-5.275500e+06
10	1	0.000000e+00	1.279577e+06	-59.159660	-120.375118	1.279577e+06	-3.995874e+06
11	1	-7.957747e+05	1.279438e+06	-69.762753	-141.059206	1.279438e+06	-2.716361e+06
12	1	-1.591549e+06	1.279217e+06	-85.022266	-170.426068	1.279217e+06	-1.437024e+06
13	1	-2.387324e+06	1.278834e+06	-108.882737	-215.517176	1.278834e+06	-1.579797e+05
14	1	-3.183099e+06	1.278071e+06	-151.570276	-294.128956	1.278071e+06	1.120521e+06
15	1	-3.978874e+06	1.276161e+06	-250.751759	-469.645592	1.276161e+06	2.397804e+06
16	1	-4.774648e+06	1.267635e+06	-861.565013	-1433.182535	1.267635e+06	3.671036e+06
17	2	-5.570423e+06	-1.279885e+06	28.538761	59.014217	-1.279885e+06	-1.295433e+07
18	2	-6.366198e+06	-1.279899e+06	26.729831	55.286354	-1.279899e+06	-1.423422e+07
19	2	-7.161972e+06	-1.279911e+06	25.025046	51.849519	-1.279911e+06	-1.551413e+07
20	2	-7.957747e+06	-1.279921e+06	23.516792	48.994110	-1.279921e+06	-1.679405e+07

We can generate a table in alternate units:

df = pd.DataFrame(
    {
        "mu0_H": hysteresis_result.H.q.to(u.T),
        "J": hysteresis_result.M.q.to(u.T),
    },
)
df.head()

	mu0_H	J
0	10.0	1.608396
1	9.0	1.608384
2	8.0	1.608369
3	7.0	1.608351
4	6.0	1.608329

Visualizing magnetization configurations

To plot the hysteresis loop (including the available configurations), run

hysteresis_result.plot(configuration_marks=True);

We can get the location of the saved configurations from the attribute configurations:

hysteresis_result.configurations

{1: PosixPath('/tmp/tmp3v0tvnk0/hystloop/hystloop_0001.vtu'),
 2: PosixPath('/tmp/tmp3v0tvnk0/hystloop/hystloop_0002.vtu')}

To inspect the configurations more conveniently directly in the notebook we can use the plot_configuration function of hysteresis_result. We need to pass the index and get an interactive 3D plot (using pyvista):

hysteresis_result.plot_configuration(1)

Note: the small object size is a consequence of the empty sphere around the cube.