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, mesh

u.set_enabled_equivalencies(u.magnetic_flux_field())

<astropy.units.core._UnitContext at 0x7ff540b6ef50>

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_filepath=mesh.CUBE_20_nm,
    Ms=me.Ms(1280000, unit="A/m"),
    A=me.A(7.7e-12, unit="J/m"),
    K1=me.Ku(4300000, unit="J/m3"),
    hstart=(10 * u.T).to("A/m"),
    hfinal=(-10 * u.T).to("A/m"),
    hnsteps=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 H, M and 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],
 unit=A / m)

hysteresis_result.M

SpontaneousMagnetization(value=
[ 1279889.69852942  1279875.8222883   1279859.14516496  1279838.85733375
  1279813.83287613  1279782.46890957  1279742.42008568  1279690.14264963
  1279620.07356178  1279523.06653747  1279383.19818258  1279170.65048994
  1278823.93770141  1278197.82587937  1276869.83117496  1273020.97305969
 -1279813.83301959],
 unit=A / m)

hysteresis_result.energy_density

EnergyDensity(value=
[-16778187.08880844 -15498304.12158992 -14218436.37373519
 -12938587.02958595 -11658760.23093237 -10378961.46710003
  -9099198.17323738  -7819480.67950905  -6539823.77827088
  -5260249.43804744  -3980791.78558299  -2701506.94435504
  -1422494.39483802   -143949.74970699   1133677.37375769
   2409024.64232318 -11658760.23093035],
 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, 2])

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

hysteresis_result.dataframe

	configuration_type	H	M	energy_density
0	1	7.957747e+06	1.279890e+06	-1.677819e+07
1	1	7.161972e+06	1.279876e+06	-1.549830e+07
2	1	6.366198e+06	1.279859e+06	-1.421844e+07
3	1	5.570423e+06	1.279839e+06	-1.293859e+07
4	1	4.774648e+06	1.279814e+06	-1.165876e+07
5	1	3.978874e+06	1.279782e+06	-1.037896e+07
6	1	3.183099e+06	1.279742e+06	-9.099198e+06
7	1	2.387324e+06	1.279690e+06	-7.819481e+06
8	1	1.591549e+06	1.279620e+06	-6.539824e+06
9	1	7.957747e+05	1.279523e+06	-5.260249e+06
10	1	0.000000e+00	1.279383e+06	-3.980792e+06
11	1	-7.957747e+05	1.279171e+06	-2.701507e+06
12	1	-1.591549e+06	1.278824e+06	-1.422494e+06
13	1	-2.387324e+06	1.278198e+06	-1.439497e+05
14	1	-3.183099e+06	1.276870e+06	1.133677e+06
15	1	-3.978874e+06	1.273021e+06	2.409025e+06
16	2	-4.774648e+06	-1.279814e+06	-1.165876e+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	1.608357
1	9.0	1.608339
2	8.0	1.608318
3	7.0	1.608293
4	6.0	1.608261

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('/home/petrocch/repo/mammos/mammos-mumag/examples/hystloop/hystloop_0001.vtu'),
 2: PosixPath('/home/petrocch/repo/mammos/mammos-mumag/examples/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.

Passing a different mesh

The hysteresis.run function can also take custom meshes that fulfil certain properties.

• the mesh must be in .fly format

• the mesh must consist of three regions:

  • the first region is the material (a cube in our case) to which the material parameters will be assigned

  • the second region is free space around the material

  • the third region is a shell sourrounding it (to help map to infinity)

The object mesh.CUBE_20_nm is actually just a path to a pre-computed mesh:

mesh.CUBE_20_nm

PosixPath('/home/petrocch/repo/mammos/mammos-mumag/src/mammos_mumag/mesh/CUBE_20_nm.fly')