Hysteresis loop calculation

In this example we calculate the hysteresis loop of a magnetic waveguide with a round wire cross section (R=50 nm radius) and permalloy material parameters.

import tetrax as tx
import numpy as np # will be required for code parts meant to collect the average magnetization for each field step

%matplotlib notebook
import matplotlib.pyplot as plt

sample = tx.create_sample(name="Round_wire_R_50nm")
sample.Msat = 800e3
sample.Aex = 13e-12
mesh = tx.geometries.round_wire_cross_section(R=50)
sample.set_geom(mesh)

Setting geometry and calculating discretized differential operators on mesh.
Done.

In the next step we define the min and max field values, the step size. In a for loop over the static external field values we set the external field to the current value, we relax the magnetization and calculate the volume averaged x, y and z components, that are collected to an aver_mag list. Thes list will be converted into a numpy array and plotted.

Bmin = -1 # min. static field value in [T]
Bmax = 1 # max. static field value in [T]
Bstep = 5e-3 # field step in [T]

exp = tx.create_experimental_setup(sample)
# we define a homogeneous vectorfield in the x direction (theta=90,phi=0)
bhom = tx.vectorfields.homogeneous(sample.xyz, 90, 0)
# external field values in a numpy array: ext_fields
ext_fields = np.arange(Bmin,Bmax+Bstep,Bstep)
sample.mag = tx.vectorfields.homogeneous(sample.xyz, 60.0, 0.0) # arguments (coordinate, theta, phi)

aver_mag = []

for Bstat in ext_fields:
    exp.Bext = Bstat * bhom # setting a homogeneous static field
    nr_trial = 0
    success = False
    while (not(success) and (nr_trial < 5)):
        success = exp.relax(tol=1e-13,continue_with_least_squares=True,verbose=False) # relaxation
        nr_trial += 1
    aver_m = tx.sample_average(sample.mag, sample) # computing the average mx, my, mz
    aver_mag.append(aver_m) # collecting for each field step

aver_mag = np.array(aver_mag)
plt.plot(ext_fields*1e3,aver_mag[:,0])
plt.plot(-ext_fields*1e3,-aver_mag[:,0]) # here we only mirror the first loop to get a hysteresis
plt.xlabel("External field (mT)")
plt.ylabel("Magnetization (normalized to Ms)")
plt.show()

NOTE: As mentioned in the documentation, for waveguide samples, the equilibration is not totally stable yet. Please use with care and check the resulting equilibrium states. Therefore might happen that re-running the hysteresis loop without changing any para,meters might lead to different results.