Cubic anisotropy#

  • this notebook can be used to compute the dispersion of films with cubic anisotropy

  • as an example, we choose Fe material parameters for a 20 nm thick film and compute the FMR frequency for anisotropy axes of two different orientation

  • NOTE: the notebook might run for several minutes, depending on the computer/notebook computational capabilities

[1]:

import tetrax as tx
import numpy as np
%matplotlib notebook
import matplotlib.pyplot as plt

We set Fe material parameters#

  • anisotropy axes: (1,0,0),(0,1,0),(0,0,1)

  • Note: you only have to set the first two axes, the third will be computed as a cross produc of them

[2]:

sample = tx.create_sample(name="Fe_film",geometry="layer")
sample.Msat = 1714e3
sample.Aex = 21e-12
sample.Kc1 = 48000
sample.v1Kc = (1,0,0)
sample.v2Kc = (0,1,0)
mesh = tx.geometries.monolayer_line_trace(20,lc=1)
sample.set_geom(mesh)

This sample does not have a mesh yet. You cannot set spatially dependent saturation for it.
This sample does not have a mesh yet. You cannot set spatially dependent exchange stiffness for it.
Setting geometry and calculating discretized differential operators on mesh.
Done.

Angular dependence of the f0 mode in the XZ plane#

[3]:

angle_ = np.linspace(0,360,181)
Bext = 300e-3
f0 = []
exp = tx.create_experimental_setup(sample,name="xz-plane")

for angle in angle_:
    sample.mag = tx.vectorfields.homogeneous(sample.xyz, angle, 0)
    exp.Bext = Bext*tx.vectorfields.homogeneous(sample.xyz, angle, 0)
    dispersion = exp.eigenmodes(num_cpus=-1,num_modes=2,k=0,save_modes=False,verbose=False)
    f0.append(dispersion.iloc[0]["f0 (GHz)"])

Plotting XZ-plane data#

[4]:

plt.rcParams["figure.figsize"] = (8,6.5)
plt.figure()
plt.plot(angle_,f0, ls="", marker="o",label="xz-plane")
plt.legend()
plt.show()

Changing anisotropy axes#

  • v1Kc = (0.707,0.707,0)

  • v2Kc = (0,0,1)

[5]:

angle = 45
sample.v1Kc = (np.sin(angle*np.pi/180),np.sin(angle*np.pi/180),0)
sample.v2Kc = (0,0,1)

[6]:

angle_ = np.linspace(0,360,181)
Bext = 300e-3
f0 = []
exp = tx.create_experimental_setup(sample,name="xz-plane")

for angle in angle_:
    sample.mag = tx.vectorfields.homogeneous(sample.xyz, angle, 0)
    exp.Bext = Bext*tx.vectorfields.homogeneous(sample.xyz, angle, 0)
    dispersion = exp.eigenmodes(num_cpus=-1,num_modes=2,k=0,save_modes=False,verbose=False)
    f0.append(dispersion.iloc[0]["f0 (GHz)"])

[7]:

plt.rcParams["figure.figsize"] = (8,6.5)
plt.figure()
plt.plot(angle_,f0, ls="", marker="o",label="xz-plane")
plt.legend()
plt.show()