Domain wall motion with surface acoustic waves

In this example we move a domain wall by setting a time and space dependent strain in a ferromagnet to simulate the effect of a SAW wave. This is based on the method used here.

import numpy as np
import matplotlib.pyplot as plt
from tqdm import tqdm

from mumaxplus import World, Grid, Ferromagnet
from mumaxplus.util import twodomain

# simulation time
run = 10e-9
steps = 1000
dt = run/steps

# simulation grid parameters
nx, ny, nz = 256, 512, 1
cx, cy, cz = 2.4e-9, 2.4e-9, 1e-9

# create a world and a magnet
cellsize = (cx, cy, cz)
grid = Grid((nx, ny, nz))
world = World(cellsize)
magnet = Ferromagnet(world, grid)

# setting magnet parameters
magnet.msat = 6e5
magnet.aex = 1e-11
magnet.alpha = 0.01
magnet.ku1 = 8e5
magnet.anisU = (0,0,1)

# setting DMI to stabilize the DW
magnet.dmi_tensor.set_interfacial_dmi(1e-3)

# Create a DW
magnet.magnetization = twodomain((0,0,1), (-1,0,0), (0,0,-1), nx*cx/3, 5*cx)

print("minimizing...")
magnet.minimize()  # minimize

# magnetoelastic coupling constants
magnet.B1 = -1.5e7
magnet.B2 = 0

# amplitude, angular frequency and wave vector of the strain
E = 6e-3
w = 200e6 * 2*np.pi
k = 4000 / w

# normal stain, given by exx = E [sin(wt)*cos(kx) - cos(wt)*sin(kx)]
# Create the first time term
magnet.rigid_norm_strain.add_time_term(lambda t: (np.sin(w*t), 0., 0.),
                                       lambda x,y,z: (E*np.cos(k*x), 0., 0.))
# Add the second time term
magnet.rigid_norm_strain.add_time_term(lambda t: (np.cos(w*t), 0., 0.),
                                       lambda x,y,z: (-E*np.sin(k*x), 0., 0.))

# plot the initial and final magnetization
fig, axs = plt.subplots(nrows=1, ncols=2, sharex="all", sharey="all")
ax1, ax2 = axs
im_extent = (-0.5*cx*1e6, (nx*cx - 0.5*cx)*1e6, -0.5*cy*1e6, (ny*cy - 0.5*cy)*1e6)

# initial magnetization
ax1.imshow(np.transpose(magnet.magnetization.get_rgb()[:,0,:,:], axes=(1,2,0)), origin="lower", extent=im_extent, aspect="equal")
ax1.set_title("Initial magnetization")
ax2.set_title("Final magnetization")
ax1.set_xlabel("x (µm)")
ax2.set_xlabel("x (µm)")
ax1.set_ylabel("y (µm)")

# function to estimate the position of the DW
def DW_position(magnet):
    m_av = magnet.magnetization.average()[2]
    return m_av*nx*cx / 2 + nx*cx/2

# run the simulation and save the DW postion
DW_pos = np.zeros(shape=(steps+1))
DW_pos[0] = DW_position(magnet)
time = np.zeros(shape=(steps+1))
time[0] = world.timesolver.time

print("running...")
for i in tqdm(range(1, steps+1)):
    world.timesolver.run(dt)
    DW_pos[i] = DW_position(magnet)
    time[i] = world.timesolver.time
print("done!")

# final magnetization
ax2.imshow(np.transpose(magnet.magnetization.get_rgb()[:,0,:,:], axes=(1,2,0)),
           origin="lower", extent=im_extent, aspect="equal")

plt.show()

# plot DW position in function of time
plt.plot(time*1e9, DW_pos*1e6)
plt.xlabel("Time (ns)")
plt.ylabel("Domain wall position (µm)")
plt.title("Domain wall position in time")
plt.show()