def test_spatially_varying_anisotropy_axis(tmpdir, debug=False):
Ms = 1e6
A = 1.3e-11
K1 = 6e5
lb = bloch_parameter(A, K1)
unit_length = 1e-9
nx = 20
Lx = nx * lb / unit_length
mesh = df.IntervalMesh(nx, 0, Lx)
# anisotropy axis goes from (0, 1, 0) at x=0 to (1, 0, 0) at x=Lx
expr_a = df.Expression(("x[0] / sqrt(pow(x[0], 2) + pow(Lx-x[0], 2))",
"(Lx-x[0]) / sqrt(pow(x[0], 2) + pow(Lx-x[0], 2))",
"0"), Lx=Lx, degree=1)
# in theory, a discontinuous Galerkin (constant over the cell) is a good
# choice to represent material parameters. In this case though, the
# parameter varies linearly, so we use the usual CG.
V = df.VectorFunctionSpace(mesh, "CG", 1, dim=3)
a = Field(V, expr_a)
sim = Simulation(mesh, Ms, unit_length)
sim.set_m((1, 1, 0))
sim.add(UniaxialAnisotropy(K1, a))
sim.relax()
# probe the easy axis and the magnetisation along the interval
points = 100
xs = np.linspace(0, Lx, points)
axis_xs = np.zeros((points, 3))
m_xs = np.zeros((points, 3))
for i, x in enumerate(xs):
axis_xs[i] = a(x)
m_xs[i] = sim.m_field(x)
# we want to the magnetisation to follow the easy axis
# it does so, except at x=0, what is happening there?
diff = np.abs(m_xs - axis_xs)
assert diff.max() < 0.02
if debug:
old = os.getcwd()
os.chdir(tmpdir)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(xs, axis_xs[:, 0], "b+", label="a_x")
ax.plot(xs, m_xs[:, 0], "r--", label="m_x")
ax.legend(loc="upper left")
ax.set_ylim((0, 1.05))
ax.set_xlabel("x (nm)")
plt.savefig('spatially_varying_easy_axis.png')
plt.close()
sim.m_field.save_pvd('spatially_varying_easy_axis.pvd')
os.chdir(old)
def run_simulation(plot=False):
mu0 = 4.0 * np.pi * 10**-7 # vacuum permeability N/A^2
Ms = 1.0e6 # saturation magnetisation A/m
A = 13.0e-12 # exchange coupling strength J/m
Km = 0.5 * mu0 * Ms**2 # magnetostatic energy density scale kg/ms^2
lexch = (A / Km)**0.5 # exchange length m
unit_length = 1e-9
K1 = Km
L = lexch / unit_length
nx = 10
Lx = nx * L
ny = 1
Ly = ny * L
nz = 30
Lz = nz * L
mesh = df.BoxMesh(df.Point(0, 0, 0), df.Point(Lx, Ly, Lz), nx, ny, nz)
# Anisotropy easy axis is (0, 0, 1) in the lower half of the film and
# (1, 0, 0) in the upper half. This is a toy model of the exchange spring
# systems that Bob Stamps is working on.
boundary = Lz / 2.0
expr_a = df.Expression(("x[2] <= b ? 0 : 1", "0", "x[2] <= b ? 1 : 0"),
b=boundary,
degree=1)
V = df.VectorFunctionSpace(mesh, "DG", 0, dim=3)
a = Field(V, expr_a)
sim = Simulation(mesh, Ms, unit_length)
sim.set_m((1, 0, 1))
sim.add(UniaxialAnisotropy(K1, a))
sim.add(Exchange(A))
sim.relax()
if plot:
points = 200
zs = np.linspace(0, Lz, points)
axis_zs = np.zeros((points, 3)) # easy axis probed along z-axis
m_zs = np.zeros((points, 3)) # magnetisation probed along z-axis
for i, z in enumerate(zs):
axis_zs[i] = a((Lx / 2.0, Ly / 2.0, z))
m_zs[i] = sim.m_field((Lx / 2.0, Ly / 2.0, z))
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(zs, axis_zs[:, 0], "-o", label="a_x")
ax.plot(zs, axis_zs[:, 2], "-x", label="a_z")
ax.plot(zs, m_zs[:, 0], "-", label="m_x")
ax.plot(zs, m_zs[:, 2], "-", label="m_z")
ax.set_xlabel("z (nm)")
ax.legend(loc="upper left")
plt.savefig(os.path.join(MODULE_DIR, "profile.png"))
sim.m_field.save_pvd(os.path.join(MODULE_DIR, 'exchangespring.pvd'))
