def relax_system():
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-10, atol=1e-10)
sim.alpha = 0.1
sim.set_m((0, 0, 1))
sim.add(Zeeman((0, 0, 1e5)))
w0 = 2 * np.pi * 1e9
def sin_fun(t):
return np.sin(w0 * t)
h0 = 1e3
theta = np.pi / 20
hx = h0 * np.sin(theta)
hz = h0 * np.cos(theta)
hx = TimeZeeman([hx, 0, hz], sin_fun, name='h')
sim.add(hx, save_field=True)
ts = np.linspace(0, 5e-9, 5001)
for t in ts:
sim.run_until(t)
def relax_system():
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-10, atol=1e-10)
sim.alpha = 0.1
sim.set_m((0, 0, 1))
sim.add(Zeeman((0, 0, 1e5)))
w0 = 2 * np.pi * 1e9
def sin_fun(t):
return np.sin(w0 * t)
h0 = 1e3
theta = np.pi / 20
hx = h0 * np.sin(theta)
hz = h0 * np.cos(theta)
hx = TimeZeeman([hx, 0, hz], sin_fun, name='h')
sim.add(hx, save_field=True)
ts = np.linspace(0, 5e-9, 5001)
for t in ts:
sim.run_until(t)
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-10, atol=1e-14)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = spatial_Ms
sim.do_procession = False
sim.set_m(init_m)
# sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
mT = 795.7747154594767
ONE_DEGREE_PER_NS = 17453292.52
sim.relax(dt=1e-13, stopping_dmdt=0.01, max_steps=5000,
save_m_steps=100, save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def relax_system(mesh):
# Only relaxation
sim = Sim(mesh, name='relax')
# Simulation parameters
sim.set_tols(rtol=1e-8, atol=1e-10)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = 8.6e5
sim.do_precession = False
# The initial state passed as a function
sim.set_m(init_m)
# sim.set_m(np.load('m0.npy'))
# Energies
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
anis = UniaxialAnisotropy(5e4)
sim.add(anis)
# dmi = DMI(D=8e-4)
# sim.add(dmi)
# mT = 795.7747154594767
# ONE_DEGREE_PER_NS = 17453292.52
# Start relaxation and save the state in m0.npy
sim.relax(dt=1e-14, stopping_dmdt=0.00001, max_steps=5000,
save_m_steps=None, save_vtk_steps=None)
np.save('m0.npy', sim.spin)
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-6, atol=1e-6)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = 8.6e5
sim.do_precession = False
sim.set_m(init_m)
# sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
dmi = DMI(D=1.3e-3)
sim.add(dmi)
anis = UniaxialAnisotropy(-3.25e4, axis=(0, 0, 1))
sim.add(anis)
zeeman = Zeeman((0, 0, 6.014576e4))
sim.add(zeeman, save_field=True)
sim.relax(dt=1e-13, stopping_dmdt=1e-2, max_steps=5000,
save_m_steps=None, save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-10, atol=1e-14)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = spatial_Ms
sim.do_procession = False
sim.set_m(init_m)
# sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
mT = 795.7747154594767
ONE_DEGREE_PER_NS = 17453292.52
sim.relax(dt=1e-13,
stopping_dmdt=0.01,
max_steps=5000,
save_m_steps=100,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def apply_field1(mesh):
sim = Sim(mesh, name="dyn")
sim.set_tols(rtol=1e-10, atol=1e-10)
sim.alpha = 0.02
sim.gamma = 2.211e5
sim.Ms = 8.0e5
sim.set_m(np.load("m0.npy"))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
mT = 0.001 / mu0
print mT
zeeman = Zeeman([-24.6 * mT, 4.3 * mT, 0], name="H")
sim.add(zeeman, save_field=True)
ts = np.linspace(0, 1e-9, 201)
for t in ts:
sim.run_until(t)
print "sim t=%g" % t
def apply_field1(mesh):
sim = Sim(mesh, name='dyn')
sim.set_tols(rtol=1e-10, atol=1e-10)
sim.alpha = 0.02
sim.gamma = 2.211e5
sim.Ms = 8.0e5
sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
mT = 0.001 / mu0
print mT
zeeman = Zeeman([-24.6 * mT, 4.3 * mT, 0], name='H')
sim.add(zeeman, save_field=True)
ts = np.linspace(0, 1e-9, 201)
for t in ts:
sim.run_until(t)
print 'sim t=%g' % t
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-10, atol=1e-10)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = 8.0e5
sim.do_procession = False
sim.set_m((1, 0.25, 0.1))
# sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
sim.relax(dt=1e-13,
stopping_dmdt=0.01,
max_steps=5000,
save_m_steps=100,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def relax_system():
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-10, atol=1e-10)
sim.alpha = 0.5
sim.set_m((1.0, 0, 0))
sim.add(Zeeman((0, 0, 1e5)))
ts = np.linspace(0, 1e-9, 1001)
for t in ts:
sim.run_until(t)
def relax_system():
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-10, atol=1e-10)
sim.alpha = 0.5
sim.set_m((1.0, 0, 0))
sim.add(Zeeman((0, 0, 1e5)))
ts = np.linspace(0, 1e-9, 1001)
for t in ts:
sim.run_until(t)
def relax_system(mesh):
# Only relaxation
sim = Sim(mesh, name='relax')
# Simulation parameters
sim.set_tols(rtol=1e-8, atol=1e-10)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = 8.6e5
sim.do_precession = False
# The initial state passed as a function
sim.set_m(init_m)
# sim.set_m(np.load('m0.npy'))
# Energies
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
anis = UniaxialAnisotropy(5e4)
sim.add(anis)
# dmi = DMI(D=8e-4)
# sim.add(dmi)
# mT = 795.7747154594767
# ONE_DEGREE_PER_NS = 17453292.52
# Start relaxation and save the state in m0.npy
sim.relax(dt=1e-14,
stopping_dmdt=0.00001,
max_steps=5000,
save_m_steps=None,
save_vtk_steps=None)
np.save('m0.npy', sim.spin)
def excite_system(mesh):
# Specify the stt dynamics in the simulation
sim = Sim(mesh, name='dyn', driver='llg_stt')
sim.set_tols(rtol=1e-12, atol=1e-14)
sim.alpha = 0.05
sim.gamma = 2.211e5
sim.Ms = 8.6e5
# sim.set_m(init_m)
sim.set_m(np.load('m0.npy'))
# Energies
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
anis = UniaxialAnisotropy(5e4)
sim.add(anis)
# dmi = DMI(D=8e-4)
# sim.add(dmi)
# Set the current in the x direction, in A / m
# beta is the parameter in the STT torque
sim.jx = -1e12
sim.beta = 1
# The simulation will run for 5 ns and save
# 500 snapshots of the system in the process
ts = np.linspace(0, 5e-9, 501)
for t in ts:
print 'time', t
sim.run_until(t)
sim.save_vtk()
sim.save_m()
def excite_system(mesh):
# Specify the stt dynamics in the simulation
sim = Sim(mesh, name='dyn', driver='llg_stt')
sim.set_tols(rtol=1e-12, atol=1e-14)
sim.alpha = 0.05
sim.gamma = 2.211e5
sim.Ms = 8.6e5
# sim.set_m(init_m)
sim.set_m(np.load('m0.npy'))
# Energies
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
anis = UniaxialAnisotropy(5e4)
sim.add(anis)
# dmi = DMI(D=8e-4)
# sim.add(dmi)
# Set the current in the x direction, in A / m
# beta is the parameter in the STT torque
sim.jx = -1e12
sim.beta = 1
# The simulation will run for 5 ns and save
# 500 snapshots of the system in the process
ts = np.linspace(0, 5e-9, 501)
for t in ts:
print 'time', t
sim.run_until(t)
sim.save_vtk()
sim.save_m()
def relax_system(mesh):
sim = Sim(mesh, name="relax")
sim.set_tols(rtol=1e-10, atol=1e-10)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = 8.0e5
sim.do_procession = False
sim.set_m((1, 0.25, 0.1))
# sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
sim.relax(dt=1e-13, stopping_dmdt=0.01, max_steps=5000, save_m_steps=100, save_vtk_steps=50)
np.save("m0.npy", sim.spin)
def excite_system(mesh):
sim = Sim(mesh, name='dyn')
sim.set_tols(rtol=1e-10, atol=1e-14)
sim.alpha = 0.01
sim.gamma = 2.211e5
sim.Ms = spatial_Ms
# sim.set_m(init_m)
sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
mT = 795.7747154594767
sigma = 0.08e-9
def gaussian_fun(t):
return np.exp(-0.5 * (t / sigma)**2)
zeeman = TimeZeeman((80 * mT, 0, 0), time_fun=gaussian_fun, name='hx')
#zeeman = Zeeman((100*mT,0,0), name='hx')
sim.add(zeeman, save_field=True)
ts = np.linspace(0, 1e-9, 501)
for t in ts:
print 'time', t
print 'length:', sim.spin_length()[0:200]
sim.run_until(t)
sim.save_vtk()
def excite_system(mesh):
sim = Sim(mesh, name='dyn')
sim.set_tols(rtol=1e-10, atol=1e-14)
sim.alpha = 0.01
sim.gamma = 2.211e5
sim.Ms = spatial_Ms
# sim.set_m(init_m)
sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
mT = 795.7747154594767
sigma = 0.08e-9
def gaussian_fun(t):
return np.exp(-0.5 * (t / sigma)**2)
zeeman = TimeZeeman((80 * mT, 0, 0), time_fun=gaussian_fun, name='hx')
#zeeman = Zeeman((100*mT,0,0), name='hx')
sim.add(zeeman, save_field=True)
ts = np.linspace(0, 1e-9, 501)
for t in ts:
print 'time', t
print 'length:', sim.spin_length()[0:200]
sim.run_until(t)
sim.save_vtk()
def test_prb88_184422():
mu0 = 4 * np.pi * 1e-7
Ms = 8.6e5
A = 16e-12
D = 3.6e-3
K = 510e3
mesh = CuboidMesh(nx=100, dx=1, unit_length=1e-9)
sim = Sim(mesh)
sim.set_tols(rtol=1e-10, atol=1e-14)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = Ms
sim.do_precession = False
sim.set_m((0, 0, 1))
sim.add(UniformExchange(A))
sim.add(DMI(-D, type='interfacial'))
sim.add(UniaxialAnisotropy(K, axis=(0, 0, 1)))
sim.relax(dt=1e-13, stopping_dmdt=0.01, max_steps=5000,
save_m_steps=None, save_vtk_steps=50)
m = sim.spin
mx, my, mz = np.split(m, 3)
x_array = np.linspace(-49.5, 49.5, 100)
#plt.plot(x_array, mx)
#plt.plot(x_array, my)
#plt.plot(x_array, mz)
mesh = df.IntervalMesh(100, -50, 50)
Delta = np.sqrt(A / K)
xi = 2 * A / D
Delta_s = Delta * 1e9
V = df.FunctionSpace(mesh, "Lagrange", 1)
u = df.TrialFunction(V)
v = df.TestFunction(V)
u_ = df.Function(V)
F = -df.inner(df.nabla_grad(u), df.nabla_grad(v)) * df.dx - \
(0.5 / Delta_s**2) * df.sin(2 * u) * v * df.dx
F = df.action(F, u_)
J = df.derivative(F, u_, u)
# the boundary condition is from equation (8)
theta0 = np.arcsin(Delta / xi)
ss = 'x[0]<0? %g: %g ' % (-theta0, theta0)
u0 = df.Expression(ss)
def u0_boundary(x, on_boundary):
return on_boundary
bc = df.DirichletBC(V, u0, u0_boundary)
problem = df.NonlinearVariationalProblem(F, u_, bcs=bc, J=J)
solver = df.NonlinearVariationalSolver(problem)
solver.solve()
u_array = u_.vector().array()
mx_df = []
for x in x_array:
mx_df.append(u_(x))
#plt.plot(x_array, mx_df)
assert abs(np.max(mx - mx_df)) < 0.05
def test_prb88_184422():
mu0 = 4 * np.pi * 1e-7
Ms = 8.6e5
A = 16e-12
D = 3.6e-3
K = 510e3
mesh = CuboidMesh(nx=100, dx=1, unit_length=1e-9)
sim = Sim(mesh)
sim.set_tols(rtol=1e-10, atol=1e-14)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = Ms
sim.do_precession = False
sim.set_m((0, 0, 1))
sim.add(UniformExchange(A))
sim.add(DMI(-D, type='interfacial'))
sim.add(UniaxialAnisotropy(K, axis=(0, 0, 1)))
sim.relax(dt=1e-13,
stopping_dmdt=0.01,
max_steps=5000,
save_m_steps=None,
save_vtk_steps=50)
m = sim.spin
mx, my, mz = np.split(m, 3)
x_array = np.linspace(-49.5, 49.5, 100)
#plt.plot(x_array, mx)
#plt.plot(x_array, my)
#plt.plot(x_array, mz)
mesh = df.IntervalMesh(100, -50, 50)
Delta = np.sqrt(A / K)
xi = 2 * A / D
Delta_s = Delta * 1e9
V = df.FunctionSpace(mesh, "Lagrange", 1)
u = df.TrialFunction(V)
v = df.TestFunction(V)
u_ = df.Function(V)
F = -df.inner(df.nabla_grad(u), df.nabla_grad(v)) * df.dx - \
(0.5 / Delta_s**2) * df.sin(2 * u) * v * df.dx
F = df.action(F, u_)
J = df.derivative(F, u_, u)
# the boundary condition is from equation (8)
theta0 = np.arcsin(Delta / xi)
ss = 'x[0]<0? %g: %g ' % (-theta0, theta0)
u0 = df.Expression(ss)
def u0_boundary(x, on_boundary):
return on_boundary
bc = df.DirichletBC(V, u0, u0_boundary)
problem = df.NonlinearVariationalProblem(F, u_, bcs=bc, J=J)
solver = df.NonlinearVariationalSolver(problem)
solver.solve()
u_array = u_.vector().array()
mx_df = []
for x in x_array:
mx_df.append(u_(x))
#plt.plot(x_array, mx_df)
assert abs(np.max(mx - mx_df)) < 0.05