def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.driver.set_tols(rtol=1e-10, atol=1e-10)
sim.driver.alpha = 0.1
sim.driver.gamma = 2.211e5
sim.Ms = spatial_Ms
print(sim.Ms)
sim.set_m(init_m)
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
dmi = DMI(D=4e-3)
sim.add(dmi)
dmi2 = DMI(D=2e-3, dmi_type="interfacial")
sim.add(dmi2)
anis = UniaxialAnisotropy(-3e4, axis=(0, 0, 1))
sim.add(anis)
sim.relax(dt=1e-13,
stopping_dmdt=5e4,
max_steps=5000,
save_m_steps=100,
save_vtk_steps=50)
#np.save('m0.npy', sim.spin)
fd = demag.compute_field(sim.spin)
fe = exch.compute_field(sim.spin)
fdmi = dmi.compute_field(sim.spin)
fdmi2 = dmi2.compute_field(sim.spin)
fanis = anis.compute_field(sim.spin)
np.savetxt(
"test_fields.txt",
np.transpose([
np.concatenate((sim.Ms, sim.Ms, sim.Ms, [0.0])),
np.concatenate((sim.spin, [100])),
np.concatenate((fd, [demag.compute_energy()])),
np.concatenate((fe, [exch.compute_energy()])),
np.concatenate((fdmi, [dmi.compute_energy()])),
np.concatenate((fdmi2, [dmi2.compute_energy()])),
np.concatenate((fanis, [anis.compute_energy()]))
]),
header=
"Generated by Fidimag. Size=20x5x3, 2.5nm x 2.5nm x 3nm, Ms=8.0e5A/m, A=1.3e-11 J/m,"
+
" D=4e-3 J/m^2, D_int=2e-3 J/m^2, Ku=-3e4 J/m^3 axis=(0,0,1).\n Ms "
+ "".ljust(20) + " m0 " + "".ljust(20) + "demag" + "".ljust(20) +
"exch" + "".ljust(22) + "dmi" + "".ljust(22) + "dmi_interfacial" +
"".ljust(22) + "anis")
def test_dw_dmi(mesh=mesh, do_plot=False):
Ms = 8.0e5
sim = Sim(mesh, name='relax')
sim.set_m(m_init_dw)
sim.set_tols(rtol=1e-8, atol=1e-12)
sim.Ms = Ms
sim.alpha = 0.5
sim.do_precession = False
A = 1.3e-11
D = 4e-4
Kx = 8e4
Kp = -6e5
sim.add(UniformExchange(A))
sim.add(DMI(D))
sim.add(UniaxialAnisotropy(Kx, axis=[1, 0, 0], name='Kx'))
sim.relax(stopping_dmdt=0.01)
xs = np.array([p[0] for p in mesh.coordinates])
mx, my, mz = analytical(xs, A=A, D=D, K=Kx)
mxyz = sim.spin.copy()
mxyz = mxyz.reshape(-1, 3)
assert max(abs(mxyz[:, 0] - mx)) < 0.002
assert max(abs(mxyz[:, 1] - my)) < 0.002
assert max(abs(mxyz[:, 2] - mz)) < 0.0006
if do_plot:
save_plot(mxyz, mx, my, mz)
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((0,0.1,1))
#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=0.5,
max_steps=5000,
save_m_steps=None,
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_procession = 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)
# 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 run_fidimag(mesh):
mu0 = 4 * np.pi * 1e-7
Ms = 8.6e5
A = 16e-12
D = -3.6e-3
K = 510e3
sim = Sim(mesh)
sim.set_tols(rtol=1e-10, atol=1e-10)
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
return m.copy()
def relax_neb(k, maxst, simname, init_im, interp, save_every=10000,
coordinates='Cartesian'):
"""
Execute a simulation with the NEB function of the FIDIMAG code, for an
elongated particle (long cylinder)
The simulations are made for a specific spring constant 'k' (a float),
number of images 'init_im', interpolations between images 'interp'
(an array) and a maximum of 'maxst' steps.
'simname' is the name of the simulation, to distinguish the
output files.
--> vtks and npys are saved in files starting with the 'simname' string
"""
# Prepare simulation
# We define the cylinder with the Magnetisation function
sim = Sim(mesh)
sim.Ms = two_part
# sim.add(UniformExchange(A=A))
# Uniaxial anisotropy along x-axis
sim.add(UniaxialAnisotropy(Kx, axis=(1, 0, 0)))
# Define many initial states close to one extreme. We want to check
# if the images in the last step, are placed mostly in equally positions
init_images = init_im
# Number of images between each state specified before (here we need only
# two, one for the states between the initial and intermediate state
# and another one for the images between the intermediate and final
# states). Thus, the number of interpolations must always be
# equal to 'the number of initial states specified', minus one.
interpolations = interp
if coordinates == 'Spherical':
neb = NEBM_Spherical(sim,
init_images,
interpolations=interpolations,
spring_constant=k,
name=simname
)
if coordinates == 'Geodesic':
neb = NEBM_Geodesic(sim,
init_images,
interpolations=interpolations,
spring_constant=k,
name=simname,
integrator='sundials'
)
neb.relax(max_iterations=2000,
save_vtks_every=save_every,
save_npys_every=save_every,
stopping_dYdt=1e-4,
dt=1e-6
)
def elongated_part_sim():
sim = Sim(mesh)
sim.Ms = lambda r: cylinder(r, centre, 8)
sim.add(UniformExchange(A=A))
sim.add(UniaxialAnisotropy(Kx, axis=(0, 1, 0))) # Anisotropy along y
sim.add(Demag())
return sim
def setup_domain_wall_cobalt(node_count=NODE_COUNT, A=A_Co, Ms=Ms_Co, K1=K1_Co, length=LENGTH, do_precession=True, unit_length=UNIT_LENGTH):
a = length / node_count # cell size
mesh = CuboidMesh(dx=a, dy=a, dz=a, nx=node_count, ny=1, nz=1, unit_length=unit_length)
sim = Sim(mesh, "dw_cobalt")
sim.Ms = Ms
sim.set_m(lambda r: initial_m(r, length))
sim.do_precession = do_precession
sim.add(UniformExchange(A))
sim.add(UniaxialAnisotropy(K1, (0, 0, 1)))
sim.pins = lambda r: 1 if (r[0] < a or r[0] > LENGTH - a) else 0
return sim
def create_simulation(mesh):
sim = Sim(mesh)
sim.Ms = 8.6e5
sim.set_m((1, 0, 0))
sim.add(UniformExchange(A=1.3e-11))
# sim.add(Demag())
#sim.add(UniaxialAnisotropy(Kx, (1, 0, 0), name='Kx'))
anis = UniaxialAnisotropy(1e5, axis=(1, 0, 0))
sim.add(anis)
return sim
def test_sim_pin():
mesh = CuboidMesh(nx=3, ny=2, nz=1)
sim = Sim(mesh, integrator='sundials_openmp')
sim.set_m((0, 0.8, 0.6))
sim.alpha = 0.1
sim.driver.gamma = 1.0
sim.pins = pin_fun
anis = UniaxialAnisotropy(Ku=1, axis=[0, 0, 1], name='Dx')
sim.add(anis)
sim.driver.run_until(1.0)
print(sim.spin)
assert sim.spin[0] == 0
assert sim.spin[2] != 0
def test_sim_pin():
mesh = CuboidMesh(nx=3, ny=2, nz=1)
sim = Sim(mesh)
sim.set_m((0, 0.8, 0.6))
sim.alpha = 0.1
sim.gamma = 1.0
sim.pins = pin_fun
anis = UniaxialAnisotropy(Ku=1, axis=[0, 0, 1], name='Dx')
sim.add(anis)
sim.run_until(1.0)
print sim.spin
assert sim.spin[0] == 0
assert sim.spin[2] != 0
def excite_system(mesh, beta=0.0):
# Specify the stt dynamics in the simulation
sim = Sim(mesh, name='dyn_%g' % beta, driver='llg_stt_cpp')
sim.driver.set_tols(rtol=1e-12, atol=1e-12)
sim.driver.alpha = 0.1
sim.driver.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)
# beta is the parameter in the STT torque
sim.a_J = global_const * 1e11
sim.p = (1, 0, 0)
sim.beta = beta
# The simulation will run for 5 ns and save
# 500 snapshots of the system in the process
ts = np.linspace(0, 0.5e-9, 21)
xs = []
thetas = []
for t in ts:
print('time', t)
sim.run_until(t)
spin = sim.spin.copy()
x, theta = extract_dw(spin)
xs.append(x)
thetas.append(theta)
sim.save_vtk()
np.savetxt('dw_%g.txt' % beta, np.transpose(np.array([ts, xs, thetas])))
def excite_system(mesh):
# Specify the stt dynamics in the simulation
sim = Sim(mesh, name='dyn2', driver='llg_stt')
sim.driver.set_tols(rtol=1e-12, atol=1e-14)
sim.driver.alpha = 0.2
sim.driver.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
def jx_func(pos, t):
T = 1e-9
return (-1e12 + -0.1e12 * np.sin(t / T))
sim.driver.jx_function = jx_func
sim.driver.beta = 0.01
# The simulation will run for 5 ns and save
# 500 snapshots of the system in the process
ts = np.linspace(0, 10e-9, 1001)
for t in ts:
print('time', t)
sim.driver.run_until(t)
print('j = {}'.format(sim.driver._jx[0]))
sim.save_vtk()
sim.save_m()
def relax_string(maxst, simname, init_im, interp, save_every=10000):
"""
"""
# Prepare simulation
# We define the cylinder with the Magnetisation function
sim = Sim(mesh)
sim.Ms = two_part
# sim.add(UniformExchange(A=A))
# Uniaxial anisotropy along x-axis
sim.add(UniaxialAnisotropy(Kx, axis=(1, 0, 0)))
# Define many initial states close to one extreme. We want to check
# if the images in the last step, are placed mostly in equally positions
init_images = init_im
# Number of images between each state specified before (here we need only
# two, one for the states between the initial and intermediate state
# and another one for the images between the intermediate and final
# states). Thus, the number of interpolations must always be
# equal to 'the number of initial states specified', minus one.
interpolations = interp
string = StringMethod(sim,
init_images,
interpolations=interpolations,
name=simname,
integrator='verlet')
string.integrator.stepsize = 1e-4
# dt = integrator.stepsize means after every integrator step, the images
# are rescaled. We can run more integrator steps if we decrease the
# stepsize, e.g. dt=1e-3 and integrator.stepsize=1e-4
string.relax(max_iterations=maxst,
save_vtks_every=save_every,
save_npys_every=save_every,
stopping_dYdt=1e-14,
dt=1e-4)
return string
def excite_system(mesh, time=5, snaps=501):
# Specify the stt dynamics in the simulation
sim = Sim(mesh, name='dyn', driver='llg_stt')
# Set the simulation parameters
sim.set_tols(rtol=1e-12, atol=1e-14)
sim.alpha = 0.05
sim.gamma = 2.211e5
sim.Ms = 8.6e5
# Load the initial state from the npy file saved
# in the realxation
sim.set_m(np.load('m0.npy'))
# Add the 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 x ns and save
# 'snaps' snapshots of the system in the process
ts = np.linspace(0, time * 1e-9, snaps)
for t in ts:
print 'time', t
sim.run_until(t)
sim.save_vtk()
sim.save_m()
sim.Ms = args.Ms
exch = UniformExchange(A=args.A)
sim.add(exch)
dmi = DMI(D=(args.D * 1e-3), type='interfacial')
sim.add(dmi)
if args.B:
zeeman = Zeeman((0, 0, args.B / mu0))
sim.add(zeeman, save_field=True)
if args.k_u:
# Uniaxial anisotropy along + z-axis
sim.add(UniaxialAnisotropy(args.k_u, axis=(0, 0, 1)))
if args.Demag:
print 'Using Demag!'
sim.add(Demag())
# -------------------------------------------------------------------------
# Load magnetisation profile ---------------------------------------------
# Change the skyrmion initial configuration according to the
# chirality of the system (give by the DMI constant)
if args.initial_state_skyrmion_down:
if args.D > 0:
sim.set_m(lambda x: generate_skyrmion_down(x, -1))
else:
