def test_mesh1():
mesh = CuboidMesh(nx=5, ny=3, nz=2, dx=0.23, dy=0.41)
assert len(mesh.coordinates) == 5 * 3 * 2
assert mesh.ny * mesh.nz == 6
assert tuple(mesh.coordinates[mesh.index(0, 0, 0)]) == (0.23 / 2, 0.41 / 2, 0.5)
assert tuple(mesh.coordinates[mesh.index(3, 2, 1)]) == (
(3 + 0.5) * 0.23, (2 + 0.5) * 0.41, 1 + 0.5)
def disable_test_sim_single_spin_llg_stt(do_plot=False):
ni = Nickel()
mesh = CuboidMesh(nx=1, ny=1, nz=1)
mesh.set_material(ni)
ni.alpha = 0.1
sim = Sim(mesh, driver='llg_stt')
sim.set_m((1, 0, 0))
H0 = 1
sim.add(Zeeman((0, 0, H0)))
dt = 1e-12
ts = np.linspace(0, 200 * dt, 101)
precession = ni.gamma / (1 + ni.alpha**2)
mz_ref = []
mxyz = []
real_ts = []
for t in ts:
sim.run_until(t)
real_ts.append(sim.t)
print(sim.t, abs(sim.spin_length()[0] - 1), sim.spin)
mz_ref.append(np.tanh(precession * ni.alpha * H0 * sim.t))
mxyz.append(np.copy(sim.spin))
mxyz = np.array(mxyz)
if do_plot:
ts_ns = np.array(real_ts) * 1e9
plt.plot(ts_ns, mxyz[:, 0], ".-", label="mx")
plt.plot(ts_ns, mxyz[:, 1], ".-", label="my")
plt.plot(ts_ns, mxyz[:, 2], ".-", label="mz")
plt.plot(ts_ns, mz_ref, "-", label="analytical")
plt.xlabel("time (ns)")
plt.ylabel("mz")
plt.title("integrating a macrospin")
plt.legend()
plt.savefig("test_llg_stt.png")
print(("Deviation = {0}".format(np.max(np.abs(mxyz[:, 2] - mz_ref)))))
assert np.max(np.abs(mxyz[:, 2] - mz_ref)) < 1e-9
def test_demag_fft_exact_oommf():
mesh = CuboidMesh(nx=5, ny=3, nz=2)
sim = Sim(mesh)
demag = Demag()
sim.add(demag)
def init_m(pos):
x = pos[0]
if x <= 2:
return (1, 0, 0)
elif x >= 4:
return (0, 0, 1)
else:
return (0, 1, 0)
sim.set_m(init_m)
fft = demag.compute_field()
exact = demag.compute_exact()
# print fft,exact
print np.max(np.abs(fft - exact))
assert np.max(np.abs(fft - exact)) < 1e-15
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_sim():
mesh = CuboidMesh(nx=121, ny=121, nz=1)
sim = Sim(mesh, name='relax')
sim.alpha = 1.0
sim.gamma = 0.5
sim.mu_s = mu_s
sim.set_m(init_m)
J = 1.0
exch = UniformExchange(J)
sim.add(exch)
D = 0.08
dmi = DMI(D)
sim.add(dmi)
K = 4e-3
anis = Anisotropy(K, direction=(0, 0, 1), name='Ku')
sim.add(anis)
return sim
def test_compute_field():
"""In an infinite film, we expect the demag tensor to be (0, 0, -1), and thus the
magnetisation, if aligned in 0, 0, 1 direction, to create a demag field pointing
with equal strength in the opposite direction.
"""
mesh = CuboidMesh(nx=1, ny=1, nz=1, dx=2.0, dy=2.0, dz=2.0,
unit_length=1e-9, periodicity=(True, True, False))
sim = Sim(mesh, name='relax')
sim.driver.set_tols(rtol=1e-10, atol=1e-14)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = 8.6e5
sim.do_precession = False
sim.set_m((0, 0, 1))
demag = Demag(pbc_2d=True)
sim.add(demag)
field = demag.compute_field()
print((1 + field[2] / 8.6e5))
assert abs(1 + field[2] / 8.6e5) < 1e-10
import numpy as np
from fidimag.common import CuboidMesh
from fidimag.micro import Sim
from fidimag.micro import UniformExchange
from fidimag.micro import UniaxialAnisotropy
from fidimag.micro import DMI
import matplotlib.pyplot as plt
mesh = CuboidMesh(dx=2, nx=150, x0=-150, unit_length=1e-9)
def m_init_dw(pos):
x = pos[0]
if x < -10:
return (1, 0, 0)
elif x > 10:
return (-1, 0, 0)
else:
return (0, 1, 0)
def analytical(xs, A=1.3e-11, D=4e-4, K=8e4):
delta = np.sqrt(A / (K - D * D / (4 * A))) * 1e9
phi = D / (2 * A) * xs * 1e-9
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
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)
if __name__ == '__main__':
mesh = CuboidMesh(nx=501,
ny=501,
nz=1,
dx=2.0,
dy=2.0,
dz=2.0,
unit_length=1e-9,
periodicity=(True, True, False))
#relax_system(mesh)
relax_system_only_exchange(mesh)
# apply_field1(mesh)
# deal_plot()
def simulation(nx,
ny,
nz,
dx,
dy,
dz,
j,
d,
kc,
bz,
mu_s,
sim_name,
add_image=None,
add_interpolations=None,
add_images_folder=None,
stopping_dydt=None,
max_steps=None,
save_m_every=None,
integrator='sundials',
integrator_stepsize=1e-3,
interpolation_method='rotation',
variable_spring_forces=None,
interpolation_energy='polynomial'):
if add_interpolations:
if (len(add_image) - 1) != len(add_interpolations):
raise Exception('(N interpolations) != (N images - 1)')
mesh = CuboidMesh(nx=nx,
ny=ny,
nz=nz,
dx=dx,
dy=dy,
dz=dz,
x0=-nx * 0.5,
y0=-ny * 0.5,
z0=-nz * 0.5,
unit_length=1.,
periodicity=(True, True, False))
# Simulation
sim = Sim(mesh, name=sim_name)
sim.mu_s = mu_s
sim.add(Exchange(j))
sim.add(DMI(d, dmi_type='bulk'))
sim.add(Zeeman((0.0, 0.0, bz * 1e-3)))
if np.abs(kc) > 0.0:
sim.add(CubicAnisotropy(kc))
# GNEBM simulation ........................................................
if add_interpolations:
# Set the initial images from the list
init_images = [np.load(image) for image in add_image]
interpolations = [i for i in add_interpolations]
elif add_images_folder:
if add_images_folder.endswith('_LAST'):
dir_list = glob.glob(add_images_folder[:-5] + '*')
dir_list = sorted(
dir_list,
key=lambda f: int(re.search(r'(?<=_)[0-9]+$', f).group(0)))
add_images_folder = dir_list[-1]
flist = sorted(os.listdir(add_images_folder))
init_images = [
np.load(os.path.join(add_images_folder, image)) for image in flist
]
interpolations = []
else:
raise Exception('Specify an option to add images')
# Start a NEB simulation passing the Simulation object and all the NEB
# parameters
string = StringMethod(sim,
init_images,
interpolations=interpolations,
name=sim_name,
openmp=True,
integrator=integrator,
interpolation_method=interpolation_method)
if integrator == 'verlet':
string.integrator.mass = 1
string.integrator.stepsize = integrator_stepsize
dt = integrator_stepsize * 10
else:
dt = integrator_stepsize
# .........................................................................
for fdir in ['interpolations', 'ndts']:
if not os.path.exists(fdir):
os.makedirs(fdir)
# Finally start the energy band relaxation
string.relax(max_iterations=max_steps,
save_vtks_every=save_m_every,
save_npys_every=save_m_every,
stopping_dYdt=stopping_dydt,
dt=dt)
# Produce a file with the data from a cubic interpolation for the band
interp_data = np.zeros((200, 2))
if interpolation_energy == 'polynomial':
string.compute_polynomial_factors()
(interp_data[:, 0],
interp_data[:,
1]) = string.compute_polynomial_approximation_energy(200)
elif interpolation_energy == 'Bernstein':
string.compute_Bernstein_polynomials()
(interp_data[:, 0],
interp_data[:,
1]) = string.compute_Bernstein_approximation_energy(200)
else:
raise Exception('No valid interpolation method')
np.savetxt('interpolations/{}_interpolation.dat'.format(sim_name),
interp_data)
# Clean files
shutil.move(sim_name + '_energy.ndt',
'ndts/{}_energy.ndt'.format(sim_name))
shutil.move(sim_name + '_dYs.ndt', 'ndts/{}_dYs.ndt'.format(sim_name))
qx = np.fft.fftfreq(nx,dx)*2*np.pi
qy = np.fft.fftfreq(ny,dy)*2*np.pi
qx = np.fft.fftshift(qx)
qy = np.fft.fftshift(qy)
plt.figure(figsize=(5,5))
#plt.imshow(np.abs(Mz)**2, aspect=1, interpolation='none', origin='lower', extent=(qx.min(), qx.max(), qy.min(), qy.max()))
plt.imshow(np.abs(Mz)**2, aspect=1, origin='lower', extent=(qx.min(), qx.max(), qy.min(), qy.max()))
#plt.axis('equal')
plt.xlim(-0.5, 0.5)
plt.ylim(-0.5, 0.5)
plt.xlabel('qx (1/nm)')
plt.ylabel('qy (1/nm)')
plt.tight_layout()
plt.savefig('skx.png')
if __name__ == '__main__':
mesh = CuboidMesh(nx=Rx*2, ny=Ry, nz=1, dx=1.0, dy=1.0, dz=1.0, unit_length=1e-9, periodicity = (True, True, False))
relax_system(mesh)
plot_mz()
do_fft()
#sim.save_vtk()
def save_plot():
data = DataReader('dyn_K.txt')
ts = data['time']
xs = data['m_x']
fig = plt.figure()
plt.plot(ts, xs)
data = DataReader('dyn_D.txt')
ts = data['time']
xs = data['m_x']
plt.plot(ts, xs, '+')
fig.savefig('test.pdf')
if __name__ == "__main__":
mesh = CuboidMesh(nx=1000, ny=1, nz=1, dx=2, dy=2, dz=2, unit_length=1e-9)
relax_system(mesh)
excite_system_D(mesh)
excite_system_K(mesh)
save_plot()
def simulation(nx,
ny,
nz,
dx,
dy,
dz,
j,
d,
kc,
mu_s,
sim_name,
bz_min,
bz_max,
bz_steps,
bz_hysteresis=False,
initial_state_one_bobber=None,
initial_state_two_bobbers=None,
initial_state_two_bobbers_asymm=None,
initial_state_sk_tube=None,
initial_state_one_dim_mod=None,
initial_state_helix_angle_x=(None, None),
stopping_dmdt=1e-5,
max_steps=4000,
save_initial_state=None):
mesh = CuboidMesh(nx=nx,
ny=ny,
nz=nz,
dx=dx,
dy=dy,
dz=dz,
x0=-nx * 0.5,
y0=-ny * 0.5,
z0=-nz * 0.5,
unit_length=1.,
periodicity=(True, True, False))
# J = 1.
# D = 0.628 # L_D = 2 PI a J / D = 10 * a => D / J = 2 PI / 10.
# Bz = 0.2 # B_z == (B_z mu_s / J)
# mu_s = 1.
sim = Sim(mesh, name=sim_name, integrator='sundials_openmp')
sim.mu_s = mu_s
sim.add(Exchange(j))
sim.add(DMI(d, dmi_type='bulk'))
sim.add(Zeeman((0.0, 0.0, bz_min * 1e-3)), save_field=True)
if np.abs(kc) > 0.0:
sim.add(CubicAnisotropy(kc))
# .........................................................................
sim.driver.alpha = 0.9
sim.driver.do_precession = False
if not os.path.exists('npys/{}'.format(sim_name)):
os.makedirs('npys/{}'.format(sim_name))
if not os.path.exists('txts'):
os.makedirs('txts')
for i, B_sweep in enumerate(np.linspace(bz_min, bz_max, bz_steps)):
print('Bz = {:.0f} mT '.format(B_sweep).ljust(80, '-'))
Zeeman_int = sim.get_interaction('Zeeman')
Zeeman_int.update_field((0.0, 0.0, B_sweep * 1e-3))
if (not bz_hysteresis) or (bz_hysteresis and i < 1):
if initial_state_one_dim_mod:
sim.set_m(lambda r: one_dim_mod(r, B_sweep * 1e-3, d))
elif initial_state_helix_angle_x[0]:
angle = initial_state_helix_angle_x[0] * np.pi / 180.
periodic = initial_state_helix_angle_x[1]
sim.set_m(lambda r: helix_angle_x(r, angle, periodic))
elif initial_state_sk_tube:
sk_rad = initial_state_sk_tube
sim.set_m(
lambda r: sk_tube(r, B_sweep * 1e-3, d, sk_rad=sk_rad))
elif initial_state_two_bobbers:
bobber_length = initial_state_two_bobbers
sim.set_m(lambda r: two_bobbers(r,
B_sweep * 1e-3,
d,
mesh.Lz,
bobber_rad=3.,
bobber_length=bobber_length))
elif initial_state_two_bobbers_asymm:
bobber_length = initial_state_two_bobbers_asymm
sim.set_m(
lambda r: two_bobbers_asymm(r,
B_sweep * 1e-3,
d,
mesh.Lz,
bobber_rad=3.,
bobber_length=bobber_length))
elif initial_state_one_bobber:
bobber_length = initial_state_one_bobber
sim.set_m(lambda r: one_bobber(r,
B_sweep * 1e-3,
d,
mesh.Lz,
bobber_rad=3.,
bobber_length=bobber_length))
else:
raise Exception('Not a valid initial state')
if save_initial_state:
save_vtk(sim, sim_name + '_INITIAL', field_mT=B_sweep)
name = 'npys/{}/m_{}_INITIAL_Bz_{:06d}.npy'.format(
sim.driver.name, sim_name, int(B_sweep))
np.save(name, sim.spin)
# .....................................................................
sim.relax(stopping_dmdt=stopping_dmdt,
max_steps=max_steps,
save_m_steps=None,
save_vtk_steps=None)
# .....................................................................
save_vtk(sim, sim_name, field_mT=B_sweep)
name = 'npys/{}/m_{}_Bz_{:06d}.npy'.format(sim.driver.name, sim_name,
int(B_sweep))
np.save(name, sim.spin)
sim.driver.reset_integrator()
shutil.move(sim_name + '.txt', 'txts/{}.txt'.format(sim_name))
sim.mu_s = const.mu_s_1
sim.T = temperature_gradient
sim.set_m(np.load("m0.npy"))
J = 50.0 * const.k_B
exch = UniformExchange(J)
sim.add(exch)
D = 0.5 * J
dmi = DMI(D)
sim.add(dmi)
Hz = 0.2 * J / const.mu_s_1
zeeman = Zeeman([0, 0, Hz])
sim.add(zeeman)
dt = 2e-14 * 50 # 1e-12
ts = np.linspace(0, 1000 * dt, 501)
for t in ts:
sim.run_until(t)
sim.save_vtk()
sim.save_m()
print 'sim t=%g' % t
if __name__ == '__main__':
mesh = CuboidMesh(nx=150, ny=50, nz=1, periodicity=(True, True, False))
relax_system(mesh)
#excite_system(mesh)
def cylinder(pos):
# Relative position
x, y = pos[0] - radius, pos[1] - radius
if x**2 + y**2 < radius**2:
return Ms
else:
return 0
# We will generate a 50 nm wide and 5nm thick disk The finite difference
# elements are 2nmx2nm cubes along the disk plane and they have a thickness of
# 1 nm
# Finite differences mesh
mesh = CuboidMesh(nx=25, ny=25, nz=5, dx=2, dy=2, dz=1, unit_length=1e-9)
# Initial magnetisation profile to get the skyrmion
# We create a small core pointing in the +z direction
def init_m(pos):
x, y = pos[0] - radius, pos[1] - radius
if x**2 + y**2 < radius**2:
return (0, 0, 1)
else:
return (0, 0, -1)
# Prepare simulation
def test_m_average():
mesh = CuboidMesh(nx=3, ny=4, nz=5)
sim = Sim(mesh)
sim.set_m((0, 0, 1))
a = sim.compute_average()
assert a[2] == 1.0
def test_save_vector_field(tmpdir):
mesh = CuboidMesh(4, 3, 2, 4, 3, 2)
s = vector_field(mesh, lambda r: (r[0], r[1], r[2]))
vtk = VTK(mesh, directory=str(tmpdir), filename="save_vector")
vtk.save_vector(s, name="s")
assert same_as_ref(vtk.write_file(), REF_DIR)
def start(self):
self.t1 = time.clock()
def end(self):
self.t2 = time.clock()
def interval(self):
return self.t2 - self.t1
# ----------------------------------------------------
# 1D chain of 50 spins with a lattice constant of 0.27 A
mesh = CuboidMesh(
nx=50,
dx=0.27,
unit_length=1e-9,
)
# Simulation Function
def relax_neb(k, maxst, simname, init_im, interp, save_every=10000):
"""
Execute a simulation with the NEB function of the FIDIMAG code
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.
fname = "m_{}_Bz_{:06d}".format(sim_name, int(field_mT)) + ".vtk"
sim.driver.VTK.vtk_data.tofile(
os.path.join('vtks/{}'.format(sim_name), fname))
# FIELD = 80
for FIELD in range(0, 181, 20):
nx, ny, nz = 30, 30, 30
dx, dy, dz = 1, 1, 1
mesh = CuboidMesh(nx=nx,
ny=ny,
nz=nz,
dx=dx,
dy=dy,
dz=dz,
x0=-nx * 0.5,
y0=-ny * 0.5,
z0=-nz * 0.5,
unit_length=1.,
periodicity=(True, True, False))
sim_name = 'sk_helix'
sim = Sim(mesh, name=sim_name, integrator='sundials_openmp')
sim.mu_s = 1
sim.add(Exchange(1))
sim.add(DMI(0.727, dmi_type='bulk'))
bz_min = FIELD
sim.add(Zeeman((0.0, 0.0, bz_min * 1e-3)), save_field=True)
kc = -0.05
# )
# Mesh ------------------------------------------------------------------------
# Define an elongated cylinder along the y direction
def cylinder(r, centre, radius):
if (r[0] - centre[0])**2. + (r[2] - centre[1])**2 <= radius**2.:
return Ms
else:
return 0
# Finite differences mesh
mesh = CuboidMesh(nx=6, ny=35, nz=6, dx=2, dy=2, dz=2, unit_length=1e-9)
centre = (np.max(mesh.coordinates[:, 0]) * 0.5,
np.max(mesh.coordinates[:, 2]) * 0.5)
# Prepare simulation ----------------------------------------------------------
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
# --------------------------------------------------------------------------
# Mesh ---------------------------------------------------------------------
nx = int(args.box_length / args.fd_max_plane)
ny = int(args.box_width / args.fd_max_plane)
nz = int(args.box_thickness / args.fd_max_thick)
dx = args.fd_max_plane
dy = args.fd_max_plane
dz = args.fd_max_thick
if not args.PBC_2D:
mesh = CuboidMesh(nx=nx,
ny=ny,
nz=nz,
dx=dx,
dy=dy,
dz=dz,
unit_length=1e-9,
)
else:
print 'Using Periodic Boundary Conditions!'
mesh = CuboidMesh(nx=nx,
ny=ny,
nz=nz,
dx=dx,
dy=dy,
dz=dz,
unit_length=1e-9,
pbc='xy'
)
mxyz = sim.spin.copy()
mxyz.shape = (3, -1)
save_plot(xs, mxyz, mx, my, mz)
def save_plot(xs, mxyz, mx, my, mz):
fig = plt.figure()
mxyz.shape = (3, -1)
plt.plot(xs, mxyz[0], '.', label='mx')
plt.plot(xs, mxyz[1], '.', label='my')
plt.plot(xs, mxyz[2], '.', label='mz')
plt.plot(xs, mx, '-')
plt.plot(xs, my, '-')
plt.plot(xs, mz, '-')
plt.ylabel('mxyz')
plt.xlabel('x/a')
plt.legend(loc=1)
plt.grid()
#plt.xlim([-150, 150])
plt.ylim([-1.2, 1.2])
fig.savefig('dw_dmi.pdf')
if __name__ == '__main__':
mesh = CuboidMesh(nx=300, ny=40, nz=1)
relax_system(mesh)
#excite_system(mesh)
def test_initialise_vector():
mesh = CuboidMesh(1, 1, 1, 1, 1, 1)
v = vector_field(mesh, lambda r: 2 * r)
assert very_close(v, np.array((1, 1, 1)))
new_path = os.path.join(MODULE_DIR, field)
command = ('rm', '-rf', new_path)
cmd = ' '.join(command)
os.system(cmd)
return m
def compute_dmi_field(mesh, init_m0, Ms=8e5, D=4e-3, field='DMExchange6Ngbr'):
gen_oommf_conf(mesh, Ms=Ms, init_m0=init_m0, D=D, field=field)
run_oommf(field)
m = get_field(mesh, field=field)
new_path = os.path.join(MODULE_DIR, field)
command = ('rm', '-rf', new_path)
cmd = ' '.join(command)
os.system(cmd)
return m
if __name__ == "__main__":
mesh = CuboidMesh(nx=5, ny=2, nz=1, dx=1.0, dy=1.0, dz=1.0)
m = compute_demag_field(mesh, init_m0='return "1 0 0"')
print(m)
def test_initialise_scalar():
mesh = CuboidMesh(1, 1, 1, 1, 1, 1)
f = scalar_field(mesh, lambda r: r[0] + r[1] + r[2])
assert very_close(f, np.array((1.5)))
neb = NEBM_Cartesian(sim,
init_images,
interpolations=[6, 6],
name='neb',
spring_constant=1e8)
# neb.add_noise(0.1)
neb.relax(dt=1e-8,
max_iterations=5000,
save_vtks_every=500,
save_npys_every=500,
stopping_dYdt=100)
if __name__ == "__main__":
mesh = CuboidMesh(nx=160,
ny=1,
nz=1,
dx=4.0,
dy=4.0,
dz=4.0,
unit_length=1e-9)
sim = create_simulation(mesh)
# relax_two_state(mesh)
relax_system(sim)
# plot_energy_2d('neb')
# plot_energy_3d('neb')
"""
def two_part(pos):
x = pos[0]
if x > 6 or x < 3:
return Ms
else:
return 0
# Finite differences mesh
mesh = CuboidMesh(nx=3,
ny=1,
nz=1,
dx=3, dy=3, dz=3,
unit_length=1e-9
)
# Simulation Function
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
np.save('m0.npy', sim.spin)
def save_plot():
fig = plt.figure()
data = np.load('m0.npy')
data.shape = (3, -1)
print data
plt.plot(data[0], '-', label='Sx')
plt.plot(data[1], '-', label='Sy')
plt.plot(data[2], '-', label='Sz')
plt.ylim([-1.2, 1.2])
plt.ylabel('S')
plt.xlabel('x/a')
plt.legend(loc=1)
plt.grid()
fig.savefig('mxyz.pdf')
if __name__ == '__main__':
mesh = CuboidMesh(nx=300, dx=0.5, dy=1, dz=1, unit_length=1e-9)
relax_system(mesh)
print 'relax system done'
save_plot()
# spin_wave(mesh,m0)
sim = Sim(mesh, name='fidimag', driver='llg_stt')
sim.driver.set_tols(rtol=1e-8, atol=1e-8)
sim.driver.alpha = 0.1
sim.driver.gamma = 2.211e5
sim.Ms = 8.0e5
sim.driver.p = 1
sim.set_m(np.load('npys/m0_cpu.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
sim.add(Demag())
sim.driver.jx = -1e12
sim.driver.beta = 0.05
ts = np.linspace(0, 8e-9, 801)
for t in ts:
print('time', t)
sim.driver.run_until(t)
if __name__ == '__main__':
mesh = CuboidMesh(nx=20, ny=20, nz=2,dx=5, dy=5, dz=5.0, unit_length=1e-9)
excite_system(mesh)
sim.add(exch)
mT = 795.7747154594767
zeeman = Zeeman([-100 * mT, 4.3 * mT, 0], name='H')
sim.add(zeeman, save_field=True)
demag = Demag()
sim.add(demag)
ONE_DEGREE_PER_NS = 17453292.52
sim.relax(dt=1e-12,
stopping_dmdt=0.01,
max_steps=5000,
save_m_steps=100,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
if __name__ == "__main__":
mesh = CuboidMesh(nx=20,
ny=20,
nz=1,
dx=2.5,
dy=2.5,
dz=3,
unit_length=1e-9)
relax_system(mesh)
def test_skx_num_micromagnetic():
"""
Compute the skyrmion number from a micromagnetic simulation,
using the continuum topological charge expression for a
2D layer:
_
1 / dM dM
Q = --- * / M . -- X -- dx dy
4 PI _ / dx dy
The skyrmion is generated in an Iron based sample, whose
magnetic parameters are in: PRL 114, 177203 (2015)
"""
# A 6 nm by 6 nm square sample with enough resolution for a
# skyrmion with Q ~= -1
mesh = CuboidMesh(nx=60,
ny=60,
nz=1,
dx=0.1,
dy=0.1,
dz=0.4,
unit_length=1e-9,
periodicity=(True, True, False))
sim = microSim(mesh, name='skx_num_micro')
sim.driver.set_tols(rtol=1e-6, atol=1e-6)
sim.driver.alpha = 1.0
sim.driver.gamma = 1.0
sim.Ms = 1.1e6
sim.set_m(lambda pos: init_m(pos, x0=3, y0=3, r=1))
sim.do_precession = False
A = 2e-12
exch = microUniformExchange(A)
sim.add(exch)
D = 3.9e-3
dmi = microDMI(D, dmi_type='interfacial')
sim.add(dmi)
zeeman = microZeeman([0, 0, 2])
sim.add(zeeman)
Ku = 2.5e6
sim.add(microUniaxialAnisotropy(Ku, (0, 0, 1), name='Ku'))
sim.relax(stopping_dmdt=1e-2,
max_steps=1000,
save_m_steps=None,
save_vtk_steps=None)
sim.save_vtk()
skn = sim.skyrmion_number()
print('skx_number', skn)
print(sim._skx_number)
assert skn > -1 and skn < -0.99
# Mesh ---------------------------------------------------------------------
nx = int(args.box_length / args.fd_max_plane)
ny = int(args.box_width / args.fd_max_plane)
nz = int(args.box_thickness / args.fd_max_thick)
dx = args.fd_max_plane
dy = args.fd_max_plane
dz = args.fd_max_thick
if not args.PBC_2D:
mesh = CuboidMesh(
nx=nx,
ny=ny,
nz=nz,
dx=dx,
dy=dy,
dz=dz,
unit_length=1e-9,
)
else:
print 'Using Periodic Boundary Conditions!'
mesh = CuboidMesh(nx=nx,
ny=ny,
nz=nz,
dx=dx,
dy=dy,
dz=dz,
unit_length=1e-9,
pbc=(True, True, False))
def test_skx_num_atomistic():
"""
Test the *finite spin chirality* or skyrmion number for
a discrete spins simulation in a two dimensional lattice
The expression is (PRL 108, 017601 (2012)) :
Q = S_i \dot ( S_{i+1} X S_{j+1} )
+ S_i \dot ( S_{i-1} X S_{j-1} )
which measures the chirality taking two triangles of spins
per lattice site i:
S_{i} , S_{i + x} , S_{i + y} and
S_{i} , S_{i - x} , S_{i - y}
The area of the two triangles cover a unit cell, thus the sum
cover the whole area of the atomic lattice
We also test the Berg and Luscher definition for a topological
charge (see the hexagonal mesh test for details) in a
square lattice.
This test generate a skyrmion pointing down with unrealistic
paremeters.
"""
mesh = CuboidMesh(nx=120, ny=120, nz=1, periodicity=(True, True, False))
sim = Sim(mesh, name='skx_num')
sim.driver.set_tols(rtol=1e-6, atol=1e-6)
sim.driver.alpha = 1.0
sim.driver.gamma = 1.0
sim.mu_s = 1.0
sim.set_m(lambda pos: init_m(pos, 60, 60, 20))
sim.do_precession = False
J = 1.0
exch = UniformExchange(J)
sim.add(exch)
D = 0.09
dmi = DMI(D)
sim.add(dmi)
zeeman = Zeeman([0, 0, 5e-3])
sim.add(zeeman)
sim.relax(dt=2.0,
stopping_dmdt=1e-2,
max_steps=1000,
save_m_steps=None,
save_vtk_steps=None)
skn = sim.skyrmion_number()
print('skx_number', skn)
skn_BL = sim.skyrmion_number(method='BergLuscher')
print('skx_number_BergLuscher', skn_BL)
# Test the finite chirality method
assert skn > -1 and skn < -0.99
# Test the Berg-Luscher method
assert np.abs(skn_BL - (-1)) < 1e-4 and np.sign(skn_BL) < 0
# Test guiding center
Rx, Ry = compute_RxRy(mesh, sim.spin)
print('Rx=%g, Ry=%g' % (Rx, Ry))
assert Rx < 60 and Rx > 58
assert Ry < 60 and Ry > 58