def excite_system(mesh):
sim = Sim(mesh, name='dyn')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.alpha = 0.04
sim.gamma = 1.0
sim.mu_s = 1.0
sim.set_m(np.load('m0.npy'))
J = 1.0
exch = UniformExchange(J)
sim.add(exch)
D = 0.09
dmi = DMI(D)
sim.add(dmi)
zeeman = Zeeman([0, 0, 3.75e-3], name='H')
sim.add(zeeman)
w0 = 0.02
def time_fun(t):
return np.exp(-w0 * t)
hx = TimeZeeman([0, 0, 1e-5], sinc_fun, name='h')
sim.add(hx, save_field=True)
ts = np.linspace(0, 20000, 5001)
for t in ts:
sim.run_until(t)
print 'sim t=%g' % t
def test_exch_3d():
"""
Test the exchange field of the spins in this 3D mesh:
bottom layer:
8 9 10 11
4 5 6 7 x 2
0 1 2 3
The assertions are the mx component
of the: 0, 1, 2, .. 7 spins
Remember the new new ordering: fx1, fy1, fz1, fx2, ...
"""
mesh = CuboidMesh(nx=4, ny=3, nz=2)
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
# print field
assert field[0] == 1
assert field[3] == 0 + 1 + 2 + 1
assert field[6] == 1 + 2 + 3 + 2
assert field[9] == 2 + 3 + 3
assert field[4 * 3] == 1
assert field[5 * 3] == 5
assert field[6 * 3] == 10
assert field[7 * 3] == 11
def relax_system(mesh):
# Only relaxation
sim = Sim(mesh, name='relax')
# Simulation parameters
sim.driver.set_tols(rtol=1e-8, atol=1e-10)
sim.alpha = 0.5
sim.driver.gamma = 2.211e5 / mu0
sim.mu_s = 1e-27 / mu0
sim.driver.do_precession = False
# The initial state passed as a function
sim.set_m(init_m)
# sim.set_m(np.load('m0.npy'))
# Energies
exch = UniformExchange(J=2e-20)
sim.add(exch)
anis = Anisotropy(0.01 * 2e-20, axis=(0, 0, 1))
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=1e4,
max_steps=5000,
save_m_steps=None,
save_vtk_steps=None)
np.save('m0.npy', sim.spin)
def test_skx_num():
mesh = CuboidMesh(nx=120, ny=120, nz=1, periodicity=(True, True, False))
sim = Sim(mesh, name='skx_num')
sim.set_tols(rtol=1e-6, atol=1e-6)
sim.alpha = 1.0
sim.gamma = 1.0
sim.mu_s = 1.0
sim.set_m(init_m)
sim.do_procession = 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
assert skn > -1 and skn < -0.99
def test_exch_2d_pbc2d():
"""
Test the exchange field components in a 2D mesh with PBCs
The mesh sites:
3 4 5 --> (0,1,0) (1,1,0) (2,1,0)
y ^ 0 1 2 (0,0,0) (1,0,0) (2,0,0)
|
x -->
The expected components are in increasing order along x
"""
mesh = CuboidMesh(nx=3, ny=2, nz=1, periodicity=(True, True, False))
print mesh.neighbours
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
expected_x = np.array([3, 4, 5, 3, 4, 5])
expected_y = np.array([2, 2, 2, 2, 2, 2])
# Since the field ordering is now: fx1 fy1 fz1 fx2 ...
# We extract the x components jumping in steps of 3
assert np.max(abs(field[::3] - expected_x)) == 0
# For the y component is similar, now we start at the 1th
# entry and jump in steps of 3
assert np.max(abs(field[1::3] - expected_y)) == 0
# Similar fot he z component
assert np.max(field[2::3]) == 0
def test_exch_1d():
"""
Test the x component of the exchange field
in a 1D mesh, with the spin ordering:
0 1 2 3 4 5
"""
mesh = CuboidMesh(nx=5, ny=1, nz=1)
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert field[0] == 1
assert field[1 * 3] == 2
assert field[2 * 3] == 4
assert field[3 * 3] == 6
assert field[4 * 3] == 3
assert np.max(field[2::3]) == 0
assert np.max(field[1::3]) == 0
def relax_system_stage1():
mesh = CuboidMesh(nx=140 , ny=140, nz=1)
sim = Sim(mesh, name='relax', driver='llg')
#sim.set_options(dt=1e-14, gamma=const.gamma, k_B=const.k_B)
sim.alpha = 0.5
sim.do_precession = False
sim.gamma = const.gamma
sim.mu_s = spatial_mu
sim.set_m(init_m)
J = 50 * const.k_B
exch = UniformExchange(J)
sim.add(exch)
D = 0.27 * J
dmi = DMI(D)
sim.add(dmi)
zeeman = Zeeman(spatial_H)
sim.add(zeeman)
sim.relax(dt=1e-14, stopping_dmdt=1e10, max_steps=1000,
save_m_steps=100, save_vtk_steps=10)
np.save('skx.npy', sim.spin)
plot_m(mesh, 'skx.npy', comp='z')
def excite_system(mesh):
sim = Sim(mesh, name='dyn', driver='sllg')
sim.set_options(dt=1e-14, gamma=const.gamma, k_B=const.k_B)
sim.alpha = 0.1
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
def excite_system(T=0.1, H=0.15):
mesh = CuboidMesh(nx=28 * 3, ny=16 * 5, nz=1, pbc='2d')
sim = Sim(mesh, name='dyn', driver='sllg')
sim.set_options(dt=1e-14, gamma=const.gamma, k_B=const.k_B)
sim.alpha = 0.1
sim.mu_s = const.mu_s_1
sim.set_m(random_m)
J = 50 * const.k_B
exch = UniformExchange(J)
sim.add(exch)
D = 0.5 * J
dmi = DMI(D)
sim.add(dmi)
Hz = H * J / const.mu_s_1
zeeman = Zeeman([0, 0, Hz])
sim.add(zeeman)
sim.T = J / const.k_B * T
ts = np.linspace(0, 5e-11, 51)
for t in ts:
sim.run_until(t)
# sim.save_vtk()
np.save('m.npy', sim.spin)
plot_m(mesh, 'm.npy', comp='z')
def relax_system(mesh):
sim = Sim(mesh, name='relax')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.driver.alpha = 1.0
sim.driver.gamma = 1.0
sim.mu_s = 1.0
sim.set_m(init_m)
# sim.set_m(random_m)
# sim.set_m(np.load('m_10000.npy'))
J = 1.0
exch = UniformExchange(J)
sim.add(exch)
D = 0.09
dmi = DMI(D)
sim.add(dmi)
zeeman = Zeeman([0, 0, 3.75e-3])
sim.add(zeeman)
sim.relax(dt=2.0,
stopping_dmdt=1e-6,
max_steps=1000,
save_m_steps=100,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_options(rtol=1e-12, atol=1e-14)
sim.do_procession = False
sim.alpha = 0.5
sim.gamma = 1.0
sim.mu_s = 1.0
sim.set_m(init_m)
J = 1.0
exch = UniformExchange(J)
sim.add(exch)
D = 0.18
dmi = DMI(D)
sim.add(dmi)
zeeman = Zeeman([0, 0e-3, 2e-2], name='H')
sim.add(zeeman)
sim.relax(dt=2.0,
stopping_dmdt=1e-8,
max_steps=10000,
save_m_steps=None,
save_vtk_steps=100)
np.save('m0.npy', sim.spin)
def relax_system(mesh, Hy=0):
sim = Sim(mesh, name='relax')
sim.driver.set_tols(rtol=1e-10, atol=1e-12)
sim.driver.alpha = 0.5
sim.driver.gamma = 1.0
sim.mu_s = 1.0
sim.do_precession = False
sim.set_m(init_m)
#sim.set_m(random_m)
#sim.set_m(np.load('m_10000.npy'))
J = 1.0
exch = UniformExchange(J)
sim.add(exch)
D = 0.18
dmi = DMI(D)
sim.add(dmi)
zeeman = Zeeman([0, Hy, 2e-2], name='H')
sim.add(zeeman)
sim.relax(dt=2.0,
stopping_dmdt=1e-7,
max_steps=10000,
save_m_steps=100,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def excite_system(mesh, Hy=0):
sim = Sim(mesh, name='dyn')
sim.driver.set_tols(rtol=1e-10, atol=1e-12)
sim.driver.alpha = 0.04
sim.driver.gamma = 1.0
sim.mu_s = 1.0
sim.set_m(np.load('m0.npy'))
J = 1.0
exch = UniformExchange(J)
sim.add(exch)
D = 0.18
dmi = DMI(D)
sim.add(dmi)
zeeman = Zeeman([0, Hy, 2e-2], name='H')
sim.add(zeeman)
hx = TimeZeeman([0, 0, 1e-5], sinc_fun, name='h')
sim.add(hx, save_field=True)
dt = 5
steps = 2001
for i in range(steps):
sim.run_until(i * dt)
sim.save_m()
print("step {}/{}".format(i, steps))
def dynamic(mesh):
sim = Sim(mesh, name='dyn', driver='slonczewski')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.driver.gamma = 1.0
sim.mu_s = 1.0
sim.set_m(np.load('m0.npy'))
J = 1.0
exch = UniformExchange(J)
sim.add(exch)
Kx = Anisotropy(Ku=0.005, axis=(1, 0, 0), name='Kx')
sim.add(Kx)
sim.p = (0, 0, 1)
sim.u0 = 0.03
sim.driver.alpha = 0.1
ts = np.linspace(0, 1e3, 101)
for t in ts:
sim.run_until(t)
sim.save_vtk()
print t
def relax_system(mesh):
sim = Sim(mesh, name='relax')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.driver.alpha = 1.0
sim.driver.gamma = 1.0
sim.mu_s = 1.0
sim.set_m(init_m)
# sim.set_m(random_m)
# sim.set_m(np.load('m_10000.npy'))
J = 1.0
exch = UniformExchange(J)
sim.add(exch)
Kx = Anisotropy(Ku=0.005, axis=(1, 0, 0), name='Kx')
sim.add(Kx)
sim.relax(dt=2.0,
stopping_dmdt=1e-6,
max_steps=1000,
save_m_steps=100,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def relax_system(mesh, Dx=0.005, Dp=0.01):
mat = UnitMaterial()
sim = Sim(mesh, name='test_energy')
print('Created sim')
sim.driver.set_tols(rtol=1e-10, atol=1e-12)
sim.alpha = mat.alpha
sim.driver.gamma = mat.gamma
sim.pins = pin_fun
exch = UniformExchange(mat.J)
sim.add(exch)
print('Added UniformExchange')
anis = Anisotropy(Dx, axis=[1, 0, 0], name='Dx')
sim.add(anis)
print('Added Anisotropy')
anis2 = Anisotropy([0, 0, -Dp], name='Dp')
sim.add(anis2)
print('Added Anisotropy 2')
sim.set_m((1, 1, 1))
T = 100
ts = np.linspace(0, T, 201)
for t in ts:
# sim.save_vtk()
sim.driver.run_until(t)
print(('Running -', t))
# sim.save_vtk()
np.save('m0.npy', sim.spin)
def relax_system_stage2():
mesh = CuboidMesh(nx=140 , ny=140, nz=1)
sim = Sim(mesh, name='dyn', driver='llg')
sim.alpha = 0.1
sim.do_precession = True
sim.gamma = const.gamma
sim.mu_s = spatial_mu
sim.set_m(np.load('skx.npy'))
J = 50 * const.k_B
exch = UniformExchange(J)
sim.add(exch)
D = 0.27 * J
dmi = DMI(D)
sim.add(dmi)
zeeman = Zeeman(spatial_H)
sim.add(zeeman)
ts = np.linspace(0, 2e-9, 201)
for t in ts:
sim.run_until(t)
sim.save_vtk()
sim.save_m()
print(t)
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_default_options(gamma=const.gamma)
sim.alpha = 0.5
sim.mu_s = const.mu_s_1
sim.set_m(init_m)
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)
ONE_DEGREE_PER_NS = 17453292.52
sim.relax(dt=1e-13, stopping_dmdt=0.01 * ONE_DEGREE_PER_NS,
max_steps=1000, save_m_steps=100, save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def test_exch_3d():
"""
Test the exchange field of the spins in this 3D mesh:
bottom layer:
8 9 10 11
4 5 6 7 x 2
0 1 2 3
Assertions are according to the mx component of the spins, since J is set
to 1
Spin components are given according to the (i, j) index position in the
lattice:
i lattice site
[[ 0. 0. 0.] --> 0 j=0
[ 1. 0. 0.] --> 1
[ 2. 0. 0.] --> 2
[ 3. 0. 0.] --> 3
[ 0. 1. 0.] --> 4 j=1
[ 1. 1. 0.]
...
Remember the field ordering: fx0, fy0, fz0, fx1, ...
"""
mesh = CuboidMesh(nx=4, ny=3, nz=2)
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
# print field
# Exchange from 0th spin
assert field[0] == 1
# Exchange from 1st spin
# spin: 2 0 5 13
# mx: 2 0 1 1
assert field[3] == 2 + 0 + 1 + 1
# Exchange from 2nd spin
# spin: 3 1 6 14
# mx: 3 1 2 2
assert field[6] == 3 + 1 + 2 + 2
# ...
assert field[9] == 2 + 3 + 3
assert field[4 * 3] == 1
assert field[5 * 3] == 5
assert field[6 * 3] == 10
assert field[7 * 3] == 11
def test_exch_energy_1d():
mesh = CuboidMesh(nx=2, ny=1, nz=1)
sim = Sim(mesh)
exch = UniformExchange(1.23)
sim.add(exch)
sim.set_m((0, 0, 1))
energy = exch.compute_energy()
assert energy == -1.23
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.
--> vtks and npys are saved in files starting with the 'simname' string
"""
# Prepare simulation
sim = Sim(mesh, name=simname)
sim.driver.gamma = const.gamma
# magnetisation in units of Bohr's magneton
sim.mu_s = 2. * const.mu_B
# Exchange constant in Joules: E = Sum J_{ij} S_i S_j
J = 12. * const.meV
exch = UniformExchange(J)
sim.add(exch)
# DMI constant in Joules: E = Sum D_{ij} S_i x S_j
D = 2. * const.meV
dmi = DMI(D, dmi_type='interfacial')
sim.add(dmi)
# Anisotropy along +z axis
ku = Anisotropy(Ku=0.5 * const.meV, axis=[0, 0, 1], name='ku')
sim.add(ku)
# Initial images
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
neb = NEB_Sundials(sim,
init_images,
interpolations=interpolations,
spring=k,
name=simname)
neb.relax(max_steps=maxst,
save_vtk_steps=save_every,
save_npy_steps=save_every,
stopping_dmdt=1e-2)
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
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.set_tols(rtol=1e-6, atol=1e-6)
sim.alpha = 1.0
sim.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)
assert skn > -1 and skn < -0.99
def relax_system():
# 1D chain of 50 spins with a lattice constant of 0.27 A
mesh = CuboidMesh(
nx=nx,
dx=dx,
unit_length=1e-9,
# pbc='1d'
)
# Initiate the simulation
sim = Sim(mesh, name=sim_name)
sim.gamma = const.gamma
# magnetisation in units of Bohr's magneton
sim.mu_s = 2 * const.mu_B
# sim.set_options(gamma=const.gamma, k_B=const.k_B)
# Initial magnetisation profile
sim.set_m(init_m)
# Exchange constant in Joules: E = Sum J_{ij} S_i S_j
J = 12. * const.meV
exch = UniformExchange(J)
sim.add(exch)
# DMI constant in Joules: E = Sum D_{ij} S_i x S_j
D = 2. * const.meV
dmi = DMI(D, dmi_type='interfacial')
sim.add(dmi)
# Anisotropy along +z axis
ku = Anisotropy(Ku=0.5 * const.meV, axis=[0, 0, 1], name='ku')
sim.add(ku)
# Faster convergence
sim.alpha = 0.5
sim.do_precession = False
sim.relax(dt=1e-13,
stopping_dmdt=0.05,
max_steps=700,
save_m_steps=1000,
save_vtk_steps=1000)
# Save the last relaxed state
np.save(sim_name + '.npy', sim.spin)
def test_exch_1d_pbc():
mesh = CuboidMesh(nx=5, ny=1, nz=1, periodicity=(True, False, False))
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert field[0] == 1 + 4
assert field[3] == 2
assert field[6] == 4
assert field[9] == 6
assert field[12] == 3 + 0
assert np.max(field[2::3]) == 0
assert np.max(field[1::3]) == 0
def test_dw_dmi_atomistic(do_plot=False):
mesh = CuboidMesh(nx=300, ny=1, nz=1)
sim = Sim(mesh, name='relax')
sim.set_default_options(gamma=const.gamma)
sim.alpha = 0.5
sim.mu_s = const.mu_s_1
sim.do_precession = False
sim.set_m(m_init_dw)
J = 50.0 * const.k_B
exch = UniformExchange(J)
sim.add(exch)
D = 0.01 * J
dmi = DMI(D)
sim.add(dmi)
K = 0.005 * J
anis = Anisotropy(K, axis=[1, 0, 0])
sim.add(anis)
ONE_DEGREE_PER_NS = 17453292.52
sim.relax(dt=1e-13,
stopping_dmdt=0.01 * ONE_DEGREE_PER_NS,
max_steps=1000,
save_m_steps=100,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
xs = np.array([p[0] for p in mesh.coordinates]) - 150
mx, my, mz = analytical(xs, A=J / 2.0, D=-D, K=K)
mxyz = sim.spin.copy()
mxyz = mxyz.reshape(-1, 3).T
assert max(abs(mxyz[0, :] - mx)) < 0.001
assert max(abs(mxyz[1, :] - my)) < 0.001
assert max(abs(mxyz[2, :] - mz)) < 0.0006
if do_plot:
save_plot(xs, mxyz, mx, my, mz)
def test_exch_2d():
mesh = CuboidMesh(nx=5, ny=2, nz=1)
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert np.max(field[2::3]) == 0
assert field[0] == 1
assert field[3] == 2 + 1
assert field[6] == 1 + 2 + 3
assert field[9] == 2 + 3 + 4
assert field[12] == 3 + 4
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.mu_s = 1e-23
sim.driver.gamma = 1.76e11
sim.driver.alpha = 1.0
J = 1e-22
exch = UniformExchange(J)
sim.add(exch)
demag = Demag()
sim.add(demag)
sim.set_m(init_m)
ts = np.linspace(0, 5e-10, 101)
for t in ts:
sim.driver.run_until(t)
sim.save_vtk()
np.save('m0.npy', sim.spin)
def create_simulation(R, B):
mu_s = 3
sim_hexagon = HexagonSim(
R, # R
0.2715, # a
mu_s, # mu_s
name='unnamed')
sim = sim_hexagon.sim
# mask = (sim.mu_s / C.mu_B) > 1e-5
exch = UniformExchange(5.881 * C.meV)
sim.add(exch)
dmi = DMI(D=1.557 * C.meV, dmi_type='interfacial')
sim.add(dmi)
sim.add(Zeeman([0., 0., B]))
sim.add(Anisotropy(0.406 * C.meV, axis=[0, 0, 1]))
return sim
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.alpha = 0.1
sim.set_m(init_m)
J = 1
exch = UniformExchange(J)
sim.add(exch)
dmi = DMI(0.05 * J)
sim.add(dmi)
ts = np.linspace(0, 1, 11)
for t in ts:
print t, sim.spin_length() - 1
sim.run_until(t)
sim.save_vtk()
return sim.spin
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_default_options(gamma=const.gamma)
sim.alpha = 0.5
sim.mu_s = const.mu_s_1
sim.do_procession = False
sim.set_m(m_init_dw)
J = 50.0 * const.k_B
exch = UniformExchange(J)
sim.add(exch)
D = 0.1 * J
dmi = DMI(D, dmi_type='interfacial')
sim.add(dmi)
K = 0.02 * J
anis = Anisotropy(K, axis=[0, 0, 1])
sim.add(anis)
ONE_DEGREE_PER_NS = 17453292.52
sim.relax(dt=1e-13,
stopping_dmdt=0.01 * ONE_DEGREE_PER_NS,
max_steps=1000,
save_m_steps=100,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
xs = np.array([p[0] for p in mesh.pos]) - 150
mx, my, mz = analytical(xs, A=J / 2.0, D=-D, K=K)
mxyz = sim.spin.copy()
mxyz.shape = (3, -1)
save_plot(xs, mxyz, mx, my, mz)