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 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_dynamic():
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='dyn_spin', driver='slonczewski')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.gamma = 1.0
sim.mu_s = 1.0
sim.set_m((0.8, 0, -1))
Kx = Anisotropy(Ku=-0.05, axis=(0, 0, 1), name='Kz')
sim.add(Kx)
sim.p = (0, 0, 1)
sim.u0 = 0.0052
sim.alpha = 0.1
ts = np.linspace(0, 1200, 401)
for t in ts:
sim.run_until(t)
mz = sim.spin[2]
alpha, K, u = 0.1, 0.05, 0.0052
print mz, u / (2 * alpha * K)
#########################################################
# The system used in this test can be solved analytically, which gives that mz = u/(2*alpha*K),
# where K represents the easy-plane anisotropy.
###
assert abs(mz - u / (2 * alpha * K)) / mz < 5e-4
def test_dynamic():
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='dyn_spin', driver='slonczewski')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.gamma = 1.0
sim.mu_s = 1.0
sim.set_m((0.8,0,-1))
Kx = Anisotropy(Ku=-0.05, axis=(0, 0, 1), name='Kz')
sim.add(Kx)
sim.p = (0,0,1)
sim.a_J = 0.0052
sim.alpha = 0.1
ts = np.linspace(0, 1200, 401)
for t in ts:
sim.run_until(t)
mz = sim.spin[2]
alpha, K, u = 0.1, 0.05, 0.0052
print(mz, u/(2*alpha*K))
#########################################################
# The system used in this test can be solved analytically, which gives that mz = u/(2*alpha*K),
# where K represents the easy-plane anisotropy.
###
assert abs(mz - u/(2*alpha*K))/mz< 5e-4
def excite_system(mesh, Hy=0):
sim=Sim(mesh,name='dyn')
sim.set_options(rtol=1e-10,atol=1e-12)
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 = 0.18
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)
def relax_system(mesh, Hy=0):
sim=Sim(mesh,name='relax')
sim.set_options(rtol=1e-10,atol=1e-12)
sim.alpha = 0.5
sim.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-8, max_steps=10000, save_m_steps=100, save_vtk_steps=50)
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 excite_system(mesh, Hy=0):
sim = Sim(mesh, name="dyn")
sim.set_options(rtol=1e-10, atol=1e-12)
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 = 0.18
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)
def relax_system(mesh, Hy=0):
sim = Sim(mesh, name="relax")
sim.set_options(rtol=1e-10, atol=1e-12)
sim.alpha = 0.5
sim.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-8, max_steps=10000, 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')
sim.set_tols(rtol=1e-10, atol=1e-12)
sim.alpha = mat.alpha
sim.gamma = mat.gamma
sim.pins = pin_fun
exch = UniformExchange(mat.J)
sim.add(exch)
anis = Anisotropy(Dx, axis=[1, 0, 0], name='Dx')
sim.add(anis)
anis2 = Anisotropy([0, 0, -Dp], name='Dp')
sim.add(anis2)
sim.set_m((1, 1, 1))
T = 100
ts = np.linspace(0, T, 201)
for t in ts:
# sim.save_vtk()
sim.run_until(t)
# sim.save_vtk()
np.save('m0.npy', sim.spin)
def dynamic(mesh):
sim = Sim(mesh, name='dyn', driver='slonczewski')
# sim.set_options(rtol=1e-10,atol=1e-14)
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)
Kx = Anisotropy(Ku=0.005, axis=(1, 0, 0), name='Kx')
sim.add(Kx)
sim.p = (0,0,1)
sim.u0 = 0.03
sim.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, Dx=0.005, Dp=0.01):
mat = UnitMaterial()
sim = Sim(mesh, name='test_energy')
print('Created sim')
sim.set_tols(rtol=1e-10, atol=1e-12)
sim.alpha = mat.alpha
sim.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.run_until(t)
print('Running -', t)
# sim.save_vtk()
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 relax_system(mesh):
sim = Sim(mesh, name='relax')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.alpha = 1.0
sim.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_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 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 relax_system(mesh):
sim=Sim(mesh,name='relax')
sim.set_options(rtol=1e-12,atol=1e-14)
sim.do_precession = 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):
sim = Sim(mesh, name='relax')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.alpha = 1.0
sim.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_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.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_sim_spins(do_plot=False):
mesh = CuboidMesh(nx=10, ny=5, nz=1)
sim = Sim(mesh, name='10spin')
alpha = 0.1
gamma = 2.21e5
sim.alpha = alpha
sim.gamma = gamma
sim.mu_s = 1.0
sim.set_m((1, 0, 0))
print(sim.spin)
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
ts = np.linspace(0, 1e-9, 101)
mx = []
my = []
mz = []
real_ts = []
for t in ts:
sim.run_until(t)
real_ts.append(sim.t)
#print sim.t, abs(sim.spin_length()[0] - 1)
av = sim.compute_average()
mx.append(av[0])
my.append(av[1])
mz.append(av[2])
#sim.save_vtk()
mz = np.array(mz)
# print mz
a_mx, a_my, a_mz = single_spin(alpha, gamma, H0, ts)
print(sim.stat())
if do_plot:
plot(real_ts,
mx,
my,
mz,
a_mx,
a_my,
a_mz,
name='spins.pdf',
title='integrating spins')
print(("Max Deviation = {0}".format(np.max(np.abs(mz - a_mz)))))
assert np.max(np.abs(mz - a_mz)) < 5e-7
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.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 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 = Anisotropy(Ku=1.0, axis=[0, 0, 1], name='Dx')
sim.add(anis)
sim.run_until(1.0)
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 = Anisotropy(Ku=1.0, axis=[0, 0, 1], name='Dx')
sim.add(anis)
sim.run_until(1.0)
assert sim.spin[0] == 0
assert sim.spin[2] != 0
def test_sim_spins(do_plot=False):
mesh = CuboidMesh(nx=10, ny=5, nz=1)
sim = Sim(mesh, name='10spin')
alpha = 0.1
gamma = 2.21e5
sim.alpha = alpha
sim.gamma = gamma
sim.mu_s = 1.0
sim.set_m((1, 0, 0))
print(sim.spin)
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
ts = np.linspace(0, 1e-9, 101)
mx = []
my = []
mz = []
real_ts = []
for t in ts:
sim.run_until(t)
real_ts.append(sim.t)
#print sim.t, abs(sim.spin_length()[0] - 1)
av = sim.compute_average()
mx.append(av[0])
my.append(av[1])
mz.append(av[2])
#sim.save_vtk()
mz = np.array(mz)
# print mz
a_mx, a_my, a_mz = single_spin(alpha, gamma, H0, ts)
print(sim.stat())
if do_plot:
plot(real_ts, mx, my, mz, a_mx, a_my, a_mz, name='spins.pdf', title='integrating spins')
print(("Max Deviation = {0}".format(
np.max(np.abs(mz - a_mz)))))
assert np.max(np.abs(mz - a_mz)) < 5e-7
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 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. PBCs are specified in the mesh
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((0, 0, 1))
# 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 relax_system(rtol=1e-10, atol=1e-12):
"""numerical solution"""
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name="relax")
sim.set_options(rtol=rtol, atol=atol)
sim.alpha = 0.5
sim.gamma = 2.21e5
sim.mu_s = 1.0
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(rtol=1e-10, atol=1e-12):
"""numerical solution"""
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='relax')
sim.set_options(rtol=rtol, atol=atol)
sim.alpha = 0.5
sim.gamma = 2.21e5
sim.mu_s = 1.0
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 test_sim_single_spin_vode(do_plot=False):
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='spin')
alpha = 0.1
gamma = 2.21e5
sim.alpha = alpha
sim.gamma = gamma
sim.mu_s = 1.0
sim.set_m((1, 0, 0))
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
ts = np.linspace(0, 1e-9, 101)
mx = []
my = []
mz = []
real_ts = []
for t in ts:
sim.run_until(t)
real_ts.append(sim.t)
#print sim.t, abs(sim.spin_length()[0] - 1)
mx.append(sim.spin[0])
my.append(sim.spin[1])
mz.append(sim.spin[2])
mz = np.array(mz)
a_mx, a_my, a_mz = single_spin(alpha, gamma, H0, ts)
print(sim.stat())
if do_plot:
plot(real_ts, mx, my, mz, a_mx, a_my, a_mz)
print(("Max Deviation = {0}".format(
np.max(np.abs(mz - a_mz)))))
assert np.max(np.abs(mz - a_mz)) < 5e-7
def test_sim_single_spin_vode(do_plot=False):
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='spin')
alpha = 0.1
gamma = 2.21e5
sim.alpha = alpha
sim.gamma = gamma
sim.mu_s = 1.0
sim.set_m((1, 0, 0))
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
ts = np.linspace(0, 1e-9, 101)
mx = []
my = []
mz = []
real_ts = []
for t in ts:
sim.run_until(t)
real_ts.append(sim.t)
#print sim.t, abs(sim.spin_length()[0] - 1)
mx.append(sim.spin[0])
my.append(sim.spin[1])
mz.append(sim.spin[2])
mz = np.array(mz)
a_mx, a_my, a_mz = single_spin(alpha, gamma, H0, ts)
print(sim.stat())
if do_plot:
plot(real_ts, mx, my, mz, a_mx, a_my, a_mz)
print(("Max Deviation = {0}".format(np.max(np.abs(mz - a_mz)))))
assert np.max(np.abs(mz - a_mz)) < 5e-7
def dynamic(mesh):
sim = Sim(mesh, name='dyn_spin', driver='slonczewski')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.gamma = 1.0
sim.mu_s = 1.0
sim.set_m((0.8, 0, -1))
Kx = Anisotropy(Ku=-0.05, axis=(0, 0, 1), name='Kz')
sim.add(Kx)
sim.p = (0, 0, 1)
sim.u0 = 0.005
sim.alpha = 0.1
ts = np.linspace(0, 1200, 401)
for t in ts:
sim.run_until(t)
#sim.save_vtk()
print t
def dynamic(mesh):
sim = Sim(mesh, name='dyn_spin', driver='slonczewski')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.gamma = 1.0
sim.mu_s = 1.0
sim.set_m((0.8,0,-1))
Kx = Anisotropy(Ku=-0.05, axis=(0, 0, 1), name='Kz')
sim.add(Kx)
sim.p = (0,0,1)
sim.u0 = 0.005
sim.alpha = 0.1
ts = np.linspace(0, 1200, 401)
for t in ts:
sim.run_until(t)
#sim.save_vtk()
print t
def single_spin(alpha=0.01):
mat = Material()
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, driver='sllg')
sim.alpha = alpha
sim.gamma = mat.gamma
sim.mu_s = mat.mu_s
sim.T = 10000
sim.set_m((1, 1, 1))
#sim.add(Zeeman(1,(0, 0, 1)))
anis = Anisotropy(mat.K, direction=(0, 0, 1))
sim.add(anis)
dt = 0.5e-12
ts = np.linspace(0, 1000 * dt, 1001)
sx = []
sy = []
for t in ts:
sim.run_until(t)
sx.append(sim.spin[0])
sy.append(sim.spin[1])
print(t)
plt.plot(sx, sy)
plt.xlabel("$S_x$")
plt.ylabel("$S_y$")
plt.grid()
plt.axis((-0.9, 0.9, -0.9, 0.9))
plt.axes().set_aspect('equal')
plt.savefig("macrospin.pdf")
def single_spin(alpha=0.01):
mat = Material()
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, driver='sllg')
sim.alpha = alpha
sim.gamma = mat.gamma
sim.mu_s = mat.mu_s
sim.T = 10000
sim.set_m((1, 1, 1))
#sim.add(Zeeman(1,(0, 0, 1)))
anis = Anisotropy(mat.K, direction=(0, 0, 1))
sim.add(anis)
dt = 0.5e-12
ts = np.linspace(0, 1000 * dt, 1001)
sx = []
sy = []
for t in ts:
sim.run_until(t)
sx.append(sim.spin[0])
sy.append(sim.spin[1])
print(t)
plt.plot(sx, sy)
plt.xlabel("$S_x$")
plt.ylabel("$S_y$")
plt.grid()
plt.axis((-0.9, 0.9, -0.9, 0.9))
plt.axes().set_aspect('equal')
plt.savefig("macrospin.pdf")
def relax_system(mesh):
sim = Sim(mesh, name='relax')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.alpha = 1.0
sim.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):
sim = Sim(mesh, name='dmi_2d')
sim.alpha = 0.1
sim.gamma = 1.76e11
sim.mu_s = 1e-22
J = 1e-20
exch = UniformExchange(J)
sim.add(exch)
dmi = DMI(0.1 * J)
sim.add(dmi)
sim.set_m(init_m)
ts = np.linspace(0, 5e-10, 101)
for t in ts:
print(t)
sim.run_until(t)
#sim.save_vtk()
return sim.spin
def relax_system(mesh):
sim = Sim(mesh, name="dmi_2d")
sim.alpha = 0.1
sim.gamma = 1.76e11
sim.mu_s = 1e-22
J = 1e-20
exch = UniformExchange(J)
sim.add(exch)
dmi = DMI(0.1 * J)
sim.add(dmi)
sim.set_m(init_m)
ts = np.linspace(0, 5e-10, 101)
for t in ts:
print t
sim.run_until(t)
# sim.save_vtk()
return sim.spin
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 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
from fidimag.atomistic import Sim from fidimag.common.cuboid_mesh import CuboidMesh from fidimag.atomistic import UniformExchange, Zeeman import fidimag.common.constant as const mesh = CuboidMesh(nx=1, ny=1, dx=1, dy=1) sim = Sim(mesh, name='relax_sk') sim.gamma = const.gamma sim.set_m((1, 0, 0)) sim.add(Zeeman((0, 0, 25.))) sim.run_until(1e-11) sim.set_tols(rtol=1e-10, atol=1e-12) sim.run_until(2e-11)
from fidimag.atomistic import Sim from fidimag.common.cuboid_mesh import CuboidMesh from fidimag.atomistic import UniformExchange, Zeeman from fidimag.atomistic import Constant # Import physical constants from fidimag const = Constant() mesh = CuboidMesh(nx=1, ny=1, dx=1, dy=1) sim = Sim(mesh, name='relax_sk') sim.gamma = const.gamma sim.set_m((1, 0, 0)) sim.add(Zeeman((0, 0, 25.))) sim.run_until(1e-11) sim.set_tols(rtol=1e-10, atol=1e-12) sim.run_until(2e-11)
