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(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(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_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 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 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 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_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_dmi_1d():
mesh = CuboidMesh(nx=2, ny=1, nz=1)
sim = Sim(mesh)
sim.set_m((1, 0, 0))
dmi = DMI(D=1)
sim.add(dmi)
field = dmi.compute_field()
expected = np.array([0, 0, 0, 0, 0, 0])
assert (field == expected).all()
energy = dmi.compute_energy()
assert energy == 0
def test_dmi_1d_field():
mesh = CuboidMesh(nx=2, ny=1, nz=1)
sim = Sim(mesh)
sim.set_m(init_m)
dmi = DMI(D=1.23)
sim.add(dmi)
field = dmi.compute_field()
expected = np.array([0, -1, 0, 0, 0, -1]) * 1.23
assert np.allclose(field, expected)
energy = dmi.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_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 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.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)
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='dmi_2d')
sim.driver.alpha = 0.1
sim.driver.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 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))
# Initiate Fidimag simulation -------------------------------------------------
sim = Sim(mesh, name=args.sim_name)
# sim.set_tols(rtol=1e-10, atol=1e-14)
if args.alpha:
sim.driver.alpha = args.alpha
# sim.gamma = 2.211e5
# Material parameters ---------------------------------------------------------
sim.mu_s = args.mu_s * const.mu_B
exch = UniformExchange(args.J * const.meV)
sim.add(exch)
dmi = DMI(D=(args.D * const.meV), dmi_type='interfacial')
sim.add(dmi)
if args.B:
zeeman = Zeeman((0, 0, args.B))
sim.add(zeeman, save_field=True)
if args.k_u:
# Uniaxial anisotropy along + z-axis
sim.add(Anisotropy(args.k_u * const.meV, axis=[0, 0, 1]))
if args.Demag:
sim.add(DemagHexagonal())
# -----------------------------------------------------------------------------
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
def test_skx_num_atomistic_hexagonal():
"""
Test the topological charge or skyrmion number for a discrete spins
simulation in a two dimensional hexagonal lattice, using Berg and Luscher
definition in [Nucl Phys B 190, 412 (1981)] and simplified in [PRB 93,
174403 (2016)], which maps a triangulated lattice (using triangles of
neighbouring spins) area into a unit sphere.
The areas of two triangles per lattice site cover a unit cell, thus the sum
cover the whole area of the atomic lattice
This test generates a skyrmion pointing down and two skyrmions pointing up
in a PdFe sample using magnetic parameters from: PRL 114, 177203 (2015)
"""
mesh = HexagonalMesh(0.2715, 41, 41, periodicity=(True, True))
sim = Sim(mesh, name='skx_number_hexagonal')
sim.driver.set_tols(rtol=1e-6, atol=1e-6)
sim.driver.alpha = 1.0
sim.driver.gamma = 1.0
sim.mu_s = 3 * const.mu_B
sim.set_m(lambda pos: init_m(pos, 16.1, 10, 2))
sim.driver.do_precession = False
J = 5.881 * const.meV
exch = UniformExchange(J)
sim.add(exch)
D = 1.557 * const.meV
dmi = DMI(D, dmi_type='interfacial')
sim.add(dmi)
sim.add(Anisotropy(0.406 * const.meV, axis=[0, 0, 1]))
zeeman = Zeeman([0, 0, 2.5])
sim.add(zeeman)
sim.relax(dt=1e-13,
stopping_dmdt=1e-2,
max_steps=2000,
save_m_steps=None,
save_vtk_steps=100)
skn_single = sim.skyrmion_number(method='BergLuscher')
print('skx_number_hexagonal', skn_single)
# Now we generate two skyrmions pointing up
sim.driver.reset_integrator()
sim.set_m(
lambda pos: init_m_multiple_sks(pos, 1, sk_pos=[(9, 6), (18, 12)]))
sim.get_interaction('Zeeman').update_field([0, 0, -2.5])
sim.relax(dt=1e-13,
stopping_dmdt=1e-2,
max_steps=2000,
save_m_steps=None,
save_vtk_steps=None)
skn_two = sim.skyrmion_number(method='BergLuscher')
print('skx_number_hexagonal_two', skn_two)
# Check that we get a right sk number
assert np.abs(skn_single - (-1)) < 1e-4 and np.sign(skn_single) < 0
assert np.abs(skn_two - (2)) < 1e-4 and np.sign(skn_two) > 0
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
if np.abs(kc) > 0.0:
sim.add(CubicAnisotropy(kc))
# .........................................................................
sim.driver.alpha = 0.9
sim.driver.do_precession = False
# Zeeman_int = sim.get_interaction('Zeeman')
# Zeeman_int.update_field((0.0, 0.0, B_sweep * 1e-3))
H_BG = np.load(
def generate_simulation(self,
do_precession=False,
gamma=1.76e11,
load_mu_s=False):
"""
Generates a simulation according to the self.simulation option
gamma :: Default is the free electron gyromagnetic ratio
load_mu_s :: A file path to a NPY file with the mu_s information
(only for the experimental_sample option)
"""
# Mesh ----------------------------------------------------------------
if self.simulation == 'experimental_sample':
self.sim_from_image = sfi.sim_from_image(sfi.default_image)
if not load_mu_s:
self.sim_from_image.generate_magnetic_moments(mu_s=self.mu_s)
else:
self.sim_from_image.generate_magnetic_moments(
load_file=load_mu_s)
self.sim = self.sim_from_image.sim
elif self.simulation == '2D_square':
# A square sized hexagonal mesh
mesh = HexagonalMesh(
self.mesh_a * 0.5,
self.mesh_nx,
self.mesh_ny,
# periodicity=(True, True),
alignment='square',
unit_length=1e-9)
self.sim = Sim(mesh)
# If we use polygon mesh tools, we can use a hexagon shaped mesh
# self.sim.mu_s = self.mu_s_in_hexagon
self.sim.mu_s = self.mu_s
elif self.simulation == '1D_chain':
# A 1D chain using a cuboid mesh
mesh = CuboidMesh(
dx=self.mesh_a,
nx=self.mesh_nx,
ny=1,
nz=1,
# periodicity=(True, True),
unit_length=1e-9)
self.sim = Sim(mesh)
# If we use polygon mesh tools, we can use a hexagon shaped mesh
# self.sim.mu_s = self.mu_s_in_hexagon
self.sim.mu_s = self.mu_s
self.sim.driver.do_precession = do_precession
self.sim.driver.gamma = gamma
# Interactions --------------------------------------------------------
exch = UniformExchange(self.J)
self.sim.add(exch)
dmi = DMI(D=(self.D), dmi_type='interfacial')
self.sim.add(dmi)
zeeman = Zeeman((self.B[0], self.B[1], self.B[2]))
self.sim.add(zeeman, save_field=True)
if self.ku:
# Uniaxial anisotropy along + z-axis
self.sim.add(Anisotropy(self.ku, axis=[0, 0, 1]))
if self.Demag:
print('Using Demag!')
self.sim.add(DemagHexagonal())
# ---------------------------------------------------------------------
self.hls = np.ones_like(self.sim.spin.reshape(-1, 3))
self.rgbs = np.ones((self.sim.spin.reshape(-1, 3).shape[0], 4))
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,
spring_constant=None,
stopping_dydt=None,
max_steps=None,
keep_sim_climbing_image_steps=None,
save_m_every=None,
climbing_image=None,
keep_sim_climbing_image=None,
keep_sim_climbing_image_again=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')
if climbing_image:
if climbing_image.isdigit():
climbing_image = int(climbing_image)
else:
try:
energies = np.loadtxt(climbing_image)[-1][1:]
energies = energies - energies[0]
climbing_image = np.where(energies == np.max(energies))[0][0]
except OSError:
raise Exception('Err trying to compute climb image from file')
print('Using climbing image: {}'.format(climbing_image))
# Start a NEB simulation passing the Simulation object and all the NEB
# parameters
neb = NEBM_Geodesic(sim,
init_images,
interpolations=interpolations,
spring_constant=spring_constant,
name=sim_name,
openmp=True,
climbing_image=climbing_image,
integrator=integrator,
interpolation_method=interpolation_method)
if integrator == 'verlet':
neb.integrator.mass = 1
neb.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
neb.relax(max_iterations=max_steps,
save_vtks_every=save_m_every,
save_npys_every=save_m_every,
stopping_dYdt=stopping_dydt,
dt=dt)
if variable_spring_forces:
neb.variable_k = True
neb.dk = spring_constant * 0.9
neb.relax(max_iterations=max_steps,
save_vtks_every=save_m_every,
save_npys_every=save_m_every,
stopping_dYdt=stopping_dydt,
dt=dt,
save_initial_state=False)
# Continue with climbing image if specified
if keep_sim_climbing_image:
if not keep_sim_climbing_image_steps:
keep_sim_climbing_image_steps = max_steps
# Find all local maxima
largest_E_im_idx = []
for i in range(2, neb.n_images - 2):
if (neb.energies[i] > neb.energies[i - 1]
and neb.energies[i - 1] > neb.energies[i - 2]
and neb.energies[i] > neb.energies[i + 1]
and neb.energies[i + 1] > neb.energies[i + 2]):
largest_E_im_idx.append(i)
elif (neb.energies[i] < neb.energies[i - 1]
and neb.energies[i - 1] < neb.energies[i - 2]
and neb.energies[i] < neb.energies[i + 1]
and neb.energies[i + 1] < neb.energies[i + 2]):
largest_E_im_idx.append(-i)
neb.climbing_image = largest_E_im_idx
print('Continuing simulation with CI = {}'.format(largest_E_im_idx))
neb.name += '_CI'
# Data will be appended to the initial NDT file, at least we create a
# new one with the CI appended to the sim name:
# neb.create_tablewriter()
# last_step_relax = neb.iterations
# Variable dk for better resolution around saddle points
# neb.variable_k = True
# neb.dk = spring_constant
neb.relax(max_iterations=keep_sim_climbing_image_steps,
save_vtks_every=save_m_every,
save_npys_every=save_m_every,
stopping_dYdt=keep_sim_climbing_image,
dt=dt,
save_initial_state=False)
# Remove initial state (same as final state from the prev relaxation)
# shutil.rmtree('vtks/{}_{}'.format(neb.name, last_step_relax))
# Continue with climbing image if specified
if keep_sim_climbing_image_again:
if not keep_sim_climbing_image_steps:
keep_sim_climbing_image_steps = max_steps
# Find all local maxima
largest_E_im_idx = []
for i in range(2, neb.n_images - 2):
if (neb.energies[i] > neb.energies[i - 1]
and neb.energies[i - 1] > neb.energies[i - 2]
and neb.energies[i] > neb.energies[i + 1]
and neb.energies[i + 1] > neb.energies[i + 2]):
largest_E_im_idx.append(i)
elif (neb.energies[i] < neb.energies[i - 1]
and neb.energies[i - 1] < neb.energies[i - 2]
and neb.energies[i] < neb.energies[i + 1]
and neb.energies[i + 1] < neb.energies[i + 2]):
largest_E_im_idx.append(-i)
neb.climbing_image = largest_E_im_idx
print('Continuing simulation with CI = {}'.format(largest_E_im_idx))
neb.name += '_CI'
neb.relax(max_iterations=keep_sim_climbing_image_steps,
save_vtks_every=save_m_every,
save_npys_every=save_m_every,
stopping_dYdt=keep_sim_climbing_image_again,
dt=dt,
save_initial_state=False)
# Produce a file with the data from a cubic interpolation for the band
interp_data = np.zeros((200, 2))
if interpolation_energy == 'polynomial':
neb.compute_polynomial_factors()
(interp_data[:, 0],
interp_data[:, 1]) = neb.compute_polynomial_approximation_energy(200)
elif interpolation_energy == 'Bernstein':
neb.compute_Bernstein_polynomials()
(interp_data[:, 0],
interp_data[:, 1]) = neb.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))
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))
