def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.driver.set_tols(rtol=1e-10, atol=1e-10)
sim.driver.alpha = 0.1
sim.driver.gamma = 2.211e5
sim.Ms = spatial_Ms
print(sim.Ms)
sim.set_m(init_m)
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
demag = Demag()
sim.add(demag)
dmi = DMI(D=4e-3)
sim.add(dmi)
dmi2 = DMI(D=2e-3, dmi_type="interfacial")
sim.add(dmi2)
anis = UniaxialAnisotropy(-3e4, axis=(0, 0, 1))
sim.add(anis)
sim.relax(dt=1e-13,
stopping_dmdt=5e4,
max_steps=5000,
save_m_steps=100,
save_vtk_steps=50)
#np.save('m0.npy', sim.spin)
fd = demag.compute_field(sim.spin)
fe = exch.compute_field(sim.spin)
fdmi = dmi.compute_field(sim.spin)
fdmi2 = dmi2.compute_field(sim.spin)
fanis = anis.compute_field(sim.spin)
np.savetxt(
"test_fields.txt",
np.transpose([
np.concatenate((sim.Ms, sim.Ms, sim.Ms, [0.0])),
np.concatenate((sim.spin, [100])),
np.concatenate((fd, [demag.compute_energy()])),
np.concatenate((fe, [exch.compute_energy()])),
np.concatenate((fdmi, [dmi.compute_energy()])),
np.concatenate((fdmi2, [dmi2.compute_energy()])),
np.concatenate((fanis, [anis.compute_energy()]))
]),
header=
"Generated by Fidimag. Size=20x5x3, 2.5nm x 2.5nm x 3nm, Ms=8.0e5A/m, A=1.3e-11 J/m,"
+
" D=4e-3 J/m^2, D_int=2e-3 J/m^2, Ku=-3e4 J/m^3 axis=(0,0,1).\n Ms "
+ "".ljust(20) + " m0 " + "".ljust(20) + "demag" + "".ljust(20) +
"exch" + "".ljust(22) + "dmi" + "".ljust(22) + "dmi_interfacial" +
"".ljust(22) + "anis")
def test_dw_dmi(mesh=mesh, do_plot=False):
Ms = 8.0e5
sim = Sim(mesh, name='relax')
sim.set_m(m_init_dw)
sim.set_tols(rtol=1e-8, atol=1e-12)
sim.Ms = Ms
sim.alpha = 0.5
sim.do_precession = False
A = 1.3e-11
D = 4e-4
Kx = 8e4
Kp = -6e5
sim.add(UniformExchange(A))
sim.add(DMI(D))
sim.add(UniaxialAnisotropy(Kx, axis=[1, 0, 0], name='Kx'))
sim.relax(stopping_dmdt=0.01)
xs = np.array([p[0] for p in mesh.coordinates])
mx, my, mz = analytical(xs, A=A, D=D, K=Kx)
mxyz = sim.spin.copy()
mxyz = mxyz.reshape(-1, 3)
assert max(abs(mxyz[:, 0] - mx)) < 0.002
assert max(abs(mxyz[:, 1] - my)) < 0.002
assert max(abs(mxyz[:, 2] - mz)) < 0.0006
if do_plot:
save_plot(mxyz, mx, my, mz)
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-6, atol=1e-6)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = 8.6e5
sim.do_precession = False
sim.set_m(init_m)
#sim.set_m((0,0.1,1))
#sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
dmi = DMI(D=1.3e-3)
sim.add(dmi)
anis = UniaxialAnisotropy(-3.25e4, axis=(0, 0, 1))
sim.add(anis)
zeeman = Zeeman((0, 0, 6.014576e4))
sim.add(zeeman, save_field=True)
sim.relax(dt=1e-13,
stopping_dmdt=0.5,
max_steps=5000,
save_m_steps=None,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_tols(rtol=1e-6, atol=1e-6)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = 8.6e5
sim.do_precession = False
sim.set_m(init_m)
exch = UniformExchange(A=1.3e-11)
sim.add(exch)
dmi = DMI(D=-4e-3)
sim.add(dmi)
zeeman = Zeeman((0, 0, 4e5))
sim.add(zeeman, save_field=True)
sim.relax(dt=1e-13,
stopping_dmdt=1e-2,
save_m_steps=None,
save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def test_dmi_field_oommf(D=4.1e-3, Ms=2.6e5):
mesh = CuboidMesh(nx=10, ny=3, nz=2, dx=0.5, unit_length=1e-9)
sim = Sim(mesh)
sim.Ms = Ms
dmi = DMI(D=D, type='interfacial')
sim.add(dmi)
def init_m(pos):
x, y, z = pos
return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0)
sim.set_m(init_m)
field = dmi.compute_field()
init_m0 = (
r'return [list [expr {sin($x * 1e9) + $y * 1e9 + $z * 2.3e9}] ' +
r' [expr {cos($x * 1e9) + $y * 1e9 + $z * 1.3e9}] ' + r'0 ' + r'] ')
# TODO: check the sign of DMI in OOMMF.
field_oommf = compute_dmi_field(mesh, Ms=Ms, init_m0=init_m0, D=-D)
mx0, mx1, mx2 = compare_fields(field_oommf, field)
assert max([mx0, mx1, mx2]) < 1e-12
def relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.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((1,1,1))
# sim.set_m(np.load('m0.npy'))
A = 1.3e-11
exch = UniformExchange(A=A)
sim.add(exch)
dmi = DMI(D=1e-3)
sim.add(dmi)
zeeman = Zeeman((0, 0, 2e4))
sim.add(zeeman, save_field=True)
sim.relax(dt=1e-13, stopping_dmdt=0.01, max_steps=5000,
save_m_steps=None, save_vtk_steps=50)
np.save('m0.npy', sim.spin)
def create_simulation(mesh, simname):
# Initiate a simulation object. PBCs are specified in the mesh
sim = Sim(mesh, name=simname)
# Use default gamma value
# sim.gamma = const.gamma
# Magnetisation in A/m
sim.Ms = 148367
# We could change the parameters using this option
# sim.set_options(gamma=const.gamma)
# Initial magnetisation profile from the function
sim.set_m((0, 0.2, 0.8))
# Exchange constant
A = 1.602e-12
exch = UniformExchange(A)
sim.add(exch)
# DMI constant
D = 3.84e-3
dmi = DMI(D, dmi_type='interfacial')
sim.add(dmi)
# Zeeman field
sim.add(Zeeman((0, 0, 25. / c.mu_0)))
# Tune the damping for faster convergence
sim.driver.alpha = 0.5
# Remove precession
sim.driver.do_precession = False
sim.driver.set_tols(rtol=1e-12, atol=1e-12)
return sim
def run_fidimag(mesh):
mu0 = 4 * np.pi * 1e-7
Ms = 8.6e5
A = 16e-12
D = -3.6e-3
K = 510e3
sim = Sim(mesh)
sim.set_tols(rtol=1e-10, atol=1e-10)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = Ms
sim.do_precession = False
sim.set_m((0, 0, 1))
sim.add(UniformExchange(A))
sim.add(DMI(D, type='interfacial'))
sim.add(UniaxialAnisotropy(K, axis=(0, 0, 1)))
sim.relax(dt=1e-13, stopping_dmdt=0.01, max_steps=5000,
save_m_steps=None, save_vtk_steps=50)
m = sim.spin
return m.copy()
def test_dmi_field_oommf(D=4.1e-3, Ms=2.6e5):
mesh = CuboidMesh(nx=10, ny=3, nz=2, dx=0.5, unit_length=1e-9)
sim = Sim(mesh)
sim.Ms = Ms
dmi = DMI(D=D, type='interfacial')
sim.add(dmi)
def init_m(pos):
x, y, z = pos
return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0)
sim.set_m(init_m)
field = dmi.compute_field()
init_m0 = """
return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 0]
"""
# TODO: check the sign of DMI in OOMMF.
#field_oommf = compute_dmi_field(mesh, Ms=Ms, init_m0=init_m0, D=-D)
omf_file = os.path.join(os.path.dirname(os.path.abspath(__file__)),'omfs','test_dmi_field_oommf.ohf')
ovf = OMF2(omf_file)
field_oommf = ovf.get_all_mags()
mx0, mx1, mx2 = compare_fields(field_oommf, field)
assert max([mx0, mx1, mx2]) < 1e-12
def relax_neb(k, maxst, simname, init_im, interp, save_every=10000):
"""
Execute a simulation with the NEB function of the FIDIMAG code, for a
nano disk
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 folders starting with the 'simname'
"""
# Prepare simulation
# We define the small cylinder with the Magnetisation function
sim = Sim(mesh)
sim.Ms = cylinder
# Energies
# Exchange
sim.add(UniformExchange(A=A))
# Bulk DMI --> This produces a Bloch DW - like skyrmion
sim.add(DMI(D=D))
# No Demag, but this could have some effect
# Demagnetization energy
# sim.add(Demag())
# Initial images (npy files or functions)
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
# Initiate the NEB algorithm driver
neb = NEB_Sundials(sim,
init_images,
interpolations=interpolations,
spring=k,
name=simname)
# Start the relaxation
neb.relax(max_steps=maxst,
save_vtk_steps=save_every,
save_npy_steps=save_every,
stopping_dmdt=1)
def test_energy_dmi(Ms=8e5, D=1.32e-3):
mesh = CuboidMesh(nx=40,
ny=50,
nz=1,
dx=2.5,
dy=2.5,
dz=3,
unit_length=1e-9)
sim = Sim(mesh)
sim.Ms = Ms
dmi = DMI(D=D, type='interfacial')
#dmi = DMI(D=D, type='bulk')
sim.add(dmi)
def init_m(pos):
x, y, z = pos
return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 1)
sim.set_m(init_m)
dmi_energy = dmi.compute_energy()
# init_m0="""
# return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 1]
#"""
#field_oommf = compute_dmi_field(mesh, Ms=Ms, init_m0=init_m0, D=D)
dmi_energy_oommf = -4.5665527749090378e-20
print('dmi energy', dmi_energy)
assert abs(dmi_energy - dmi_energy_oommf) / dmi_energy_oommf < 1e-15
def excite_system(mesh):
sim = Sim(mesh, name='dyn', driver='llg_stt')
sim.set_tols(rtol=1e-8, atol=1e-10)
sim.alpha = 0.5
sim.gamma = 2.211e5
sim.Ms = 8.6e5
sim.set_m(np.load('m0.npy'))
exch = UniformExchange(A=1.3e-11)
sim.add(exch)
dmi = DMI(D=-4e-3)
sim.add(dmi)
zeeman = Zeeman((0, 0, 4e5))
sim.add(zeeman, save_field=True)
sim.jx = -5e12
sim.beta = 0
ts = np.linspace(0, 0.5e-9, 101)
for t in ts:
print 'time', t
sim.run_until(t)
sim.save_vtk()
# sim.driver.set_tols(rtol=1e-10, atol=1e-14)
sim.driver.alpha = args.alpha
# sim.driver.gamma = 2.211e5
if args.no_precession:
sim.do_precession = False
# Material parameters -----------------------------------------------------
sim.Ms = args.Ms
exch = UniformExchange(A=args.A)
sim.add(exch)
dmi = DMI(D=(args.D * 1e-3), type='interfacial')
sim.add(dmi)
if args.B:
zeeman = Zeeman((0, 0, args.B / mu0))
sim.add(zeeman, save_field=True)
if args.k_u:
# Uniaxial anisotropy along + z-axis
sim.add(UniaxialAnisotropy(args.k_u, axis=(0, 0, 1)))
if args.Demag:
print 'Using Demag!'
sim.add(Demag())
# -------------------------------------------------------------------------
# We define the cylinder with the Magnetisation function
sim = Sim(mesh, name='skyrmion')
sim.Ms = cylinder
# To get a faster relaxation, we tune the LLG equation parameters
sim.do_precession = False
sim.alpha = 0.5
# Initial magnetisation:
sim.set_m(init_m)
# Energies:
# Exchange
sim.add(UniformExchange(A=A))
# Bulk DMI
sim.add(DMI(D=D))
# Relax the system
sim.relax(dt=1e-12,
stopping_dmdt=0.0001,
max_steps=5000,
save_m_steps=None,
save_vtk_steps=None)
# Save the final relaxed state and a vtk file
np.save('sk_up.npy', sim.spin)
sim.save_vtk()
# -----------------------------------------------------------------------------
A = 13e-12 # J * m**-1
D = 3e-3 # J * m**-2
Ku = 0e6 # J * m**-3
Ms = 0.86e6 # A / m
B0 = 0.4 # T
sim.Ms = Ms
sim.add(UniformExchange(A))
sim.add(Demag())
# sim.add(UniaxialAnisotropy(Ku, (0, 0, 1)))
# Periodic DMI
sim.add(DMI(D, dmi_type='interfacial'))
# External field along the stripe length
sim.add(Zeeman((0, B0 / mu0, 0)), save_field=True)
# -----------------------------------------------------------------------------
# Relax the system first
sim.driver.alpha = 0.9
sim.driver.do_precession = False
sim.driver.relax(stopping_dmdt=0.01)
np.save('initial_state.npy', sim.spin)
# Remove automatically saved files
shutil.rmtree('unnamed_npys/')
shutil.rmtree('unnamed_vtks/')
def relax_neb(mesh, k, maxst, simname, init_im, interp,
save_every=10000, stopping_dYdt=0.01):
"""
Execute a simulation with the NEBM algorithm of the FIDIMAG code
Here we use always the 21x21 Spins Mesh and don't vary the material
parameters. This can be changed adding those parameters as variables.
We create a new Simulation object every time this function is called
since it can be modified in the process
k :: NEBM spring constant
maxst :: Maximum number of iterations
simname :: Simulation name. VTK and NPY files are saved in folders
starting with the 'simname' string
init_im :: A list with magnetisation states (usually loaded from
NPY files or from a function) that will be used as
images in the energy band, e.g. for two states:
[np.load('skyrmion.npy'), np.load('ferromagnet.npy')]
interp :: Array or list with the numbers of interpolations between
every pair of the 'init_im' list. The length of this array
is: len(__init_im) - 1
save_every :: Save VTK and NPY files every 'save_every' number of steps
"""
# Initialise a simulation object and set the default gamma for the LLG
# equation
sim = Sim(mesh, name=simname)
# sim.gamma = const.gamma
# Magnetisation in A/m
sim.Ms = 148367
# Interactions ------------------------------------------------------------
# Exchange constant
A = 1.602e-12
exch = UniformExchange(A)
sim.add(exch)
# DMI constant
D = 3.84e-3
dmi = DMI(D, dmi_type='interfacial')
sim.add(dmi)
# Zeeman field
sim.add(Zeeman((0, 0, 25. / c.mu_0)))
# -------------------------------------------------------------------------
# Set the initial images from the list
init_images = init_im
# The number of interpolations must always be
# equal to 'the number of initial states specified', minus one.
interpolations = interp
# Start a NEB simulation passing the Simulation object and all the NEB
# parameters
neb = NEBM_Geodesic(sim,
init_images,
interpolations=interpolations,
spring_constant=k,
name=simname,
)
# Finally start the energy band relaxation
neb.relax(max_iterations=maxst,
save_vtks_every=save_every,
save_npys_every=save_every,
stopping_dYdt=stopping_dYdt
)
# Produce a file with the data from a cubic interpolation for the band
interp_data = np.zeros((200, 2))
interp_data[:, 0], interp_data[:, 1] = neb.compute_polynomial_approximation(200)
np.savetxt(simname + 'interpolation.dat', interp_data)