def minimise_system_energy(L, m_init):
N = 16 # discretisation in one dimension
cubesize = 100e-9 # cube edge length (m)
cellsize = cubesize / N # discretisation in all three dimensions.
lex = cubesize / L # exchange length.
Km = 1e6 # magnetostatic energy density (J/m**3)
Ms = np.sqrt(2 * Km / oc.mu0) # magnetisation saturation (A/m)
A = 0.5 * oc.mu0 * Ms**2 * lex**2 # exchange energy constant
K = 0.1 * Km # Uniaxial anisotropy constant
u = (0, 0, 1) # Uniaxial anisotropy easy-axis
p1 = (0, 0, 0) # Minimum sample coordinate.
p2 = (cubesize, cubesize, cubesize) # Maximum sample coordinate.
cell = (cellsize, cellsize, cellsize) # Discretisation.
mesh = oc.Mesh(p1=(0, 0, 0),
p2=(cubesize, cubesize, cubesize),
cell=(cellsize, cellsize, cellsize))
system = oc.System(name=name)
system.hamiltonian = oc.Exchange(A) + oc.UniaxialAnisotropy(K, u) + \
oc.Demag()
system.m = df.Field(mesh, value=m_init, norm=Ms)
md = oc.MinDriver()
md.drive(system)
return system
def test_script(self):
system = oc.System(name="test_system")
system.mesh = oc.Mesh((0, 0, 0), (5, 5, 5), (1, 1, 1))
system.hamiltonian += oc.Exchange(1e-12)
system.hamiltonian += oc.Demag()
system.hamiltonian += oc.UniaxialAnisotropy(1e3, (0, 1, 0))
system.hamiltonian += oc.Zeeman((0, 1e6, 0))
system.dynamics += oc.Precession(2.211e5)
system.dynamics += oc.Damping(0.1)
system.m = lambda pos: (0, 1, 0)
script = system.script()
assert script[0] == "#"
assert script[-1] == "\n"
assert script.count("#") == 6
assert script.count("Specify") == 6
assert "Exchange" in script
assert "Demag" in script
assert "Zeeman" in script
assert "UniaxialAnisotropy" in script
assert "BoxAtlas" in script
assert "RectangularMesh" in script
def __init__(self,
A=20e-12,
Ms=0.648,
B=0.1,
L=400e-9,
thickness=100e-9,
init_state_radius=80e-9,
cell=(4e-9, 4e-9, 4e-9)):
self.A = A
self.Ms = Ms / mu0
self.Ku = A / 2.3e-16
self.B = B
self.L = L
self.thickness = thickness
print('Exch length lex = ',
1e9 * np.sqrt(2 * self.A / (mu0 * self.Ms**2)), 'nm')
self.mesh = oc.Mesh(p1=(-self.L / 2, -self.L / 2, -self.thickness / 2),
p2=(self.L / 2, self.L / 2, self.thickness / 2),
cell=cell)
self.system = oc.System(name='oommf_typeII_bubble')
# Add interactions
self.system.hamiltonian = (
oc.Exchange(A=self.A) +
oc.UniaxialAnisotropy(K1=self.Ku, u=(0, 0, 1)) + oc.Demag() +
oc.Zeeman((0, 0, self.B / mu0)))
self.system.m = df.Field(
self.mesh,
value=lambda r: init_type2bubble_bls_II(r, init_state_radius),
norm=self.Ms)
# self.system.m = df.Field(self.mesh, value=(0, 0.1, 0.99),
# norm=self.Ms)
self.md = oc.MinDriver()
# Get system cordinates
self.coordinates = np.array(list(self.system.m.mesh.coordinates))
# Turn coordinates into a (N, 3) array and save in corresponding
# variables scaled in nm
self.x, self.y, self.z = (self.coordinates[:, 0] * 1e9,
self.coordinates[:, 1] * 1e9,
self.coordinates[:, 2] * 1e9)
# Array with uniue z coordinates
self.xs = np.unique(self.x)
self.ys = np.unique(self.y)
self.zs = np.unique(self.z)
self.z_layers = {}
for i, z in enumerate(self.zs):
self.z_layers[i] = '{:.2f} nm'.format(z)
# Compute the initial magnetisation profile
self.compute_magnetisation()
def setup(self):
self.system = oc.System(name='tds')
mesh = oc.Mesh((0, 0, 0), (100e-9, 100e-9, 10e-9),
(10e-9, 10e-9, 10e-9))
self.system.hamiltonian += oc.Exchange(1.5e-11)
self.system.hamiltonian += oc.Demag()
self.system.dynamics += oc.Precession(2.211e5)
self.system.dynamics += oc.Damping(0.02)
self.system.m = df.Field(mesh, value=(0, 1, 0), norm=8e5)
def setup(self):
self.name = "derive_tests"
if os.path.exists(self.name):
shutil.rmtree(self.name)
self.system = oc.System(name=self.name)
self.system.hamiltonian += oc.Exchange(A=1e-12)
self.system.hamiltonian += oc.Demag()
self.system.hamiltonian += oc.Zeeman(H=(8e6, 0, 0))
self.system.hamiltonian += oc.UniaxialAnisotropy(K1=1e4, u=(0, 0, 1))
mesh = oc.Mesh(p1=(0, 0, 0),
p2=(4e-9, 4e-9, 2e-9),
cell=(1e-9, 1e-9, 1e-9))
self.system.m = df.Field(mesh, value=(0, 0, 1), norm=8e6)
def setup(self):
A = 1e-12
self.exchange = oc.Exchange(A)
H = (0, 0, 1.2e6)
self.zeeman = oc.Zeeman(H)
K = 1e4
u = (0, 1, 0)
self.uniaxialanisotropy = oc.UniaxialAnisotropy(K, u)
self.demag = oc.Demag()
self.terms = [self.exchange,
self.zeeman,
self.uniaxialanisotropy,
self.demag]
def test_stdprob5():
name = "stdprob5"
# Remove any previous simulation directories.
if os.path.exists(name):
shutil.rmtree(name)
# Geometry
lx = 100e-9 # x dimension of the sample(m)
ly = 100e-9 # y dimension of the sample (m)
lz = 10e-9 # sample thickness (m)
# Material (permalloy) parameters
Ms = 8e5 # saturation magnetisation (A/m)
A = 1.3e-11 # exchange energy constant (J/m)
# Dynamics (LLG + STT equation) parameters
gamma = 2.211e5 # gyromagnetic ratio (m/As)
alpha = 0.1 # Gilbert damping
ux = -72.35 # velocity in x direction
beta = 0.05 # non-adiabatic STT parameter
system = oc.System(name=name)
mesh = oc.Mesh(p1=(0, 0, 0),
p2=(100e-9, 100e-9, 10e-9),
cell=(5e-9, 5e-9, 5e-9))
system.mesh = mesh
system.hamiltonian = oc.Exchange(A) + oc.Demag()
def m_vortex(pos):
x, y, z = pos[0] / 1e-9 - 50, pos[1] / 1e-9 - 50, pos[2] / 1e-9
return (-y, x, 10)
system.m = df.Field(mesh, value=m_vortex, normalisedto=Ms)
md = oc.MinDriver()
md.drive(system)
system.dynamics += oc.Precession(gamma) + oc.Damping(alpha) + \
oc.STT(u=(ux, 0, 0), beta=beta)
td = oc.TimeDriver()
td.drive(system, t=8e-9, n=100)
mx = system.dt["mx"].as_matrix()
assert -0.03 < mx.max() < 0
assert -0.35 < mx.min() < -0.30
shutil.rmtree(name)
def test_script(self):
for A in self.valid_args:
exchange = oc.Exchange(A)
script = exchange._script
assert script.count("\n") == 5
assert script[0] == "#"
assert script[-1] == "\n"
lines = script.split("\n")
assert len(lines) == 6
assert lines[0] == "# UniformExchange"
assert lines[1] == "Specify Oxs_UniformExchange {"
assert lines[2] == " A {}".format(A)
assert lines[3] == "}"
def bar():
system = oc.System(name="example-bar")
shape = (100e-9, 30e-9, 30e-9)
d = 10e-9
mesh = oc.Mesh(p1=(0, 0, 0), p2=shape, cell=(d, d, d))
# Permalloy
A = 1e-12
H = (0, 0, 0) # no Zeeman field, but provide interaction as convenience
system.hamiltonian = oc.Exchange(A=A) + oc.Demag() + oc.Zeeman(H=H)
alpha = 0.2
system.dynamics = oc.Precession(gamma=oc.gamma0) + oc.Damping(alpha=alpha)
Ms = 8e6 # A/m
system.m = df.Field(mesh, value=(1, 0, 1), norm=Ms)
return system
def test_skyrmion():
name = "skyrmion"
# Remove any previous simulation directories.
if os.path.exists(name):
shutil.rmtree(name)
mesh = oc.Mesh(p1=(-50e-9, -50e-9, 0),
p2=(50e-9, 50e-9, 10e-9),
cell=(5e-9, 5e-9, 5e-9))
system = oc.System(name="skyrmion")
system.hamiltonian = oc.Exchange(A=1.6e-11) + \
oc.DMI(D=4e-3, kind="interfacial") + \
oc.UniaxialAnisotropy(K1=0.51e6, K2=0.1, u=(0, 0, 1)) + \
oc.Demag() + \
oc.Zeeman(H=(0, 0, 2e5))
Ms = 1.1e6
def Ms_fun(pos):
x, y, z = pos
if (x**2 + y**2)**0.5 < 50e-9:
return Ms
else:
return 0
def m_init(pos):
x, y, z = pos
if (x**2 + y**2)**0.5 < 10e-9:
return (0, 0.1, -1)
else:
return (0, 0.1, 1)
system.m = df.Field(mesh, value=m_init, norm=Ms_fun)
md = oc.MinDriver()
md.drive(system)
# Check the magnetisation at the sample centre.
assert system.m((0, 0, 0))[2] / Ms < -0.97
# Check the magnetisation at the sample edge.
assert system.m((50e-9, 0, 0))[2] / Ms > 0
shutil.rmtree(name)
def test_stdprobfmr():
name = "stdprobfmr"
# Remove any previous simulation directories.
if os.path.exists(name):
shutil.rmtree(name)
lx = ly = 120e-9 # x and y dimensions of the sample(m)
lz = 10e-9 # sample thickness (m)
dx = dy = dz = 10e-9 # discretisation in x, y, and z directions (m)
Ms = 8e5 # saturation magnetisation (A/m)
A = 1.3e-11 # exchange energy constant (J/m)
H = 8e4 * np.array([0.81345856316858023, 0.58162287266553481, 0.0])
alpha = 0.008 # Gilbert damping
gamma = 2.211e5
mesh = oc.Mesh(p1=(0, 0, 0), p2=(lx, ly, lz), cell=(dx, dy, dz))
system = oc.System(name="stdprobfmr")
system.hamiltonian = oc.Exchange(A) + oc.Demag() + oc.Zeeman(H)
system.dynamics = oc.Precession(gamma) + oc.Damping(alpha)
system.m = df.Field(mesh, value=(0, 0, 1), norm=Ms)
md = oc.MinDriver()
md.drive(system)
H = 8e4 * np.array([0.81923192051904048, 0.57346234436332832, 0.0])
system.hamiltonian.zeeman.H = H
T = 20e-9
n = 4000
td = oc.TimeDriver()
td.drive(system, t=T, n=n)
t = system.dt['t'].as_matrix()
my = system.dt['mx'].as_matrix()
psd = np.log10(np.abs(scipy.fftpack.fft(my))**2)
f_axis = scipy.fftpack.fftfreq(4000, d=20e-9/4000)
shutil.rmtree(name)
def test_stdprob1():
name = "stdprob1"
# Geometry
lx = 2e-6 # x dimension of the sample(m)
ly = 1e-6 # y dimension of the sample (m)
lz = 20e-9 # sample thickness (m)
# Material parameters
Ms = 8e5 # saturation magnetisation (A/m)
A = 1.3e-11 # exchange energy constant (J/m)
K = 0.5e3 # uniaxial anisotropy constant (J/m**3)
u = (1, 0, 0) # uniaxial anisotropy axis
# Create a mesh object.
mesh = oc.Mesh(p1=(0, 0, 0), p2=(lx, ly, lz), cell=(20e-9, 20e-9, 20e-9))
system = oc.System(name=name)
system.hamiltonian = oc.Exchange(A) + oc.UniaxialAnisotropy(K, u) + \
oc.Demag()
system.m = df.Field(mesh, value=(-10, -1, 0), norm=Ms)
Hmax = (50e-3 / oc.mu0, 0.87275325e-3 / oc.mu0, 0)
Hmin = (-50e-3 / oc.mu0, -0.87275325e-3 / oc.mu0, 0)
n = 10
hd = oc.HysteresisDriver()
hd.drive(system, Hmax=Hmax, Hmin=Hmin, n=n)
Bx = system.dt["Bx"].as_matrix()
mx = system.dt["mx"].as_matrix()
assert len(mx) == 21
assert len(Bx) == 21
shutil.rmtree(name)
name = "test_sample"
# Remove any previous simulation directories.
if os.path.exists(name):
shutil.rmtree(name)
L = 30e-9 # (m)
cellsize = (10e-9, 15e-9, 5e-9) # (m)
mesh = oc.Mesh((0, 0, 0), (L, L, L), cellsize)
system = oc.System(name=name)
A = 1.3e-11 # (J/m)
H = (1e6, 0.0, 2e5)
system.hamiltonian = oc.Exchange(A=A) + oc.Zeeman(H=H)
gamma = 2.211e5 # (m/As)
alpha = 0.02
system.dynamics = oc.Precession(gamma) + oc.Damping(alpha)
Ms = 8e5 # (A/m)
system.m = df.Field(mesh, value=(0.0, 0.25, 0.1), norm=Ms)
td = oc.TimeDriver()
td.drive(system, t=25e-12, n=25) # updates system.m in-place
td.drive(system, t=15e-12, n=15)
td.drive(system, t=5e-12, n=10)
md = oc.MinDriver()
md.drive(system)
def test_stdprob4():
name = "stdprob4"
# Remove any previous simulation directories.
if os.path.exists(name):
shutil.rmtree(name)
L, d, th = 500e-9, 125e-9, 3e-9 # (m)
cellsize = (5e-9, 5e-9, 3e-9) # (m)
mesh = oc.Mesh((0, 0, 0), (L, d, th), cellsize)
system = oc.System(name=name)
A = 1.3e-11 # (J/m)
system.hamiltonian = oc.Exchange(A) + oc.Demag()
gamma = 2.211e5 # (m/As)
alpha = 0.02
system.dynamics = oc.Precession(gamma) + oc.Damping(alpha)
Ms = 8e5 # (A/m)
system.m = df.Field(mesh, value=(1, 0.25, 0.1), norm=Ms)
md = oc.MinDriver()
md.drive(system) # updates system.m in-place
dirname = os.path.join(name, "")
miffilename = os.path.join(name, "{}.mif".format(name))
assert os.path.exists(dirname)
assert os.path.isfile(miffilename)
omf_files = list(glob.iglob("{}/*.omf".format(name)))
odt_files = list(glob.iglob("{}/*.odt".format(name)))
assert len(omf_files) == 2
omffilename = os.path.join(name, "m0.omf")
assert omffilename in omf_files
assert len(odt_files) == 1
shutil.rmtree(name)
H = (-24.6e-3/oc.mu0, 4.3e-3/oc.mu0, 0)
system.hamiltonian += oc.Zeeman(H)
td = oc.TimeDriver()
td.drive(system, t=1e-9, n=200)
dirname = os.path.join(name, "")
miffilename = os.path.join(name, "{}.mif".format(name))
assert os.path.exists(dirname)
assert os.path.isfile(miffilename)
omf_files = list(glob.iglob("{}/*.omf".format(name)))
odt_files = list(glob.iglob("{}/*.odt".format(name)))
assert len(omf_files) == 201
omffilename = os.path.join(name, "m0.omf")
assert omffilename in omf_files
assert len(odt_files) == 1
myplot = system.dt.plot("t", "my")
figfilename = os.path.join(name, "stdprob4-t-my.pdf")
myplot.figure.savefig(figfilename)
assert os.path.isfile(figfilename)
t = system.dt["t"].as_matrix()
my = system.dt["my"].as_matrix()
assert abs(min(t) - 5e-12) < 1e-20
assert abs(max(t) - 1e-9) < 1e-20
# Eye-norm test.
assert 0.7 < max(my) < 0.8
assert -0.5 < min(my) < -0.4
shutil.rmtree(name)
import oommfc as mc # import mumaxc as mc import discretisedfield as df L = 10e-9 d = 1e-9 Ms = 8e6 # saturation magnetisation (A/m) A = 1e-12 # exchange energy constant (J/m) H = (5e6, 0, 0) # external magnetic field in the x-direction (A/m) gamma = 2.211e5 # gamma parameter (m/As) alpha = 0.2 # Gilbert damping mesh = mc.Mesh(p1=(0, 0, 0), p2=(L, L, L), cell=(d, d, d)) system = mc.System(name='example2') system.hamiltonian = mc.Exchange(A=A) + mc.Demag() + mc.Zeeman(H=H) system.dynamics = mc.Precession(gamma=gamma) + mc.Damping(alpha=alpha) system.m = df.Field(mesh, value=(0, 0, 1), norm=Ms) td = mc.TimeDriver() td.drive(system, t=1e-9, n=10, overwrite=True) mx, my, mz = system.m.average assert mx > my assert mx > mz print(system.m.average)
