def test_init_invalid_args(self):
for K, u in self.invalid_args:
with pytest.raises((TypeError, ValueError)):
term = mm.UniaxialAnisotropy(K=K, u=u)
with pytest.raises(AttributeError):
term = mm.UniaxialAnisotropy(wrong=1)
def test_repr(self):
for K1, K2, u in self.valid_args:
anisotropy = mm.UniaxialAnisotropy(K1=K1, K2=K2, u=u)
exp_str = ("UniaxialAnisotropy(K1={}, K2={}, u={}, "
"name=\"{}\")").format(K1, K2, u, "uniaxialanisotropy")
assert repr(anisotropy) == exp_str
anisotropy = mm.UniaxialAnisotropy(1000, (0, 0, 1), name="test_name")
assert repr(anisotropy) == ("UniaxialAnisotropy(K1=1000, K2=0, "
"u=(0, 0, 1), name=\"test_name\")")
def test_repr(self):
for K1, K2, u in self.valid_args:
anisotropy = mm.UniaxialAnisotropy(K1=K1, K2=K2, u=u)
exp_str = ('UniaxialAnisotropy(K1={}, K2={}, u={}, '
'name=\'{}\')').format(K1, K2, u, 'uniaxialanisotropy')
assert repr(anisotropy) == exp_str
anisotropy = mm.UniaxialAnisotropy(1000, (0, 0, 1), name='test_name')
assert repr(anisotropy) == ('UniaxialAnisotropy(K1=1000, K2=0, '
'u=(0, 0, 1), name=\'test_name\')')
def test_exchange_dmi_zeeman_uniaxialanisotropy_demag(self):
name = 'exchange_dmi_zeeman_uniaxialanisotropy'
mesh = df.Mesh(region=self.region,
cell=self.cell,
subregions=self.subregions)
# Very weak DMI and strong Zeeman to make the final
# magnetisation uniform.
A = {'r1': 1e-12, 'r2': 3e-12, 'r1:r2': 2e-12}
D = {'r1': 1e-9, 'r2': 0, 'r1:r2': 5e-9} # Very weak DMI
H = df.Field(mesh, dim=3, value=(1e12, 0, 0))
K = 1e6
u = (1, 0, 0)
Ms = 1e5
system = mm.System(name=name)
system.energy = mm.Exchange(A=A) + \
mm.DMI(D=D, crystalclass='Cnv') + \
mm.UniaxialAnisotropy(K=K, u=u) + \
mm.Zeeman(H=H) + \
mm.Demag()
system.m = df.Field(mesh, dim=3, value=(1, 0.3, 0), norm=Ms)
md = self.calculator.MinDriver()
md.drive(system)
value = system.m(mesh.region.random_point())
assert np.linalg.norm(np.subtract(value, (Ms, 0, 0))) < 1
self.calculator.delete(system)
def test_field_vector(self):
name = 'uniaxialanisotropy_field_vector'
def value_fun(pos):
x, y, z = pos
if x <= 0:
return 0
else:
return 1e5
mesh = df.Mesh(region=self.region, cell=self.cell)
K = df.Field(mesh, dim=1, value=value_fun)
u = (0, 0, 1)
Ms = 1e6
system = mm.System(name=name)
system.energy = mm.UniaxialAnisotropy(K=K, u=u)
system.m = df.Field(mesh, dim=3, value=(0, 0.3, 1), norm=Ms)
md = self.calculator.MinDriver()
md.drive(system)
value = system.m((-2e-9, -2e-9, -2e-9))
assert np.linalg.norm(np.cross(value, (0, 0.3*Ms, Ms))) < 1e-3
value = system.m((2e-9, 2e-9, 2e-9))
assert np.linalg.norm(np.subtract(value, (0, 0, Ms))) < 1e-3
self.calculator.delete(system)
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/mm.consts.mu0) # magnetisation saturation (A/m)
A = 0.5 * mm.consts.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.
region = df.Region(p1=p1, p2=p2)
mesh = df.Mesh(region=region, cell=cell)
system = mm.System(name=name)
system.energy = (mm.Exchange(A=A) + mm.UniaxialAnisotropy(K=K, u=u) +
mm.Demag())
system.m = df.Field(mesh, dim=3, value=m_init, norm=Ms)
md = calculator.MinDriver()
md.drive(system)
calculator.delete(system)
return system
def test_scalar_field(self):
name = 'uniaxialanisotropy_scalar_field'
def value_fun(pos):
x, y, z = pos
if x <= 0:
return (1, 0, 0)
else:
return (0, 1, 0)
mesh = df.Mesh(region=self.region, cell=self.cell)
K = 1e5
u = df.Field(mesh, dim=3, value=value_fun)
Ms = 1e6
system = mm.System(name=name)
system.energy = mm.UniaxialAnisotropy(K=K, u=u)
system.m = df.Field(mesh, dim=3, value=(1, 1, 0), norm=Ms)
md = self.calculator.MinDriver()
md.drive(system)
value = system.m((-2e-9, -2e-9, -2e-9))
assert np.linalg.norm(np.subtract(value, (Ms, 0, 0))) < 1e-3
value = system.m((2e-9, 2e-9, 2e-9))
assert np.linalg.norm(np.subtract(value, (0, Ms, 0))) < 1e-3
self.calculator.delete(system)
def setup(self):
A = 1e-12
self.exchange = mm.Exchange(A=A)
H = (0, 0, 1.2e6)
self.zeeman = mm.Zeeman(H=H)
K1 = 1e4
K2 = 3e2
u = (0, 1, 0)
self.uniaxialanisotropy = mm.UniaxialAnisotropy(K1=K1, K2=K2, u=u)
self.demag = mm.Demag()
D = 1e-3
crystalclass = 't'
self.dmi = mm.DMI(D=D, crystalclass=crystalclass)
K1 = 5e6
u1 = (0, 0, 1)
u2 = (0, 1, 0)
self.cubicanisotropy = mm.CubicAnisotropy(K1=K1, u1=u1, u2=u2)
self.terms = [
self.exchange, self.zeeman, self.uniaxialanisotropy, self.demag,
self.dmi, self.cubicanisotropy
]
self.invalid_terms = [
1, 2.5, 0, 'abc', [3, 7e-12], [self.exchange, self.zeeman]
]
def test_init_valid_args(self):
for K, u in self.valid_args:
term = mm.UniaxialAnisotropy(K=K, u=u)
check_term(term)
assert hasattr(term, 'K')
assert hasattr(term, 'u')
assert term.name == 'uniaxialanisotropy'
assert re.search(r'^UniaxialAnisotropy\(K=.+, u=.+\)$', repr(term))
def test_init_valid_args(self):
for K1, K2, u in self.valid_args:
anisotropy = mm.UniaxialAnisotropy(K1=K1, K2=K2, u=u)
assert anisotropy.K1 == K1
assert anisotropy.K2 == K2
assert isinstance(anisotropy.K1, numbers.Real)
assert isinstance(anisotropy.K2, numbers.Real)
assert isinstance(anisotropy.u, (tuple, list, np.ndarray))
assert len(anisotropy.u) == 3
assert all([isinstance(i, numbers.Real) for i in anisotropy.u])
def test_skyrmion(calculator):
name = 'skyrmion'
Ms = 1.1e6
A = 1.6e-11
D = 4e-3
K = 0.51e6
u = (0, 0, 1)
H = (0, 0, 2e5)
p1 = (-50e-9, -50e-9, 0)
p2 = (50e-9, 50e-9, 10e-9)
cell = (5e-9, 5e-9, 5e-9)
region = df.Region(p1=p1, p2=p2)
mesh = df.Mesh(p1=p1, p2=p2, cell=cell)
system = mm.System(name=name)
system.energy = (mm.Exchange(A=A) + mm.DMI(D=D, crystalclass='Cnv') +
mm.UniaxialAnisotropy(K=K, u=u) + mm.Demag() +
mm.Zeeman(H=H))
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, dim=3, value=m_init, norm=Ms_fun)
md = calculator.MinDriver()
md.drive(system)
# Check the magnetisation at the sample centre.
value = system.m((0, 0, 0))
assert value[2] / Ms < -0.97
# Check the magnetisation at the sample edge.
value = system.m((50e-9, 0, 0))
assert value[2] / Ms > 0.5
self.calculator.delete(system)
def setup(self):
name = 'compute_tests'
p1 = (0, 0, 0)
p2 = (10e-9, 2e-9, 2e-9)
cell = (2e-9, 2e-9, 2e-9)
region = df.Region(p1=p1, p2=p2)
mesh = df.Mesh(region=region, cell=cell)
self.system = mm.System(name=name)
self.system.energy = (
mm.Exchange(A=1e-12) + mm.Demag() + mm.Zeeman(H=(8e6, 0, 0)) +
mm.UniaxialAnisotropy(K=1e4, u=(0, 0, 1)) +
mm.CubicAnisotropy(K=1e3, u1=(1, 0, 0), u2=(0, 1, 0)))
self.system.m = df.Field(mesh, dim=3, value=(0, 0, 1), norm=8e6)
def test_repr_latex(self):
for K1, K2, u in self.valid_args:
anisotropy = mm.UniaxialAnisotropy(K1=K1, K2=K2, u=u)
latex = anisotropy._repr_latex_()
# Assert some characteristics of LaTeX string.
assert isinstance(latex, str)
assert latex[0] == latex[-1] == '$'
assert 'K_{1}' in latex
assert '\mathbf{u}' in latex
assert '\mathbf{m}' in latex
assert '^{2}' in latex
assert '\cdot' in latex
if K2 != 0:
assert 'K_{2}' in latex
assert '^{4}' in latex
def setup(self):
self.exchange = mm.Exchange(A=1e-12)
self.zeeman = mm.Zeeman(H=(0, 0, 1.2e6))
self.uniaxialanisotropy = mm.UniaxialAnisotropy(K=1e4, u=(0, 1, 0))
self.demag = mm.Demag()
self.dmi = mm.DMI(D=1e-3, crystalclass='T')
self.cubicanisotropy = mm.CubicAnisotropy(K={
'r1': 1e6,
'r2': 5e6
},
u1=(0, 0, 1),
u2=(0, 1, 0))
self.terms = [
self.exchange, self.zeeman, self.uniaxialanisotropy, self.demag,
self.dmi, self.cubicanisotropy
]
self.invalid_terms = [1, 2.5, 0, 'abc', [3, 7e-12], [self.exchange, 2]]
def test_scalar_vector(self):
name = 'uniaxialanisotropy_scalar_vector'
K = 1e5
u = (0, 0, 1)
Ms = 1e6
system = mm.System(name=name)
system.energy = mm.UniaxialAnisotropy(K=K, u=u)
mesh = df.Mesh(region=self.region, cell=self.cell)
system.m = df.Field(mesh, dim=3, value=(0, 0.3, 1), norm=Ms)
md = self.calculator.MinDriver()
md.drive(system)
value = system.m(mesh.region.random_point())
assert np.linalg.norm(np.subtract(value, (0, 0, Ms))) < 1e-3
self.calculator.delete(system)
def test_field_dict(self):
name = 'uniaxialanisotropy_field_dict'
def K_fun(pos):
x, y, z = pos
if -2e-9 <= x <= 2e-9:
return 0
else:
return 1e5
def u_fun(pos):
x, y, z = pos
if x <= 0:
return (1, 0, 0)
else:
return (0, 1, 0)
mesh = df.Mesh(region=self.region, cell=self.cell)
K = df.Field(mesh, dim=1, value=K_fun)
u = df.Field(mesh, dim=3, value=u_fun)
Ms = 1e6
system = mm.System(name=name)
system.energy = mm.UniaxialAnisotropy(K=K, u=u)
system.m = df.Field(mesh, dim=3, value=(1, 1, 0), norm=Ms)
md = self.calculator.MinDriver()
md.drive(system)
value = system.m((-3e-9, -3e-9, -3e-9))
assert np.linalg.norm(np.subtract(value, (Ms, 0, 0))) < 1e-3
value = system.m((3e-9, 3e-9, 3e-9))
assert np.linalg.norm(np.subtract(value, (0, Ms, 0))) < 1e-3
value = system.m((0, 0, 0))
assert np.linalg.norm(np.cross(value, (Ms, Ms, 0))) < 1e-3
self.calculator.delete(system)
def test_dict_vector(self):
name = 'uniaxialanisotropy_dict_vector'
mesh = df.Mesh(region=self.region, cell=self.cell,
subregions=self.subregions)
K = {'r1': 0, 'r2': 1e5}
u = (0, 0, 1)
Ms = 1e6
system = mm.System(name=name)
system.energy = mm.UniaxialAnisotropy(K=K, u=u)
system.m = df.Field(mesh, dim=3, value=(0, 0.3, 1), norm=Ms)
md = self.calculator.MinDriver()
md.drive(system)
value = system.m((-2e-9, -2e-9, -2e-9))
assert np.linalg.norm(np.cross(value, (0, 0.3*Ms, Ms))) < 1e-3
value = system.m((2e-9, 2e-9, 2e-9))
assert np.linalg.norm(np.subtract(value, (0, 0, Ms))) < 1e-3
self.calculator.delete(system)
def test_exchange_uniaxialanisotropy(self):
name = 'exchange_uniaxialanisotropy'
A = {'r1': 1e-12, 'r2': 0}
K = 1e5
u = (1, 0, 0)
Ms = 1e6
mesh = df.Mesh(region=self.region,
cell=self.cell,
subregions=self.subregions)
system = mm.System(name=name)
system.energy = mm.Exchange(A=A) + \
mm.UniaxialAnisotropy(K=K, u=u)
system.m = df.Field(mesh, dim=3, value=(0.5, 1, 0), norm=Ms)
md = self.calculator.MinDriver()
md.drive(system)
value = system.m(mesh.region.random_point())
assert np.linalg.norm(np.subtract(value, (Ms, 0, 0))) < 1e-3
self.calculator.delete(system)
def test_script(self):
for K1, K2, u in self.valid_args:
anisotropy = mm.UniaxialAnisotropy(K1=K1, K2=K2, u=u)
with pytest.raises(NotImplementedError):
script = anisotropy._script
def test_name(self):
for K1, K2, u in self.valid_args:
anisotropy = mm.UniaxialAnisotropy(K1=K1, K2=K2, u=u)
assert anisotropy.name == 'uniaxialanisotropy'
def test_init_invalid_args(self):
for K1, K2, u in self.invalid_args:
with pytest.raises(Exception):
anisotropy = mm.UniaxialAnisotropy(K1=K1, K2=K2, u=u)
