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_demag_pbc(self):
name = 'demag_pbc'
Ms = 1e6
system = mm.System(name=name)
system.energy = mm.Demag()
md = self.calculator.MinDriver()
# 1D pbc
mesh = df.Mesh(region=self.region, cell=self.cell, bc='x')
system.m = df.Field(mesh, dim=3, value=(0, 0, 1), norm=Ms)
md.drive(system)
# 2D pbc
mesh = df.Mesh(region=self.region, cell=self.cell, bc='xy')
system.m = df.Field(mesh, dim=3, value=(0, 0, 1), norm=Ms)
with pytest.raises(ValueError):
md.drive(system)
# 3D pbc
mesh = df.Mesh(region=self.region, cell=self.cell, bc='xyz')
system.m = df.Field(mesh, dim=3, value=(0, 0, 1), norm=Ms)
with pytest.raises(ValueError):
md.drive(system)
self.calculator.delete(system)
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 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_set_hamiltonian_with_zero(self):
system = mm.System()
system.hamiltonian = mm.Exchange(1e-12) + mm.Demag()
assert isinstance(system.hamiltonian, mm.Hamiltonian)
assert len(system.hamiltonian.terms) == 2
system.hamiltonian = 0
assert isinstance(system.hamiltonian, mm.Hamiltonian)
assert len(system.hamiltonian.terms) == 0
def test_init(self):
system = mm.System(name="test_sim")
assert isinstance(system.hamiltonian, mm.Hamiltonian)
assert system.hamiltonian.terms == []
system.hamiltonian = mm.Exchange(1e-12) + mm.Demag()
assert len(system.hamiltonian.terms)
assert isinstance(system.dynamics, mm.Dynamics)
assert system.dynamics.terms == []
assert system.name == "test_sim"
def test_repr_latex_(self):
demag = mm.Demag()
latex = demag._repr_latex_()
# Assert some characteristics of LaTeX string.
assert isinstance(latex, str)
assert latex[0] == latex[-1] == '$'
assert r'\mu_{0}' in latex
assert r'\mathbf{H}_\text{d}' in latex
assert r'\mathbf{m}' in latex
assert r'\cdot' in latex
assert r'M_\text{s}' in latex
assert r'\frac{1}{2}' in latex
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_demag_asymptotic_radius(self):
name = 'demag_asymptotic_radius'
Ms = 1e6
system = mm.System(name=name)
system.energy = mm.Demag(asymptotic_radius=6)
system.m = df.Field(self.mesh, dim=3, value=(0, 0, 1), norm=Ms)
md = self.calculator.MinDriver()
md.drive(system)
# Check if it runs. Tests to be added here.
self.calculator.delete(system)
def test_stdprob5(calculator):
name = 'stdprob5'
# 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 + ZhangLi equation) parameters
gamma0 = 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 = mm.System(name=name)
p1 = (0, 0, 0)
p2 = (lx, ly, lz)
cell = (5e-9, 5e-9, 5e-9)
region = df.Region(p1=p1, p2=p2)
mesh = df.Mesh(region=region, cell=cell)
system.energy = mm.Exchange(A=A) + mm.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, dim=3, value=m_vortex, norm=Ms)
md = calculator.MinDriver()
md.drive(system)
system.dynamics += (mm.Precession(gamma0=gamma0) +
mm.Damping(alpha=alpha) + mm.ZhangLi(u=ux, beta=beta))
td = calculator.TimeDriver()
td.drive(system, t=8e-9, n=100)
mx = system.table.data['mx'].values
assert -0.35 < mx.min() < -0.30
assert -0.03 < mx.max() < 0
calculator.delete(system)
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_stdprob4(calculator):
name = 'stdprob4'
L, d, th = 500e-9, 125e-9, 3e-9 # (m)
cell = (5e-9, 5e-9, 3e-9) # (m)
p1 = (0, 0, 0)
p2 = (L, d, th)
region = df.Region(p1=p1, p2=p2)
mesh = df.Mesh(region=region, cell=cell)
Ms = 8e5 # (A/m)
A = 1.3e-11 # (J/m)
system = mm.System(name=name)
system.energy = mm.Exchange(A=A) + mm.Demag()
gamma0 = 2.211e5 # (m/As)
alpha = 0.02
system.dynamics = mm.Precession(gamma0=gamma0) + mm.Damping(alpha=alpha)
system.m = df.Field(mesh, dim=3, value=(1, 0.25, 0.1), norm=Ms)
md = calculator.MinDriver()
md.drive(system) # updates system.m in-place
H = (-24.6e-3 / mm.consts.mu0, 4.3e-3 / mm.consts.mu0, 0)
system.energy += mm.Zeeman(H=H)
td = calculator.TimeDriver()
td.drive(system, t=1e-9, n=200)
t = system.table.data['t'].values
my = system.table.data['my'].values
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
calculator.delete(system)
def test_init_valid_args(self):
system = mm.System()
check_system(system)
assert len(system.energy) == 0
assert len(system.dynamics) == 0
assert system.m is None
assert system.T == 0
assert system.name == 'unnamed' # Default value
system.energy = mm.Exchange(A=1e-12) + mm.Demag()
check_system(system)
assert len(system.energy) == 2
system.dynamics = mm.Precession(gamma0=2.21e5) + mm.Damping(alpha=1)
check_system(system)
assert len(system.dynamics) == 2
system.m = self.m
system.T = 5
check_system(system)
def test_init_valid_arg(self):
term = mm.Demag()
check_term(term)
assert term.name == 'demag'
assert re.search(r'^Demag\(.*\)$', repr(term))
def test_script(self):
demag = mm.Demag()
with pytest.raises(NotImplementedError):
script = demag._script
def test_repr(self):
demag = mm.Demag()
assert repr(demag) == 'Demag(name=\'demag\')'
def test_name(self):
demag = mm.Demag()
assert demag.name == 'demag'
