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(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 dynamic(mesh):
sim = Sim(mesh, name='dyn', driver='slonczewski')
# sim.set_options(rtol=1e-10,atol=1e-14)
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)
Kx = Anisotropy(Ku=0.005, axis=(1, 0, 0), name='Kx')
sim.add(Kx)
sim.p = (0, 0, 1)
sim.u0 = 0.03
sim.driver.alpha = 0.1
ts = np.linspace(0, 1e3, 101)
for t in ts:
sim.run_until(t)
sim.save_vtk()
print t
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 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_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)
Kx = Anisotropy(Ku=0.005, axis=(1, 0, 0), name='Kx')
sim.add(Kx)
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 test_full_exch_hex_3_shells_lattice_pos():
"""
Test the x component of the exchange field when using 3 shells of
neighbours in a 9 x 9 hexagonal lattice with square arrangement
We set the s_x and s_y spin components as the (i, j) index of the
lattice positions:
"""
a = 1
shells = 3
mesh = HexagonalMesh(a * 0.5,
nx=9,
ny=9,
shells=shells,
alignment='square')
sim = Sim(mesh)
# Set the indexes (i, j) as their s_x, s_y position
sim.set_m(lambda r: init_m(r, a), normalise=False)
Js = np.ones(shells)
exch = Exchange(Js)
sim.add(exch)
field = exch.compute_field()
assert field[3 * 0] == (1 + 1 + 0) + (2 + 0) + (2 + 1) # f_x 1st spin
assert field[3 * 11] == ((3 + 1 + 2 + 1 + 1 + 2) +
(3 + 0 + 2 + 0 + 0 + 3) + (4 + 0 + 3 + 0 + 1 + 0))
def dynamic(mesh):
sim = Sim(mesh, name='dyn', driver='slonczewski')
# sim.set_options(rtol=1e-10,atol=1e-14)
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)
Kx = Anisotropy(Ku=0.005, axis=(1, 0, 0), name='Kx')
sim.add(Kx)
sim.p = (0,0,1)
sim.u0 = 0.03
sim.alpha = 0.1
ts = np.linspace(0, 1e3, 101)
for t in ts:
sim.run_until(t)
sim.save_vtk()
print 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 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):
sim=Sim(mesh,name='relax')
sim.set_options(rtol=1e-12,atol=1e-14)
sim.do_precession = 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):
# Only relaxation
sim = Sim(mesh, name='relax')
# Simulation parameters
sim.driver.set_tols(rtol=1e-8, atol=1e-10)
sim.alpha = 0.5
sim.driver.gamma = 2.211e5 / mu0
sim.mu_s = 1e-27 / mu0
sim.driver.do_precession = False
# The initial state passed as a function
sim.set_m(init_m)
# sim.set_m(np.load('m0.npy'))
# Energies
exch = UniformExchange(J=2e-20)
sim.add(exch)
anis = Anisotropy(0.01 * 2e-20, axis=(0, 0, 1))
sim.add(anis)
# dmi = DMI(D=8e-4)
# sim.add(dmi)
# Start relaxation and save the state in m0.npy
sim.relax(dt=1e-14,
stopping_dmdt=1e4,
max_steps=5000,
save_m_steps=None,
save_vtk_steps=None)
np.save('m0.npy', sim.spin)
def test_sim_init_m_fun():
mesh = CuboidMesh(nx=3, ny=4, nz=5)
sim = Sim(mesh)
sim.set_m(init_m, normalise=False)
assert (sim.spin_at(1, 2, 3)[0] == 1)
assert (sim.spin_at(1, 2, 3)[1] == 2)
assert (sim.spin_at(1, 2, 3)[2] == 3)
def test_sim_init_m():
mesh = CuboidMesh(nx=3, ny=4, nz=5)
sim = Sim(mesh)
sim.set_m((0, 1, 0))
sim.spin.shape = (3, -1)
spin_y = sim.spin[1]
assert (spin_y.any() == 1)
def test_dynamic():
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='dyn_spin', driver='llg_stt_cpp')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.driver.gamma = 1.0
sim.mu_s = 1.0
sim.set_m((0.8,0,-1))
Kx = Anisotropy(Ku=-0.05, axis=(0, 0, 1), name='Kz')
sim.add(Kx)
sim.p = (0,0,1)
sim.a_J = 0.0052
sim.alpha = 0.1
ts = np.linspace(0, 1200, 401)
for t in ts:
sim.driver.run_until(t)
mz = sim.spin[2]
alpha, K, u = 0.1, 0.05, 0.0052
print(mz, u/(2*alpha*K))
#########################################################
# The system used in this test can be solved analytically, which gives that mz = u/(2*alpha*K),
# where K represents the easy-plane anisotropy.
###
assert abs(mz - u/(2*alpha*K))/mz< 5e-4
def test_sim_init_m_fun():
mesh = CuboidMesh(nx=3, ny=4, nz=5)
sim = Sim(mesh)
sim.set_m(init_m, normalise=False)
assert(sim.spin_at(1, 2, 3)[0] == 1)
assert(sim.spin_at(1, 2, 3)[1] == 2)
assert(sim.spin_at(1, 2, 3)[2] == 3)
def test_exch_3d():
"""
Test the exchange field of the spins in this 3D mesh:
bottom layer:
8 9 10 11
4 5 6 7 x 2
0 1 2 3
The assertions are the mx component
of the: 0, 1, 2, .. 7 spins
Remember the new new ordering: fx1, fy1, fz1, fx2, ...
"""
mesh = CuboidMesh(nx=4, ny=3, nz=2)
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
# print field
assert field[0] == 1
assert field[3] == 0 + 1 + 2 + 1
assert field[6] == 1 + 2 + 3 + 2
assert field[9] == 2 + 3 + 3
assert field[4 * 3] == 1
assert field[5 * 3] == 5
assert field[6 * 3] == 10
assert field[7 * 3] == 11
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_exch_1d():
"""
Test the x component of the exchange field
in a 1D mesh, with the spin ordering:
0 1 2 3 4 5
"""
mesh = CuboidMesh(nx=5, ny=1, nz=1)
sim = Sim(mesh)
exch = Exchange(1.0)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert field[0] == 1
assert field[1 * 3] == 2
assert field[2 * 3] == 4
assert field[3 * 3] == 6
assert field[4 * 3] == 3
assert np.max(field[2::3]) == 0
assert np.max(field[1::3]) == 0
def relax_system(mesh):
sim = Sim(mesh, name='relax')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.alpha = 1.0
sim.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):
# Only relaxation
sim = Sim(mesh, name='relax')
# Simulation parameters
sim.driver.set_tols(rtol=1e-8, atol=1e-10)
sim.alpha = 0.5
sim.driver.gamma = 2.211e5 / mu0
sim.mu_s = 1e-27 / mu0
sim.driver.do_precession = False
# The initial state passed as a function
sim.set_m(init_m)
# sim.set_m(np.load('m0.npy'))
# Energies
exch = UniformExchange(J=2e-20)
sim.add(exch)
anis = Anisotropy(0.01*2e-20, axis=(0, 0, 1))
sim.add(anis)
# dmi = DMI(D=8e-4)
# sim.add(dmi)
# Start relaxation and save the state in m0.npy
sim.relax(dt=1e-14, stopping_dmdt=1e4, max_steps=5000,
save_m_steps=None, save_vtk_steps=None)
np.save('m0.npy', sim.spin)
def test_dynamic():
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='dyn_spin', driver='llg_stt_cpp')
# sim.set_options(rtol=1e-10,atol=1e-14)
sim.driver.gamma = 1.0
sim.mu_s = 1.0
sim.set_m((0.8, 0, -1))
Kx = Anisotropy(Ku=-0.05, axis=(0, 0, 1), name='Kz')
sim.add(Kx)
sim.p = (0, 0, 1)
sim.a_J = 0.0052
sim.alpha = 0.1
ts = np.linspace(0, 1200, 401)
for t in ts:
sim.driver.run_until(t)
mz = sim.spin[2]
alpha, K, u = 0.1, 0.05, 0.0052
print(mz, u / (2 * alpha * K))
#########################################################
# The system used in this test can be solved analytically, which gives that mz = u/(2*alpha*K),
# where K represents the easy-plane anisotropy.
###
assert abs(mz - u / (2 * alpha * K)) / mz < 5e-4
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 test_exch_2d_pbc2d():
"""
Test the exchange field components in a 2D mesh with PBCs
The mesh sites:
3 4 5 --> (0,1,0) (1,1,0) (2,1,0)
y ^ 0 1 2 (0,0,0) (1,0,0) (2,0,0)
|
x -->
The expected components are in increasing order along x
"""
mesh = CuboidMesh(nx=3, ny=2, nz=1, periodicity=(True, True, False))
print mesh.neighbours
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
expected_x = np.array([3, 4, 5, 3, 4, 5])
expected_y = np.array([2, 2, 2, 2, 2, 2])
# Since the field ordering is now: fx1 fy1 fz1 fx2 ...
# We extract the x components jumping in steps of 3
assert np.max(abs(field[::3] - expected_x)) == 0
# For the y component is similar, now we start at the 1th
# entry and jump in steps of 3
assert np.max(abs(field[1::3] - expected_y)) == 0
# Similar fot he z component
assert np.max(field[2::3]) == 0
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.driver.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 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 test_exch_1d():
"""
Test the x component of the exchange field
in a 1D mesh, with the spin ordering:
0 1 2 3 4 5
"""
mesh = CuboidMesh(nx=5, ny=1, nz=1)
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert field[0] == 1
assert field[1 * 3] == 2
assert field[2 * 3] == 4
assert field[3 * 3] == 6
assert field[4 * 3] == 3
assert np.max(field[2::3]) == 0
assert np.max(field[1::3]) == 0
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 excite_system(mesh, Hy=0):
sim = Sim(mesh, name="dyn")
sim.set_options(rtol=1e-10, atol=1e-12)
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 = 0.18
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)
def relax_system(mesh, Hy=0):
sim = Sim(mesh, name="relax")
sim.set_options(rtol=1e-10, atol=1e-12)
sim.alpha = 0.5
sim.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-8, max_steps=10000, save_m_steps=100, save_vtk_steps=50)
np.save("m0.npy", sim.spin)
def test_sim_init_m():
mesh = CuboidMesh(nx=3, ny=4, nz=5)
sim = Sim(mesh)
sim.set_m((0, 1, 0))
sim.spin.shape = (3, -1)
spin_y = sim.spin[1]
assert(spin_y.any() == 1)
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 relax_system(mesh):
sim = Sim(mesh, name='relax')
sim.set_default_options(gamma=const.gamma)
sim.driver.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 excite_system(mesh):
sim = Sim(mesh, name='dyn')
# sim.set_options(rtol=1e-10,atol=1e-14)
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 = 0.09
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 relax_system(mesh, Dx=0.005, Dp=0.01):
mat = UnitMaterial()
sim = Sim(mesh, name='test_energy')
print('Created sim')
sim.driver.set_tols(rtol=1e-10, atol=1e-12)
sim.alpha = mat.alpha
sim.driver.gamma = mat.gamma
sim.pins = pin_fun
exch = UniformExchange(mat.J)
sim.add(exch)
print('Added UniformExchange')
anis = Anisotropy(Dx, axis=[1, 0, 0], name='Dx')
sim.add(anis)
print('Added Anisotropy')
anis2 = Anisotropy([0, 0, -Dp], name='Dp')
sim.add(anis2)
print('Added Anisotropy 2')
sim.set_m((1, 1, 1))
T = 100
ts = np.linspace(0, T, 201)
for t in ts:
# sim.save_vtk()
sim.driver.run_until(t)
print(('Running -', t))
# sim.save_vtk()
np.save('m0.npy', sim.spin)
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_exch_3d():
"""
Test the exchange field of the spins in this 3D mesh:
bottom layer:
8 9 10 11
4 5 6 7 x 2
0 1 2 3
Assertions are according to the mx component of the spins, since J is set
to 1
Spin components are given according to the (i, j) index position in the
lattice:
i lattice site
[[ 0. 0. 0.] --> 0 j=0
[ 1. 0. 0.] --> 1
[ 2. 0. 0.] --> 2
[ 3. 0. 0.] --> 3
[ 0. 1. 0.] --> 4 j=1
[ 1. 1. 0.]
...
Remember the field ordering: fx0, fy0, fz0, fx1, ...
"""
mesh = CuboidMesh(nx=4, ny=3, nz=2)
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
# print field
# Exchange from 0th spin
assert field[0] == 1
# Exchange from 1st spin
# spin: 2 0 5 13
# mx: 2 0 1 1
assert field[3] == 2 + 0 + 1 + 1
# Exchange from 2nd spin
# spin: 3 1 6 14
# mx: 3 1 2 2
assert field[6] == 3 + 1 + 2 + 2
# ...
assert field[9] == 2 + 3 + 3
assert field[4 * 3] == 1
assert field[5 * 3] == 5
assert field[6 * 3] == 10
assert field[7 * 3] == 11
def test_sim_spins(do_plot=False):
mesh = CuboidMesh(nx=10, ny=5, nz=1)
sim = Sim(mesh, name='10spin')
alpha = 0.1
gamma = 2.21e5
sim.alpha = alpha
sim.gamma = gamma
sim.mu_s = 1.0
sim.set_m((1, 0, 0))
print(sim.spin)
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
ts = np.linspace(0, 1e-9, 101)
mx = []
my = []
mz = []
real_ts = []
for t in ts:
sim.run_until(t)
real_ts.append(sim.t)
#print sim.t, abs(sim.spin_length()[0] - 1)
av = sim.compute_average()
mx.append(av[0])
my.append(av[1])
mz.append(av[2])
#sim.save_vtk()
mz = np.array(mz)
# print mz
a_mx, a_my, a_mz = single_spin(alpha, gamma, H0, ts)
print(sim.stat())
if do_plot:
plot(real_ts,
mx,
my,
mz,
a_mx,
a_my,
a_mz,
name='spins.pdf',
title='integrating spins')
print(("Max Deviation = {0}".format(np.max(np.abs(mz - a_mz)))))
assert np.max(np.abs(mz - a_mz)) < 5e-7
def test_demag_two_spin_xx():
mesh = CuboidMesh(nx=2, ny=1, nz=1)
sim = Sim(mesh)
demag = Demag()
sim.add(demag)
sim.set_m((1, 0, 0))
field = demag.compute_field()
print(field)
assert (field[0] == 2e-7)
assert (field[3] == 2e-7)
def test_exch_energy_1d():
mesh = CuboidMesh(nx=2, ny=1, nz=1)
sim = Sim(mesh)
exch = UniformExchange(1.23)
sim.add(exch)
sim.set_m((0, 0, 1))
energy = exch.compute_energy()
assert energy == -1.23
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 test_demag_two_spin_xx():
mesh = CuboidMesh(nx=2, ny=1, nz=1)
sim = Sim(mesh)
demag = Demag()
sim.add(demag)
sim.set_m((1, 0, 0))
field = demag.compute_field()
print field
assert(field[0] == 2e-7)
assert(field[3] == 2e-7)
def test_sim_single_spin_sllg(do_plot=False):
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='spin', driver='sllg')
alpha = 0.1
gamma = 2.21e5
sim.set_options(dt=5e-15, gamma=gamma)
sim.alpha = alpha
sim.mu_s = 1.0
sim.set_m((1, 0, 0))
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
ts = np.linspace(0, 1e-10, 101)
mx = []
my = []
mz = []
real_ts = []
for t in ts:
sim.run_until(t)
real_ts.append(sim.t)
print(sim.t, abs(sim.spin_length()[0] - 1))
mx.append(sim.spin[0])
my.append(sim.spin[1])
mz.append(sim.spin[2])
mz = np.array(mz)
a_mx, a_my, a_mz = single_spin(alpha, gamma, H0, ts)
if do_plot:
plot(real_ts,
mx,
my,
mz,
a_mx,
a_my,
a_mz,
name='spin_sllg.pdf',
title='integrating a spin')
print(("Max Deviation = {0}".format(np.max(np.abs(mz - a_mz)))))
assert np.max(np.abs(mz - a_mz)) < 1e-8
def test_sim_pin():
mesh = CuboidMesh(nx=3, ny=2, nz=1)
sim = Sim(mesh)
sim.set_m((0, 0.8, 0.6))
sim.alpha = 0.1
sim.gamma = 1.0
sim.pins = pin_fun
anis = Anisotropy(Ku=1.0, axis=[0, 0, 1], name='Dx')
sim.add(anis)
sim.run_until(1.0)
assert sim.spin[0] == 0
assert sim.spin[2] != 0
def test_sim_pin():
mesh = CuboidMesh(nx=3, ny=2, nz=1)
sim = Sim(mesh)
sim.set_m((0, 0.8, 0.6))
sim.alpha = 0.1
sim.gamma = 1.0
sim.pins = pin_fun
anis = Anisotropy(Ku=1.0, axis=[0, 0, 1], name='Dx')
sim.add(anis)
sim.run_until(1.0)
assert sim.spin[0] == 0
assert sim.spin[2] != 0
def test_sim_spins(do_plot=False):
mesh = CuboidMesh(nx=10, ny=5, nz=1)
sim = Sim(mesh, name='10spin')
alpha = 0.1
gamma = 2.21e5
sim.alpha = alpha
sim.gamma = gamma
sim.mu_s = 1.0
sim.set_m((1, 0, 0))
print(sim.spin)
H0 = 1e5
sim.add(Zeeman((0, 0, H0)))
ts = np.linspace(0, 1e-9, 101)
mx = []
my = []
mz = []
real_ts = []
for t in ts:
sim.run_until(t)
real_ts.append(sim.t)
#print sim.t, abs(sim.spin_length()[0] - 1)
av = sim.compute_average()
mx.append(av[0])
my.append(av[1])
mz.append(av[2])
#sim.save_vtk()
mz = np.array(mz)
# print mz
a_mx, a_my, a_mz = single_spin(alpha, gamma, H0, ts)
print(sim.stat())
if do_plot:
plot(real_ts, mx, my, mz, a_mx, a_my, a_mz, name='spins.pdf', title='integrating spins')
print(("Max Deviation = {0}".format(
np.max(np.abs(mz - a_mz)))))
assert np.max(np.abs(mz - a_mz)) < 5e-7
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_exch_1d_pbc():
mesh = CuboidMesh(nx=5, ny=1, nz=1, periodicity=(True, False, False))
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert field[0] == 1 + 4
assert field[3] == 2
assert field[6] == 4
assert field[9] == 6
assert field[12] == 3 + 0
assert np.max(field[2::3]) == 0
assert np.max(field[1::3]) == 0
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. PBCs are specified in the mesh
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((0, 0, 1))
# 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 relax_system(rtol=1e-10, atol=1e-12):
"""numerical solution"""
mesh = CuboidMesh(nx=1, ny=1, nz=1)
sim = Sim(mesh, name='relax')
sim.driver.set_tols(rtol=rtol, atol=atol)
sim.driver.alpha = 0.5
sim.driver.gamma = 2.21e5
sim.mu_s = 1.0
sim.set_m((1.0, 0, 0))
sim.add(Zeeman((0, 0, 1e5)))
ts = np.linspace(0, 1e-9, 1001)
for t in ts:
sim.driver.run_until(t)
def disable_test_sim_single_spin_llg_stt(do_plot=False):
ni = Nickel()
mesh = CuboidMesh(nx=1, ny=1, nz=1)
mesh.set_material(ni)
ni.alpha = 0.1
sim = Sim(mesh, driver='llg_stt')
sim.set_m((1, 0, 0))
H0 = 1
sim.add(Zeeman((0, 0, H0)))
dt = 1e-12
ts = np.linspace(0, 200 * dt, 101)
precession = ni.gamma / (1 + ni.alpha**2)
mz_ref = []
mxyz = []
real_ts = []
for t in ts:
sim.run_until(t)
real_ts.append(sim.t)
print(sim.t, abs(sim.spin_length()[0] - 1), sim.spin)
mz_ref.append(np.tanh(precession * ni.alpha * H0 * sim.t))
mxyz.append(np.copy(sim.spin))
mxyz = np.array(mxyz)
if do_plot:
ts_ns = np.array(real_ts) * 1e9
plt.plot(ts_ns, mxyz[:, 0], ".-", label="mx")
plt.plot(ts_ns, mxyz[:, 1], ".-", label="my")
plt.plot(ts_ns, mxyz[:, 2], ".-", label="mz")
plt.plot(ts_ns, mz_ref, "-", label="analytical")
plt.xlabel("time (ns)")
plt.ylabel("mz")
plt.title("integrating a macrospin")
plt.legend()
plt.savefig("test_llg_stt.png")
print(("Deviation = {0}".format(np.max(np.abs(mxyz[:, 2] - mz_ref)))))
assert np.max(np.abs(mxyz[:, 2] - mz_ref)) < 1e-9
def test_exch_2d():
mesh = CuboidMesh(nx=5, ny=2, nz=1)
sim = Sim(mesh)
exch = UniformExchange(1)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert np.max(field[2::3]) == 0
assert field[0] == 1
assert field[3] == 2 + 1
assert field[6] == 1 + 2 + 3
assert field[9] == 2 + 3 + 4
assert field[12] == 3 + 4
