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 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_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 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_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 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 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-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 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, 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 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): 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_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): 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): # 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 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_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 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 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 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(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_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
def relax_neb(k, maxst, simname, init_im, interp, save_every=10000): """ Execute a simulation with the NEB function of the FIDIMAG code 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 files starting with the 'simname' string """ # Prepare simulation sim = Sim(mesh, name=simname) sim.driver.gamma = const.gamma # magnetisation in units of Bohr's magneton sim.mu_s = 2. * const.mu_B # 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) # Initial images 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 neb = NEB_Sundials(sim, init_images, interpolations=interpolations, spring=k, name=simname) neb.relax(max_steps=maxst, save_vtk_steps=save_every, save_npy_steps=save_every, stopping_dmdt=1e-2)
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 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_dw_dmi_atomistic(do_plot=False): mesh = CuboidMesh(nx=300, ny=1, nz=1) sim = Sim(mesh, name='relax') sim.set_default_options(gamma=const.gamma) sim.alpha = 0.5 sim.mu_s = const.mu_s_1 sim.do_precession = False sim.set_m(m_init_dw) J = 50.0 * const.k_B exch = UniformExchange(J) sim.add(exch) D = 0.01 * J dmi = DMI(D) sim.add(dmi) K = 0.005 * J anis = Anisotropy(K, axis=[1, 0, 0]) sim.add(anis) 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) xs = np.array([p[0] for p in mesh.coordinates]) - 150 mx, my, mz = analytical(xs, A=J / 2.0, D=-D, K=K) mxyz = sim.spin.copy() mxyz = mxyz.reshape(-1, 3).T assert max(abs(mxyz[0, :] - mx)) < 0.001 assert max(abs(mxyz[1, :] - my)) < 0.001 assert max(abs(mxyz[2, :] - mz)) < 0.0006 if do_plot: save_plot(xs, mxyz, mx, my, mz)
def create_simulation(R, B): mu_s = 3 sim_hexagon = HexagonSim( R, # R 0.2715, # a mu_s, # mu_s name='unnamed') sim = sim_hexagon.sim # mask = (sim.mu_s / C.mu_B) > 1e-5 exch = UniformExchange(5.881 * C.meV) sim.add(exch) dmi = DMI(D=1.557 * C.meV, dmi_type='interfacial') sim.add(dmi) sim.add(Zeeman([0., 0., B])) sim.add(Anisotropy(0.406 * C.meV, axis=[0, 0, 1])) return sim
def relax_system(mesh): sim = Sim(mesh, name='relax') sim.mu_s = 1e-23 sim.driver.gamma = 1.76e11 sim.driver.alpha = 1.0 J = 1e-22 exch = UniformExchange(J) sim.add(exch) demag = Demag() sim.add(demag) sim.set_m(init_m) ts = np.linspace(0, 5e-10, 101) for t in ts: sim.driver.run_until(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.do_procession = False sim.set_m(m_init_dw) J = 50.0 * const.k_B exch = UniformExchange(J) sim.add(exch) D = 0.1 * J dmi = DMI(D, dmi_type='interfacial') sim.add(dmi) K = 0.02 * J anis = Anisotropy(K, axis=[0, 0, 1]) sim.add(anis) 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) xs = np.array([p[0] for p in mesh.pos]) - 150 mx, my, mz = analytical(xs, A=J / 2.0, D=-D, K=K) mxyz = sim.spin.copy() mxyz.shape = (3, -1) save_plot(xs, mxyz, mx, my, mz)
def relax_system(mesh): sim = Sim(mesh, name='relax') sim.alpha = 0.1 sim.set_m(init_m) J = 1 exch = UniformExchange(J) sim.add(exch) dmi = DMI(0.05 * J) sim.add(dmi) ts = np.linspace(0, 1, 11) for t in ts: print t, sim.spin_length() - 1 sim.run_until(t) sim.save_vtk() return sim.spin