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 = (-1, 3) spin_y = sim.spin[:, 1] assert(spin_y.any() == 1)
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 = (-1, 3) spin_y = sim.spin[:, 1] assert (spin_y.any() == 1)
def compute_field(): mesh = CuboidMesh(nx=1, ny=1, nz=1, dx=2.0, dy=2.0, dz=2.0, unit_length=1e-9, periodicity=(True, True, False)) sim = Sim(mesh, name='relax') sim.driver.set_tols(rtol=1e-10, atol=1e-14) sim.driver.alpha = 0.5 sim.driver.gamma = 2.211e5 sim.Ms = 8.6e5 sim.do_precession = False sim.set_m((0, 0, 1)) # sim.set_m(np.load('m0.npy')) A = 1.3e-11 exch = UniformExchange(A=A) sim.add(exch) demag = Demag(pbc_2d=True) sim.add(demag) field = demag.compute_field() print(field) np.save('m0.npy', sim.spin)
def relax_neb(k, maxst, simname, init_im, interp, save_every=10000, coordinates='Cartesian'): """ Execute a simulation with the NEB function of the FIDIMAG code, for an elongated particle (long cylinder) 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 # We define the cylinder with the Magnetisation function sim = Sim(mesh) sim.Ms = two_part # sim.add(UniformExchange(A=A)) # Uniaxial anisotropy along x-axis sim.add(UniaxialAnisotropy(Kx, axis=(1, 0, 0))) # Define many initial states close to one extreme. We want to check # if the images in the last step, are placed mostly in equally positions 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 if coordinates == 'Spherical': neb = NEBM_Spherical(sim, init_images, interpolations=interpolations, spring_constant=k, name=simname ) if coordinates == 'Geodesic': neb = NEBM_Geodesic(sim, init_images, interpolations=interpolations, spring_constant=k, name=simname, integrator='sundials' ) neb.relax(max_iterations=2000, save_vtks_every=save_every, save_npys_every=save_every, stopping_dYdt=1e-4, dt=1e-6 )
def setup_simulation(mesh, m0, simulation_name, integrator="sundials", use_jac=False): sim = Sim(mesh, name=simulation_name, integrator=integrator, use_jac) sim.set_m(m0) sim.Ms = Ms sim.alpha = alpha sim.gamma = gamma sim.add(UniformExchange(A)) sim.add(Demag()) return sim
def excite_system(mesh): # Specify the stt dynamics in the simulation sim = Sim(mesh, name='fidimag', driver='llg_stt') sim.driver.set_tols(rtol=1e-8, atol=1e-8) sim.driver.alpha = 0.1 sim.driver.gamma = 2.211e5 sim.Ms = 8.0e5 sim.driver.p = 1 sim.set_m(np.load('npys/m0_cpu.npy')) A = 1.3e-11 exch = UniformExchange(A=A) sim.add(exch) sim.add(Demag()) sim.driver.jx = -1e12 sim.driver.beta = 0.05 ts = np.linspace(0, 8e-9, 801) for t in ts: print('time', t) sim.driver.run_until(t)
def compute_field(): mesh = CuboidMesh(nx=1, ny=1, nz=1, dx=2.0, dy=2.0, dz=2.0, unit_length=1e-9, periodicity=(True, True, False)) sim = Sim(mesh, name='relax') sim.driver.set_tols(rtol=1e-10, atol=1e-14) sim.driver.alpha = 0.5 sim.driver.gamma = 2.211e5 sim.Ms = 8.6e5 sim.do_precession = False sim.set_m((0,0,1)) # sim.set_m(np.load('m0.npy')) A = 1.3e-11 exch = UniformExchange(A=A) sim.add(exch) demag = Demag(pbc_2d=True) sim.add(demag) field=demag.compute_field() print(field) np.save('m0.npy', sim.spin)
def test_zeeman_energy(): mu0 = 4 * np.pi * 1e-7 # A system of 8 cells ( not using nm units) mesh = CuboidMesh(dx=2, dy=2, dz=2, nx=2, ny=2, nz=2 ) sim = Sim(mesh) Ms = 1e5 sim.set_Ms(Ms) sim.set_m((0, 0, 1)) H = 0.1 / mu0 zeeman = Zeeman((0, 0, H)) sim.add(zeeman) field = zeeman.compute_field() zf = sim.get_interaction('Zeeman') # -> -> # Expected energy: Int ( -mu0 M * H ) dV # Since we have 8 cells with the same M, we just sum their contrib exp_energy = 8 * (-mu0 * H * Ms * mesh.dx * mesh.dy * mesh.dz) assert np.abs(zf.compute_energy() - exp_energy) < 1e-10
def setup_domain_wall_cobalt(node_count=NODE_COUNT, A=A_Co, Ms=Ms_Co, K1=K1_Co, length=LENGTH, do_precession=True, unit_length=UNIT_LENGTH): a = length / node_count # cell size mesh = CuboidMesh(dx=a, dy=a, dz=a, nx=node_count, ny=1, nz=1, unit_length=unit_length) sim = Sim(mesh, "dw_cobalt") sim.Ms = Ms sim.set_m(lambda r: initial_m(r, length)) sim.do_precession = do_precession sim.add(UniformExchange(A)) sim.add(UniaxialAnisotropy(K1, (0, 0, 1))) sim.pins = lambda r: 1 if (r[0] < a or r[0] > LENGTH - a) else 0 return sim
def test_sim_init_m_fun(): mesh = CuboidMesh(nx=3, ny=4, nz=5) sim = Sim(mesh) sim.set_m(init_m, normalise=False) print sim.spin.reshape(-1, 3).shape print sim.mesh.index(1, 2, 3) 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 elongated_part_sim(): sim = Sim(mesh) sim.Ms = lambda r: cylinder(r, centre, 8) sim.add(UniformExchange(A=A)) sim.add(UniaxialAnisotropy(Kx, axis=(0, 1, 0))) # Anisotropy along y sim.add(Demag()) return sim
def test_init(): """ This tests (mx, my, mx) for the first 2 spins """ mesh = CuboidMesh(nx=100, ny=1, nz=1) sim = Sim(mesh) sim.set_m(init_m) expected = np.array([0, 0, 1, 0, np.sin(0.1), np.cos(0.1)]) assert max(abs(sim.spin[:6] - expected)) < 1e-15
def test_with_oommf_spatial_Ms(A=1e-11): def spatial_Ms(pos): x, y = pos[0], pos[1] if x**2 + y**2 < 5**2: return 2e4 else: return 0 init_m0 = ( r'return [list [expr {sin($x * 1e9) + $y * 1e9 + $z * 2.3e9}] ' + r' [expr {cos($x * 1e9) + $y * 1e9 + $z * 1.3e9}] ' + r'0 ' + r'] ') init_Ms = """ if { ($x * $x + $y * $y) < 5e-9 * 5e-9 } { return 2e4 } else { return 0 } """ mesh = CuboidMesh(nx=12, ny=10, nz=2, dx=0.5, unit_length=1e-9) sim = Sim(mesh) sim.Ms = spatial_Ms def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) exch = UniformExchange(A=A) sim.add(exch) demag = Demag() sim.add(demag) field = exch.compute_field() field_oommf = compute_exch_field(mesh, init_m0=init_m0, A=A, spatial_Ms=init_Ms) mx0, mx1, mx2 = compare_fields(field_oommf, field) assert max([mx0, mx1, mx2]) < 1e-12 field = demag.compute_field() field_oommf = compute_demag_field(mesh, spatial_Ms=init_Ms, init_m0=init_m0) mx0, mx1, mx2 = compare_fields(field_oommf, field) assert max([mx0, mx1, mx2]) < 1e-11
def test_zeeman(): mesh = CuboidMesh(nx=5, ny=2, nz=1) sim = Sim(mesh) sim.set_m((1, 0, 0)) zeeman = Zeeman(varying_field) sim.add(zeeman) field = zeeman.compute_field() assert field[6] == 1.2 * (2 + 0.5) assert field[7] == 2.3 * 0.5
def run(integrator, jacobian): name = "sim_" + integrator if integrator == "sundials": name += "_J1" if jacobian else "_J0" sim = Sim(mesh, name, integrator, use_jac=jacobian) sim.Ms = 0.86e6 sim.driver.alpha = 0.5 sim.set_m((1, 0, 1)) sim.add(UniformExchange(A=13e-12)) sim.add(Demag()) ts = np.linspace(0, 3e-10, 61) for t in ts: sim.run_until(t)
def test_sim_single_spin(do_plot=False): mesh = CuboidMesh(nx=1, ny=1, nz=1) sim = Sim(mesh, name='spin') alpha = 0.1 gamma = 2.21e5 sim.alpha = alpha sim.driver.gamma = gamma sim.mu_s = 1.0 sim.set_m((1, 0, 0)) 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.driver.run_until(t) real_ts.append(sim.driver.t) print(sim.driver.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) # print mz a_mx, a_my, a_mz = single_spin(alpha, gamma, H0, ts) print(sim.driver.stat()) if do_plot: ts_ns = np.array(real_ts) * 1e9 plt.plot(ts_ns, mx, ".", label="mx", color='DarkGreen') plt.plot(ts_ns, my, ".", label="my", color='darkslateblue') plt.plot(ts_ns, mz, ".", label="mz", color='m') plt.plot(ts_ns, a_mx, "--", label="analytical", color='b') plt.plot(ts_ns, a_my, "--", color='b') plt.plot(ts_ns, a_mz, "--", color='b') plt.xlabel("time (ns)") plt.ylabel("m") plt.title("integrating a macrospin") plt.legend() plt.savefig("single_spin.pdf") print(("Max Deviation = {0}".format( np.max(np.abs(mz - a_mz))))) assert np.max(np.abs(mz - a_mz)) < 5e-7
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 = UniaxialAnisotropy(Ku=1, axis=[0, 0, 1], name='Dx') sim.add(anis) sim.run_until(1.0) print sim.spin assert sim.spin[0] == 0 assert sim.spin[2] != 0
def create_simulation(mesh): sim = Sim(mesh) sim.Ms = 8.6e5 sim.set_m((1, 0, 0)) sim.add(UniformExchange(A=1.3e-11)) # sim.add(Demag()) #sim.add(UniaxialAnisotropy(Kx, (1, 0, 0), name='Kx')) anis = UniaxialAnisotropy(1e5, axis=(1, 0, 0)) sim.add(anis) return sim
def relax_neb(k, maxst, simname, init_im, interp, save_every=10000): """ Execute a simulation with the NEB function of the FIDIMAG code, for an elongated particle (long cylinder) 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 # We define the cylinder with the Magnetisation function sim = Sim(mesh) sim.Ms = two_part #sim.add(UniformExchange(A=A)) # Uniaxial anisotropy along x-axis sim.add(UniaxialAnisotropy(Kx, axis=(1, 0, 0))) # Define many initial states close to one extreme. We want to check # if the images in the last step, are placed mostly in equally positions 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_with_oommf_spatial_Ms(A=1e-11): def spatial_Ms(pos): x, y = pos[0], pos[1] if x ** 2 + y ** 2 < 5 ** 2: return 2e4 else: return 0 init_m0 = (r'return [list [expr {sin($x * 1e9) + $y * 1e9 + $z * 2.3e9}] ' + r' [expr {cos($x * 1e9) + $y * 1e9 + $z * 1.3e9}] ' + r'0 ' + r'] ') init_Ms = """ if { ($x * $x + $y * $y) < 5e-9 * 5e-9 } { return 2e4 } else { return 0 } """ mesh = CuboidMesh(nx=12, ny=10, nz=2, dx=0.5, unit_length=1e-9) sim = Sim(mesh) sim.Ms = spatial_Ms def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) exch = UniformExchange(A=A) sim.add(exch) demag = Demag() sim.add(demag) field = exch.compute_field() field_oommf = compute_exch_field( mesh, init_m0=init_m0, A=A, spatial_Ms=init_Ms) mx0, mx1, mx2 = compare_fields(field_oommf, field) assert max([mx0, mx1, mx2]) < 1e-12 field = demag.compute_field() field_oommf = compute_demag_field( mesh, spatial_Ms=init_Ms, init_m0=init_m0) mx0, mx1, mx2 = compare_fields(field_oommf, field) assert max([mx0, mx1, mx2]) < 1e-11
def test_dmi_field_oommf(D=4.1e-3, Ms=2.6e5): mesh = CuboidMesh(nx=10, ny=3, nz=2, dx=0.5, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms dmi = DMI(D=D, type='interfacial') sim.add(dmi) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) field = dmi.compute_field() init_m0 = """ return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 0] """ # TODO: check the sign of DMI in OOMMF. #field_oommf = compute_dmi_field(mesh, Ms=Ms, init_m0=init_m0, D=-D) omf_file = os.path.join(os.path.dirname(os.path.abspath(__file__)),'omfs','test_dmi_field_oommf.ohf') ovf = OMF2(omf_file) field_oommf = ovf.get_all_mags() mx0, mx1, mx2 = compare_fields(field_oommf, field) assert max([mx0, mx1, mx2]) < 1e-12
def test_exch_field_oommf(A=1e-11, Ms=2.6e5): mesh = CuboidMesh(nx=10, ny=3, nz=2, dx=0.5, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms exch = UniformExchange(A=A) sim.add(exch) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) field = exch.compute_field() init_m0 = """ return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 0] """ omf_file = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'omfs', 'test_exch_field_oommf.ohf' ) ovf = OMF2(omf_file) field_oommf = ovf.get_all_mags() #field_oommf = compute_exch_field(mesh, Ms=Ms, init_m0=init_m0, A=A) mx0, mx1, mx2 = compare_fields(field_oommf, field) assert max([mx0, mx1, mx2]) < 1e-12
def test_exch_field_oommf(A=1e-11, Ms=2.6e5): """ Compare the exchange field from Fidimag with an equivalent OOMMF simulation. OOMMF field data is taken from an OVF file. """ mesh = CuboidMesh(nx=10, ny=3, nz=2, dx=0.5, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms exch = UniformExchange(A=A) sim.add(exch) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) field = exch.compute_field() # An equivalent initial magnetisation for OOMMF # The spatial variables are rescale since they are in nm init_m0 = ( r'return [list [expr {sin($x * 1e9) + $y * 1e9 + $z * 2.3e9}] ' + r' [expr {cos($x * 1e9) + $y * 1e9 + $z * 1.3e9}] ' + r'0 ' + r'] ') field_oommf = compute_exch_field(mesh, Ms=Ms, init_m0=init_m0, A=A) mx0, mx1, mx2 = compare_fields(field_oommf, field) # Test if the maximum relative errors between both simulations # is small enough, for every field component assert max([mx0, mx1, mx2]) < 1e-12
def test_sim_single_spin(do_plot=False): mesh = CuboidMesh(nx=80, ny=3, nz=3) sim = Sim(mesh, name='spin', integrator='sundials_openmp') alpha = 0.1 gamma = 2.21e5 sim.alpha = alpha sim.driver.gamma = gamma sim.mu_s = 1.0 sim.set_m((1, 0, 0)) H0 = 1e5 sim.add(Zeeman((0, 0, H0))) ts = np.linspace(0, 1e-9, 101) mx = [] my = [] mz = [] real_ts = [] for t in ts: sim.driver.run_until(t) real_ts.append(sim.driver.t) print(sim.driver.t, abs(sim.spin_length()[0] - 1)) mx.append(sim.spin[0]) my.append(sim.spin[1]) mz.append(sim.spin[2]) mz = np.array(mz) # print mz a_mx, a_my, a_mz = single_spin(alpha, gamma, H0, ts) print(sim.driver.stat()) if do_plot: ts_ns = np.array(real_ts) * 1e9 plt.plot(ts_ns, mx, ".", label="mx", color='DarkGreen') plt.plot(ts_ns, my, ".", label="my", color='darkslateblue') plt.plot(ts_ns, mz, ".", label="mz", color='m') plt.plot(ts_ns, a_mx, "--", label="analytical", color='b') plt.plot(ts_ns, a_my, "--", color='b') plt.plot(ts_ns, a_mz, "--", color='b') plt.xlabel("time (ns)") plt.ylabel("m") plt.title("integrating a macrospin") plt.legend() plt.savefig("single_spin.pdf") print(("Max Deviation = {0}".format( np.max(np.abs(mz - a_mz))))) assert np.max(np.abs(mz - a_mz)) < 5e-7
def test_dmi_field_oommf(D=4.1e-3, Ms=2.6e5): mesh = CuboidMesh(nx=10, ny=3, nz=2, dx=0.5, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms dmi = DMI(D=D, type='interfacial') sim.add(dmi) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) field = dmi.compute_field() init_m0 = ( r'return [list [expr {sin($x * 1e9) + $y * 1e9 + $z * 2.3e9}] ' + r' [expr {cos($x * 1e9) + $y * 1e9 + $z * 1.3e9}] ' + r'0 ' + r'] ') # TODO: check the sign of DMI in OOMMF. field_oommf = compute_dmi_field(mesh, Ms=Ms, init_m0=init_m0, D=-D) mx0, mx1, mx2 = compare_fields(field_oommf, field) assert max([mx0, mx1, mx2]) < 1e-12
def relax_string(maxst, simname, init_im, interp, save_every=10000): """ """ # Prepare simulation # We define the cylinder with the Magnetisation function sim = Sim(mesh) sim.Ms = two_part # sim.add(UniformExchange(A=A)) # Uniaxial anisotropy along x-axis sim.add(UniaxialAnisotropy(Kx, axis=(1, 0, 0))) # Define many initial states close to one extreme. We want to check # if the images in the last step, are placed mostly in equally positions 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 string = StringMethod(sim, init_images, interpolations=interpolations, name=simname, integrator='verlet') string.integrator.stepsize = 1e-4 # dt = integrator.stepsize means after every integrator step, the images # are rescaled. We can run more integrator steps if we decrease the # stepsize, e.g. dt=1e-3 and integrator.stepsize=1e-4 string.relax(max_iterations=maxst, save_vtks_every=save_every, save_npys_every=save_every, stopping_dYdt=1e-14, dt=1e-4) return string
def relax_system_only_exchange(mesh): sim = Sim(mesh, name='relax_exchange_only') sim.driver.set_tols(rtol=1e-6, atol=1e-6) sim.driver.alpha = 0.5 sim.driver.gamma = 2.211e5 sim.Ms = 8.6e5 sim.do_precession = False sim.set_m(init_m_BP) A = 1.3e-11 exch = UniformExchange(A=A) sim.add(exch) sim.relax(dt=1e-13, stopping_dmdt=0.5, max_steps=5000, save_m_steps=None, save_vtk_steps=50) np.save('m0.npy', sim.spin)
def test_demag_field_oommf_large(Ms=8e5, A=1.3e-11): mesh = CuboidMesh(nx=150, ny=50, nz=1, dx=2.5, dy=2.5, dz=3, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms exch = UniformExchange(A=A) sim.add(exch) demag = Demag() sim.add(demag) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) demag_field = demag.compute_field() exch_field = exch.compute_field() #exact = demag.compute_exact() init_m0 = """ return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 0] """ #demag_oommf = compute_demag_field(mesh, Ms=Ms, init_m0=init_m0) #exch_oommf = compute_exch_field(mesh, Ms=Ms, init_m0=init_m0, A=A) omf_file = os.path.join(os.path.dirname(os.path.abspath(__file__)),'omfs','test_demag_field_oommf_large_Demag.ohf') ovf = OMF2(omf_file) demag_oommf = ovf.get_all_mags() omf_file = os.path.join(os.path.dirname(os.path.abspath(__file__)),'omfs','test_demag_field_oommf_large_Exchange.ohf') ovf = OMF2(omf_file) exch_oommf = ovf.get_all_mags() mx0, mx1, mx2 = compare_fields(demag_oommf, demag_field) #print mx0, mx1, mx2 assert max([mx0,mx1,mx2])< 5e-10 mx0, mx1, mx2 = compare_fields(exch_oommf, exch_field) #print mx0, mx1, mx2 assert max([mx0, mx1, mx2]) < 1e-11
def test_exch_field_oommf(A=1e-11, Ms=2.6e5): """ Compare the exchange field from Fidimag with an equivalent OOMMF simulation. OOMMF field data is taken from an OVF file. """ mesh = CuboidMesh(nx=10, ny=3, nz=2, dx=0.5, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms exch = UniformExchange(A=A) sim.add(exch) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) field = exch.compute_field() # An equivalent initial magnetisation for OOMMF # The spatial variables are rescale since they are in nm init_m0 = (r'return [list [expr {sin($x * 1e9) + $y * 1e9 + $z * 2.3e9}] ' + r' [expr {cos($x * 1e9) + $y * 1e9 + $z * 1.3e9}] ' + r'0 ' + r'] ') field_oommf = compute_exch_field(mesh, Ms=Ms, init_m0=init_m0, A=A) mx0, mx1, mx2 = compare_fields(field_oommf, field) # Test if the maximum relative errors between both simulations # is small enough, for every field component assert max([mx0, mx1, mx2]) < 1e-12
def test_energy_dmi(Ms=8e5, D=1.32e-3): mesh = CuboidMesh(nx=40, ny=50, nz=1, dx=2.5, dy=2.5, dz=3, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms dmi = DMI(D=D, type='interfacial') #dmi = DMI(D=D, type='bulk') sim.add(dmi) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 1) sim.set_m(init_m) dmi_energy = dmi.compute_energy() # init_m0=""" # return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 1] #""" #field_oommf = compute_dmi_field(mesh, Ms=Ms, init_m0=init_m0, D=D) dmi_energy_oommf = -4.5665527749090378e-20 print 'dmi energy', dmi_energy assert abs(dmi_energy - dmi_energy_oommf) / dmi_energy_oommf < 1e-15
def test_dmi_field_oommf(D=4.1e-3, Ms=2.6e5): mesh = CuboidMesh(nx=10, ny=3, nz=2, dx=0.5, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms dmi = DMI(D=D, type='interfacial') sim.add(dmi) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) field = dmi.compute_field() init_m0 = (r'return [list [expr {sin($x * 1e9) + $y * 1e9 + $z * 2.3e9}] ' + r' [expr {cos($x * 1e9) + $y * 1e9 + $z * 1.3e9}] ' + r'0 ' + r'] ') # TODO: check the sign of DMI in OOMMF. field_oommf = compute_dmi_field(mesh, Ms=Ms, init_m0=init_m0, D=-D) mx0, mx1, mx2 = compare_fields(field_oommf, field) assert max([mx0, mx1, mx2]) < 1e-12
def run_sim(): mesh = CuboidMesh() sim = Sim(mesh, name='spin') alpha = 0.1 gamma = 2.21e5 sim.alpha = alpha sim.driver.gamma = gamma sim.mu_s = 1.0 sim.set_m((1, 0, 0)) H0 = 1e5 sim.add(Zeeman((0, 0, H0))) sim.driver.run_until(1e-10) sim.driver.run_until(0.5e-10)
def test_dmi_field_oommf(D=4.1e-3, Ms=2.6e5): mesh = CuboidMesh(nx=10, ny=3, nz=2, dx=0.5, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms dmi = DMI(D=D, dmi_type='interfacial') sim.add(dmi) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) field = dmi.compute_field() init_m0 = """ return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 0] """ # TODO: check the sign of DMI in OOMMF. #field_oommf = compute_dmi_field(mesh, Ms=Ms, init_m0=init_m0, D=-D) omf_file = os.path.join(os.path.dirname(os.path.abspath(__file__)),'omfs','test_dmi_field_oommf.ohf') ovf = OMF2(omf_file) field_oommf = ovf.get_all_mags() mx0, mx1, mx2 = compare_fields(field_oommf, field) assert max([mx0, mx1, mx2]) < 1e-12
def relax_system(): mesh = CuboidMesh(nx=1, ny=1, nz=1) sim = Sim(mesh, name='relax') sim.driver.set_tols(rtol=1e-10, atol=1e-10) sim.driver.alpha = 0.5 sim.set_m((1.0, 0, 0)) sim.add(Zeeman((0, 0, 1e5))) ts = np.linspace(0, 1e-9, 1001) for t in ts: sim.run_until(t)
def test_energy(Ms=8e5, A=1.3e-11, D=1.32e-3): mesh = CuboidMesh(nx=40, ny=50, nz=1, dx=2.5, dy=2.5, dz=3, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms exch = UniformExchange(A=A) sim.add(exch) demag = Demag() sim.add(demag) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) demag_energy = demag.compute_energy() exch_energy = exch.compute_energy() # init_m0=""" # return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 0] #""" #field_oommf = compute_exch_field(mesh, Ms=Ms, init_m0=init_m0, A=A) exch_energy_oommf = 1.9885853028738599e-19 demag_energy_oommf = 5.5389695779175673e-19 dmi_energy_oommf = 2.6657360769014251e-20 print(demag_energy, exch_energy) assert abs(exch_energy - exch_energy_oommf) / exch_energy_oommf < 3e-15 assert abs(demag_energy - demag_energy_oommf) / demag_energy_oommf < 1e-10
def test_demag_field_oommf_large(Ms=8e5, A=1.3e-11): mesh = CuboidMesh(nx=150, ny=50, nz=1, dx=2.5, dy=2.5, dz=3, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms exch = UniformExchange(A=A) sim.add(exch) demag = Demag() sim.add(demag) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) demag_field = demag.compute_field() exch_field = exch.compute_field() #exact = demag.compute_exact() init_m0 = ( r'return [list [expr {sin($x * 1e9) + $y * 1e9 + $z * 2.3e9}] ' + r' [expr {cos($x * 1e9) + $y * 1e9 + $z * 1.3e9}] ' + r'0 ' + r'] ') demag_oommf = compute_demag_field(mesh, Ms=Ms, init_m0=init_m0) exch_oommf = compute_exch_field(mesh, Ms=Ms, init_m0=init_m0, A=A) mx0, mx1, mx2 = compare_fields(demag_oommf, demag_field) #print mx0, mx1, mx2 assert max([mx0, mx1, mx2]) < 5e-10 mx0, mx1, mx2 = compare_fields(exch_oommf, exch_field) #print mx0, mx1, mx2 assert max([mx0, mx1, mx2]) < 1e-11
def relax_neb(k, maxst, simname, init_im, interp, save_every=10000): """ Execute a simulation with the NEB function of the FIDIMAG code, for a nano disk 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 folders starting with the 'simname' """ # Prepare simulation # We define the small cylinder with the Magnetisation function sim = Sim(mesh) sim.Ms = cylinder # Energies # Exchange sim.add(UniformExchange(A=A)) # Bulk DMI --> This produces a Bloch DW - like skyrmion sim.add(DMI(D=D)) # No Demag, but this could have some effect # Demagnetization energy # sim.add(Demag()) # Initial images (npy files or functions) 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 # Initiate the NEB algorithm driver neb = NEB_Sundials(sim, init_images, interpolations=interpolations, spring=k, name=simname) # Start the relaxation neb.relax(max_steps=maxst, save_vtk_steps=save_every, save_npy_steps=save_every, stopping_dmdt=1)
def test_sim_pin(): mesh = CuboidMesh(nx=3, ny=2, nz=1) sim = Sim(mesh, integrator='sundials_openmp') sim.set_m((0, 0.8, 0.6)) sim.alpha = 0.1 sim.driver.gamma = 1.0 sim.pins = pin_fun anis = UniaxialAnisotropy(Ku=1, axis=[0, 0, 1], name='Dx') sim.add(anis) sim.driver.run_until(1.0) print(sim.spin) assert sim.spin[0] == 0 assert sim.spin[2] != 0
def test_compute_field(): """In an infinite film, we expect the demag tensor to be (0, 0, -1), and thus the magnetisation, if aligned in 0, 0, 1 direction, to create a demag field pointing with equal strength in the opposite direction. """ mesh = CuboidMesh(nx=1, ny=1, nz=1, dx=2.0, dy=2.0, dz=2.0, unit_length=1e-9, periodicity=(True, True, False)) sim = Sim(mesh, name='relax') sim.driver.set_tols(rtol=1e-10, atol=1e-14) sim.alpha = 0.5 sim.gamma = 2.211e5 sim.Ms = 8.6e5 sim.do_precession = False sim.set_m((0, 0, 1)) demag = Demag(pbc_2d=True) sim.add(demag) field = demag.compute_field() print((1 + field[2] / 8.6e5)) assert abs(1 + field[2] / 8.6e5) < 1e-10
def test_sim_init_m_fun(): mesh = CuboidMesh(nx=3, ny=4, nz=5) sim = Sim(mesh) sim.set_m(init_m, normalise=False) print(sim.spin.reshape(-1, 3).shape) print(sim.mesh.index(1, 2, 3)) 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_1d(do_plot=False): # Initiate the 1D mesh and magnetisation as before mesh = CuboidMesh(nx=100, ny=1, nz=1) sim = Sim(mesh) sim.set_m(init_m) # Simplify the magnetic parameters mu0 = 4 * np.pi * 1e-7 sim.Ms = 1.0 / mu0 exch = UniformExchange(1) sim.add(exch) # Compute the exchange field and reshape it in order # to leave every row as the [f_x, f_y, f_z] array # for every spin field = exch.compute_field() field.shape = (-1, 3) # We know that the field in x is always zero ( see the # analytical calculation at the beginning) assert max(abs(field[:, 0])) == 0 # These are the analytical values for the exchange field in y,z # In this case, k=0.1 , then 2 * k^2 evaluates as 0.02 xs = np.linspace(0, 99, 100) epy = -0.02 * np.sin(0.1 * xs) epz = -0.02 * np.cos(0.1 * xs) # Compare the analytical value # of the y component of the exchange field, with Fidimag's # result (second column of the reshaped field array) # WARNING: NOTICE that we are not considering the extremes since # there is a wrong expression in the border of the exchange field # with NO PBCs. We must FIX this test! assert max(abs(epy[1:-1] - field[1:-1, 1])) < 3e-5 if do_plot: plt.plot(xs, field[:, 1], "-.", label="my", color='DarkGreen') plt.plot(xs, field[:, 2], "-.", label="mz", color='DarkGreen') plt.plot(xs, epy, "--", label="analytical", color='b') plt.plot(xs, epz, "--", color='r') plt.xlabel("xs") plt.ylabel("field") plt.legend() plt.savefig("exchange_field.pdf")
def test_demag_field_oommf(Ms=6e5): mesh = CuboidMesh(nx=5, ny=2, nz=3, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms demag = Demag() sim.add(demag) def init_m(pos): x = pos[0] if x <= 2: return (1, 0, 0) elif x >= 4: return (0, 0, 1) else: return (0, 1, 0) sim.set_m(init_m) field = demag.compute_field() exact = demag.compute_exact() init_m0 = """ if { $x <=2e-9 } { return "1 0 0" } elseif { $x >= 4e-9 } { return "0 0 1" } else { return "0 1 0" } """ field_oommf = compute_demag_field(mesh, Ms=Ms, init_m0=init_m0) mx0, mx1, mx2 = compare_fields(field_oommf, exact) print(mx0, mx1, mx2) assert max([mx0, mx1, mx2]) < 2e-14 mx0, mx1, mx2 = compare_fields(field_oommf, field) print(mx0, mx1, mx2) assert np.max(abs(field - field_oommf)) < 2e-9
def test_demag_field_oommf_large(Ms=8e5, A=1.3e-11): mesh = CuboidMesh(nx=150, ny=50, nz=1, dx=2.5, dy=2.5, dz=3, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms exch = UniformExchange(A=A) sim.add(exch) demag = Demag() sim.add(demag) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) demag_field = demag.compute_field() exch_field = exch.compute_field() #exact = demag.compute_exact() init_m0 = (r'return [list [expr {sin($x * 1e9) + $y * 1e9 + $z * 2.3e9}] ' + r' [expr {cos($x * 1e9) + $y * 1e9 + $z * 1.3e9}] ' + r'0 ' + r'] ') demag_oommf = compute_demag_field(mesh, Ms=Ms, init_m0=init_m0) exch_oommf = compute_exch_field(mesh, Ms=Ms, init_m0=init_m0, A=A) mx0, mx1, mx2 = compare_fields(demag_oommf, demag_field) #print mx0, mx1, mx2 assert max([mx0, mx1, mx2]) < 5e-10 mx0, mx1, mx2 = compare_fields(exch_oommf, exch_field) #print mx0, mx1, mx2 assert max([mx0, mx1, mx2]) < 1e-11
def test_energy(Ms=8e5, A=1.3e-11, D=1.32e-3): mesh = CuboidMesh(nx=40, ny=50, nz=1, dx=2.5, dy=2.5, dz=3, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms exch = UniformExchange(A=A) sim.add(exch) demag = Demag() sim.add(demag) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 0) sim.set_m(init_m) demag_energy = demag.compute_energy() exch_energy = exch.compute_energy() # init_m0=""" # return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 0] #""" #field_oommf = compute_exch_field(mesh, Ms=Ms, init_m0=init_m0, A=A) exch_energy_oommf = 1.9885853028738599e-19 demag_energy_oommf = 5.5389695779175673e-19 dmi_energy_oommf = 2.6657360769014251e-20 print demag_energy, exch_energy assert abs(exch_energy - exch_energy_oommf) / exch_energy_oommf < 3e-15 assert abs(demag_energy - demag_energy_oommf) / demag_energy_oommf < 1e-10
def test_demag_field_oommf(Ms=6e5): mesh = CuboidMesh(nx=5, ny=2, nz=3, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms demag = Demag() sim.add(demag) def init_m(pos): x = pos[0] if x <= 2: return (1, 0, 0) elif x >= 4: return (0, 0, 1) else: return (0, 1, 0) sim.set_m(init_m) field = demag.compute_field() exact = demag.compute_exact() init_m0 = """ if { $x <=2e-9 } { return "1 0 0" } elseif { $x >= 4e-9 } { return "0 0 1" } else { return "0 1 0" } """ field_oommf = compute_demag_field(mesh, Ms=Ms, init_m0=init_m0) mx0, mx1, mx2 = compare_fields(field_oommf, exact) print mx0, mx1, mx2 assert max([mx0, mx1, mx2]) < 2e-14 mx0, mx1, mx2 = compare_fields(field_oommf, field) print mx0, mx1, mx2 assert np.max(abs(field - field_oommf)) < 2e-9
def test_energy_dmi(Ms=8e5, D=1.32e-3): mesh = CuboidMesh(nx=40, ny=50, nz=1, dx=2.5, dy=2.5, dz=3, unit_length=1e-9) sim = Sim(mesh) sim.Ms = Ms dmi = DMI(D=D, type='interfacial') #dmi = DMI(D=D, type='bulk') sim.add(dmi) def init_m(pos): x, y, z = pos return (np.sin(x) + y + 2.3 * z, np.cos(x) + y + 1.3 * z, 1) sim.set_m(init_m) dmi_energy = dmi.compute_energy() # init_m0=""" # return [list [expr {sin($x*1e9)+$y*1e9+$z*2.3e9}] [expr {cos($x*1e9)+$y*1e9+$z*1.3e9}] 1] #""" #field_oommf = compute_dmi_field(mesh, Ms=Ms, init_m0=init_m0, D=D) dmi_energy_oommf = -4.5665527749090378e-20 print('dmi energy', dmi_energy) assert abs(dmi_energy - dmi_energy_oommf) / dmi_energy_oommf < 1e-15
dz=dz, unit_length=1e-9, ) else: print 'Using Periodic Boundary Conditions!' mesh = CuboidMesh(nx=nx, ny=ny, nz=nz, dx=dx, dy=dy, dz=dz, unit_length=1e-9, pbc=(True, True, False)) # Initiate Fidimag simulation --------------------------------------------- sim = Sim(mesh, name=args.sim_name) # sim.driver.set_tols(rtol=1e-10, atol=1e-14) sim.driver.alpha = args.alpha # sim.driver.gamma = 2.211e5 if args.no_precession: sim.do_precession = False # Material parameters ----------------------------------------------------- sim.Ms = args.Ms exch = UniformExchange(A=args.A) sim.add(exch)