Fidimag
Author: Marijan Beg, Weiwei Wang
Date: 18 Mar 2016
This notebook can be downloaded from the github repository, found here.
The simulated sample is a 1D nanowire cuboid with \(L=1000 \,\text{nm}\) length with finite difference discretisation \(d_{x} = d_{y} = d_{z} = 2 \,\text{nm}\).
The material parameters (similar to permalloy) are:
exchange energy constant \(A = 1.3 \times 10^{-11} \,\text{J/m}\),
magnetisation saturation \(M_\text{s} = 8.6 \times 10^{5} \,\text{A/m}\),
uniaxial anisotropy constant \(K=5 \times 10^{4} \,\text{J/m}^{3}\) with \((0, 0, 1)\) easy-axis,
Gilbert damping \(\alpha = 0.5\).
After the system is relaxed to a domain wall, a spin-polarised current with \(J=1 \times 10^{12} \text{A/m}^{2}\) density is applied in the positive x direction \((1, 0, 0)\).
[1]:
import matplotlib.pyplot as plt import numpy as np from fidimag.micro import Sim, UniformExchange, UniaxialAnisotropy from fidimag.common import CuboidMesh %matplotlib inline
We start by defining parameters and a function for initialising the system so that it relaxes to the domain wall.
[2]:
Ms = 8.6e5 # magnetisation saturation (A/m) A = 1.3e-11 # exchange energy constant (J/m) alpha = 0.5 # Gilbert damping gamma = 2.211e5 # gyromagnetic ration (m/As) K = 5e4 # uniaxial anisotropy constant (J/m**3) J = 1e12 # spin-polarised current density (A/m**2) beta = 1 # STT parameter def init_m(pos): x = pos[0] if x < 200: return (1, 0, 0) elif 200 <= x < 300: return (0, 1, 1) else: return (-1, 0, 0)
Using this function, we create a new function which relaxes the system to its equilibrium (domain wall) state according to the problem specification.
[3]:
def relax_system(mesh): # Create a simulation object. sim = Sim(mesh) # Set simulation parameters. sim.driver.set_tols(rtol=1e-8, atol=1e-8) sim.driver.alpha = alpha sim.driver.gamma = gamma sim.Ms = Ms # Add energies to the system. sim.add(UniformExchange(A=A)) sim.add(UniaxialAnisotropy(K)) # Initialise the system. sim.set_m(init_m) # Relax the system and save the state in m0.npy sim.driver.relax(dt=1e-14, stopping_dmdt=0.01, max_steps=5000, save_m_steps=None, save_vtk_steps=None) np.save('m0.npy', sim.spin)
A plot of the system’s magnetisation can be created using the following convenience function.
[4]:
def plot_magnetisation(components): plt.figure(figsize=(8, 6)) comp = {'mx': 0, 'my': 1, 'mz': 2} for element in components: data = np.load(element[0]) data.shape = (-1, 3) mc = data[:, comp[element[1]]] # The label is the component and the file name plt.plot(mc, label=element[1]) plt.legend() plt.xlabel('x (nm)') plt.ylabel('mx, my') plt.grid() plt.ylim([-1.05, 1.05])
Finally, we create a function for driving a domain wall using the spin-polarised current. All npy and vtk files are saved in the **{simulation_name}_npys** and **{simulation_name}_vtks** folders, respectively.
[5]:
def excite_system(mesh, time, snapshots): # Specify the stt dynamics in the simulation sim = Sim(mesh, name='dyn', driver='llg_stt') # Set the simulation parameters sim.driver.set_tols(rtol=1e-12, atol=1e-14) sim.driver.alpha = alpha sim.driver.gamma = gamma sim.Ms = Ms # Add energies to the system. sim.add(UniformExchange(A=A)) sim.add(UniaxialAnisotropy(K)) # Load the initial state from the npy file saved in the realxation stage. sim.set_m(np.load('m0.npy')) # Set the spin-polarised current in the x direction. sim.driver.jx = J sim.driver.beta = beta # The simulation will run for x ns and save # 'snaps' snapshots of the system in the process ts = np.linspace(0, time, snapshots) for t in ts: sim.driver.run_until(t) sim.save_vtk() sim.save_m()
Before we run a simulation using previously defined functions, a finite difference mesh must be created.
[6]:
L = 2000 # nm dx = dy = dz = 2 # nm mesh = CuboidMesh(nx=int(L/dx), ny=1, nz=1, dx=dx, dy=dy, dz=dz, unit_length=1e-9)
Now, the system is relaxed and the domain wall equilibrium state is obtained, saved, and later used in the next stage.
[7]:
#NBVAL_IGNORE_OUTPUT relax_system(mesh)
#1 t=1e-14 dt=1e-14 max_dmdt=6.47e+04 #2 t=2e-14 dt=1e-14 max_dmdt=6.48e+04 #3 t=3.05e-14 dt=1.05e-14 max_dmdt=6.48e+04 #4 t=4.09e-14 dt=1.05e-14 max_dmdt=6.47e+04 #5 t=5.14e-14 dt=1.05e-14 max_dmdt=6.47e+04 #6 t=6.19e-14 dt=1.05e-14 max_dmdt=6.45e+04 #7 t=7.23e-14 dt=1.05e-14 max_dmdt=6.43e+04 #8 t=8.28e-14 dt=1.05e-14 max_dmdt=6.41e+04 #9 t=9.33e-14 dt=1.05e-14 max_dmdt=6.38e+04 #10 t=1.04e-13 dt=1.05e-14 max_dmdt=6.35e+04 #11 t=1.23e-13 dt=1.91e-14 max_dmdt=6.29e+04 #12 t=1.42e-13 dt=1.91e-14 max_dmdt=6.21e+04 #13 t=1.61e-13 dt=1.91e-14 max_dmdt=6.11e+04 #14 t=1.8e-13 dt=1.91e-14 max_dmdt=6e+04 #15 t=1.99e-13 dt=1.91e-14 max_dmdt=5.88e+04 #16 t=2.18e-13 dt=1.91e-14 max_dmdt=5.74e+04 #17 t=2.37e-13 dt=1.91e-14 max_dmdt=5.6e+04 #18 t=2.56e-13 dt=1.91e-14 max_dmdt=5.44e+04 #19 t=2.75e-13 dt=1.91e-14 max_dmdt=5.28e+04 #20 t=3.09e-13 dt=3.37e-14 max_dmdt=5.03e+04 #21 t=3.43e-13 dt=3.37e-14 max_dmdt=4.7e+04 #22 t=3.77e-13 dt=3.37e-14 max_dmdt=4.59e+04 #23 t=4.01e-13 dt=2.47e-14 max_dmdt=4.51e+04 #24 t=4.26e-13 dt=2.47e-14 max_dmdt=4.42e+04 #25 t=4.51e-13 dt=2.47e-14 max_dmdt=4.31e+04 #26 t=4.75e-13 dt=2.47e-14 max_dmdt=4.2e+04 #27 t=5e-13 dt=2.47e-14 max_dmdt=4.07e+04 #28 t=5.25e-13 dt=2.47e-14 max_dmdt=3.92e+04 #29 t=5.49e-13 dt=2.47e-14 max_dmdt=3.77e+04 #30 t=5.74e-13 dt=2.47e-14 max_dmdt=3.61e+04 #31 t=5.99e-13 dt=2.47e-14 max_dmdt=3.45e+04 #32 t=6.37e-13 dt=3.85e-14 max_dmdt=3.23e+04 #33 t=6.76e-13 dt=3.85e-14 max_dmdt=2.96e+04 #34 t=7.14e-13 dt=3.85e-14 max_dmdt=2.75e+04 #35 t=7.52e-13 dt=3.85e-14 max_dmdt=2.64e+04 #36 t=7.91e-13 dt=3.85e-14 max_dmdt=2.52e+04 #37 t=8.29e-13 dt=3.85e-14 max_dmdt=2.46e+04 #38 t=8.68e-13 dt=3.85e-14 max_dmdt=2.4e+04 #39 t=9.06e-13 dt=3.85e-14 max_dmdt=2.32e+04 #40 t=9.45e-13 dt=3.85e-14 max_dmdt=2.23e+04 #41 t=9.83e-13 dt=3.85e-14 max_dmdt=2.15e+04 #42 t=1.02e-12 dt=3.85e-14 max_dmdt=2.15e+04 #43 t=1.06e-12 dt=3.85e-14 max_dmdt=2.13e+04 #44 t=1.1e-12 dt=3.85e-14 max_dmdt=2.1e+04 #45 t=1.14e-12 dt=3.85e-14 max_dmdt=2.06e+04 #46 t=1.18e-12 dt=3.85e-14 max_dmdt=2.01e+04 #47 t=1.21e-12 dt=3.85e-14 max_dmdt=1.94e+04 #48 t=1.25e-12 dt=3.85e-14 max_dmdt=1.87e+04 #49 t=1.29e-12 dt=3.85e-14 max_dmdt=1.79e+04 #50 t=1.33e-12 dt=3.85e-14 max_dmdt=1.71e+04 #51 t=1.37e-12 dt=3.85e-14 max_dmdt=1.63e+04 #52 t=1.41e-12 dt=3.85e-14 max_dmdt=1.54e+04 #53 t=1.44e-12 dt=3.85e-14 max_dmdt=1.49e+04 #54 t=1.48e-12 dt=3.85e-14 max_dmdt=1.47e+04 #55 t=1.52e-12 dt=3.85e-14 max_dmdt=1.44e+04 #56 t=1.56e-12 dt=3.85e-14 max_dmdt=1.41e+04 #57 t=1.6e-12 dt=3.85e-14 max_dmdt=1.37e+04 #58 t=1.64e-12 dt=3.85e-14 max_dmdt=1.33e+04 #59 t=1.68e-12 dt=3.85e-14 max_dmdt=1.28e+04 #60 t=1.71e-12 dt=3.85e-14 max_dmdt=1.24e+04 #61 t=1.75e-12 dt=3.85e-14 max_dmdt=1.2e+04 #62 t=1.79e-12 dt=3.85e-14 max_dmdt=1.19e+04 #63 t=1.83e-12 dt=3.85e-14 max_dmdt=1.17e+04 #64 t=1.87e-12 dt=3.85e-14 max_dmdt=1.16e+04 #65 t=1.91e-12 dt=3.85e-14 max_dmdt=1.13e+04 #66 t=1.94e-12 dt=3.85e-14 max_dmdt=1.11e+04 #67 t=1.98e-12 dt=3.85e-14 max_dmdt=1.09e+04 #68 t=2.02e-12 dt=3.85e-14 max_dmdt=1.06e+04 #69 t=2.06e-12 dt=3.85e-14 max_dmdt=1.03e+04 #70 t=2.1e-12 dt=3.85e-14 max_dmdt=1e+04 #71 t=2.14e-12 dt=3.85e-14 max_dmdt=9.71e+03 #72 t=2.18e-12 dt=3.85e-14 max_dmdt=9.49e+03 #73 t=2.21e-12 dt=3.85e-14 max_dmdt=9.38e+03 #74 t=2.25e-12 dt=3.85e-14 max_dmdt=9.25e+03 #75 t=2.29e-12 dt=3.85e-14 max_dmdt=9.09e+03 #76 t=2.33e-12 dt=3.85e-14 max_dmdt=8.92e+03 #77 t=2.37e-12 dt=3.85e-14 max_dmdt=8.74e+03 #78 t=2.41e-12 dt=3.85e-14 max_dmdt=8.54e+03 #79 t=2.44e-12 dt=3.85e-14 max_dmdt=8.34e+03 #80 t=2.48e-12 dt=3.85e-14 max_dmdt=8.13e+03 #81 t=2.54e-12 dt=5.79e-14 max_dmdt=7.86e+03 #82 t=2.6e-12 dt=5.79e-14 max_dmdt=7.53e+03 #83 t=2.66e-12 dt=5.79e-14 max_dmdt=7.21e+03 #84 t=2.71e-12 dt=5.79e-14 max_dmdt=6.9e+03 #85 t=2.77e-12 dt=5.79e-14 max_dmdt=6.59e+03 #86 t=2.83e-12 dt=5.79e-14 max_dmdt=6.46e+03 #87 t=2.89e-12 dt=5.79e-14 max_dmdt=6.33e+03 #88 t=2.95e-12 dt=5.79e-14 max_dmdt=6.29e+03 #89 t=3e-12 dt=5.79e-14 max_dmdt=6.23e+03 #90 t=3.06e-12 dt=5.79e-14 max_dmdt=6.15e+03 #91 t=3.12e-12 dt=5.79e-14 max_dmdt=6.06e+03 #92 t=3.18e-12 dt=5.79e-14 max_dmdt=5.96e+03 #93 t=3.24e-12 dt=5.79e-14 max_dmdt=5.85e+03 #94 t=3.29e-12 dt=5.79e-14 max_dmdt=5.73e+03 #95 t=3.35e-12 dt=5.79e-14 max_dmdt=5.6e+03 #96 t=3.41e-12 dt=5.79e-14 max_dmdt=5.48e+03 #97 t=3.47e-12 dt=5.79e-14 max_dmdt=5.36e+03 #98 t=3.52e-12 dt=5.79e-14 max_dmdt=5.23e+03 #99 t=3.58e-12 dt=5.79e-14 max_dmdt=5.11e+03 #100 t=3.64e-12 dt=5.79e-14 max_dmdt=4.99e+03 #101 t=3.7e-12 dt=5.79e-14 max_dmdt=4.87e+03 #102 t=3.76e-12 dt=5.79e-14 max_dmdt=4.76e+03 #103 t=3.81e-12 dt=5.79e-14 max_dmdt=4.65e+03 #104 t=3.87e-12 dt=5.79e-14 max_dmdt=4.54e+03 #105 t=3.93e-12 dt=5.79e-14 max_dmdt=4.45e+03 #106 t=3.99e-12 dt=5.79e-14 max_dmdt=4.38e+03 #107 t=4.08e-12 dt=8.74e-14 max_dmdt=4.28e+03 #108 t=4.16e-12 dt=8.74e-14 max_dmdt=4.17e+03 #109 t=4.25e-12 dt=8.74e-14 max_dmdt=4.08e+03 #110 t=4.34e-12 dt=8.74e-14 max_dmdt=4.02e+03 #111 t=4.43e-12 dt=8.74e-14 max_dmdt=3.96e+03 #112 t=4.51e-12 dt=8.74e-14 max_dmdt=3.89e+03 #113 t=4.6e-12 dt=8.74e-14 max_dmdt=3.82e+03 #114 t=4.69e-12 dt=8.74e-14 max_dmdt=3.75e+03 #115 t=4.77e-12 dt=8.74e-14 max_dmdt=3.68e+03 #116 t=4.86e-12 dt=8.74e-14 max_dmdt=3.61e+03 #117 t=4.95e-12 dt=8.74e-14 max_dmdt=3.53e+03 #118 t=5.04e-12 dt=8.74e-14 max_dmdt=3.46e+03 #119 t=5.12e-12 dt=8.74e-14 max_dmdt=3.38e+03 #120 t=5.21e-12 dt=8.74e-14 max_dmdt=3.31e+03 #121 t=5.3e-12 dt=8.74e-14 max_dmdt=3.25e+03 #122 t=5.39e-12 dt=8.74e-14 max_dmdt=3.2e+03 #123 t=5.47e-12 dt=8.74e-14 max_dmdt=3.15e+03 #124 t=5.56e-12 dt=8.74e-14 max_dmdt=3.1e+03 #125 t=5.65e-12 dt=8.74e-14 max_dmdt=3.05e+03 #126 t=5.74e-12 dt=8.74e-14 max_dmdt=3e+03 #127 t=5.82e-12 dt=8.74e-14 max_dmdt=2.96e+03 #128 t=5.91e-12 dt=8.74e-14 max_dmdt=2.91e+03 #129 t=6e-12 dt=8.74e-14 max_dmdt=2.86e+03 #130 t=6.09e-12 dt=8.74e-14 max_dmdt=2.82e+03 #131 t=6.17e-12 dt=8.74e-14 max_dmdt=2.78e+03 #132 t=6.26e-12 dt=8.74e-14 max_dmdt=2.73e+03 #133 t=6.35e-12 dt=8.74e-14 max_dmdt=2.69e+03 #134 t=6.44e-12 dt=8.74e-14 max_dmdt=2.65e+03 #135 t=6.52e-12 dt=8.74e-14 max_dmdt=2.61e+03 #136 t=6.61e-12 dt=8.74e-14 max_dmdt=2.57e+03 #137 t=6.7e-12 dt=8.74e-14 max_dmdt=2.53e+03 #138 t=6.78e-12 dt=8.74e-14 max_dmdt=2.49e+03 #139 t=6.87e-12 dt=8.74e-14 max_dmdt=2.45e+03 #140 t=6.96e-12 dt=8.74e-14 max_dmdt=2.42e+03 #141 t=7.05e-12 dt=8.74e-14 max_dmdt=2.38e+03 #142 t=7.13e-12 dt=8.74e-14 max_dmdt=2.35e+03 #143 t=7.22e-12 dt=8.74e-14 max_dmdt=2.31e+03 #144 t=7.31e-12 dt=8.74e-14 max_dmdt=2.29e+03 #145 t=7.4e-12 dt=8.74e-14 max_dmdt=2.27e+03 #146 t=7.48e-12 dt=8.74e-14 max_dmdt=2.25e+03 #147 t=7.57e-12 dt=8.74e-14 max_dmdt=2.23e+03 #148 t=7.66e-12 dt=8.74e-14 max_dmdt=2.21e+03 #149 t=7.75e-12 dt=8.74e-14 max_dmdt=2.18e+03 #150 t=7.83e-12 dt=8.74e-14 max_dmdt=2.16e+03 #151 t=7.92e-12 dt=8.74e-14 max_dmdt=2.14e+03 #152 t=8.01e-12 dt=8.74e-14 max_dmdt=2.12e+03 #153 t=8.1e-12 dt=8.74e-14 max_dmdt=2.1e+03 #154 t=8.18e-12 dt=8.74e-14 max_dmdt=2.08e+03 #155 t=8.27e-12 dt=8.74e-14 max_dmdt=2.06e+03 #156 t=8.36e-12 dt=8.74e-14 max_dmdt=2.04e+03 #157 t=8.45e-12 dt=8.74e-14 max_dmdt=2.02e+03 #158 t=8.53e-12 dt=8.74e-14 max_dmdt=2e+03 #159 t=8.62e-12 dt=8.74e-14 max_dmdt=1.98e+03 #160 t=8.71e-12 dt=8.74e-14 max_dmdt=1.96e+03 #161 t=8.79e-12 dt=8.74e-14 max_dmdt=1.94e+03 #162 t=8.88e-12 dt=8.74e-14 max_dmdt=1.92e+03 #163 t=8.97e-12 dt=8.74e-14 max_dmdt=1.9e+03 #164 t=9.06e-12 dt=8.74e-14 max_dmdt=1.88e+03 #165 t=9.14e-12 dt=8.74e-14 max_dmdt=1.86e+03 #166 t=9.28e-12 dt=1.32e-13 max_dmdt=1.84e+03 #167 t=9.41e-12 dt=1.32e-13 max_dmdt=1.81e+03 #168 t=9.54e-12 dt=1.32e-13 max_dmdt=1.78e+03 #169 t=9.67e-12 dt=1.32e-13 max_dmdt=1.76e+03 #170 t=9.81e-12 dt=1.32e-13 max_dmdt=1.73e+03 #171 t=1e-11 dt=2.01e-13 max_dmdt=1.7e+03 #172 t=1.02e-11 dt=2.01e-13 max_dmdt=1.66e+03 #173 t=1.04e-11 dt=2.01e-13 max_dmdt=1.63e+03 #174 t=1.06e-11 dt=2.01e-13 max_dmdt=1.59e+03 #175 t=1.08e-11 dt=2.01e-13 max_dmdt=1.57e+03 #176 t=1.1e-11 dt=2.01e-13 max_dmdt=1.54e+03 #177 t=1.12e-11 dt=2.01e-13 max_dmdt=1.52e+03 #178 t=1.14e-11 dt=2.01e-13 max_dmdt=1.5e+03 #179 t=1.16e-11 dt=2.01e-13 max_dmdt=1.47e+03 #180 t=1.18e-11 dt=2.01e-13 max_dmdt=1.45e+03 #181 t=1.2e-11 dt=2.01e-13 max_dmdt=1.43e+03 #182 t=1.22e-11 dt=2.01e-13 max_dmdt=1.41e+03 #183 t=1.24e-11 dt=2.01e-13 max_dmdt=1.38e+03 #184 t=1.26e-11 dt=2.01e-13 max_dmdt=1.36e+03 #185 t=1.28e-11 dt=2.01e-13 max_dmdt=1.34e+03 #186 t=1.3e-11 dt=2.01e-13 max_dmdt=1.32e+03 #187 t=1.32e-11 dt=2.01e-13 max_dmdt=1.3e+03 #188 t=1.34e-11 dt=2.01e-13 max_dmdt=1.28e+03 #189 t=1.36e-11 dt=2.01e-13 max_dmdt=1.26e+03 #190 t=1.38e-11 dt=2.01e-13 max_dmdt=1.24e+03 #191 t=1.4e-11 dt=2.01e-13 max_dmdt=1.22e+03 #192 t=1.42e-11 dt=2.01e-13 max_dmdt=1.21e+03 #193 t=1.44e-11 dt=2.01e-13 max_dmdt=1.19e+03 #194 t=1.46e-11 dt=2.01e-13 max_dmdt=1.17e+03 #195 t=1.48e-11 dt=2.01e-13 max_dmdt=1.15e+03 #196 t=1.51e-11 dt=3.05e-13 max_dmdt=1.14e+03 #197 t=1.54e-11 dt=3.05e-13 max_dmdt=1.12e+03 #198 t=1.58e-11 dt=3.05e-13 max_dmdt=1.1e+03 #199 t=1.61e-11 dt=3.05e-13 max_dmdt=1.08e+03 #200 t=1.64e-11 dt=3.05e-13 max_dmdt=1.06e+03 #201 t=1.67e-11 dt=3.05e-13 max_dmdt=1.05e+03 #202 t=1.7e-11 dt=3.05e-13 max_dmdt=1.03e+03 #203 t=1.73e-11 dt=3.05e-13 max_dmdt=1.01e+03 #204 t=1.76e-11 dt=3.05e-13 max_dmdt=997 #205 t=1.79e-11 dt=3.05e-13 max_dmdt=980 #206 t=1.82e-11 dt=3.05e-13 max_dmdt=965 #207 t=1.85e-11 dt=3.05e-13 max_dmdt=949 #208 t=1.88e-11 dt=3.05e-13 max_dmdt=934 #209 t=1.91e-11 dt=3.05e-13 max_dmdt=920 #210 t=1.94e-11 dt=3.05e-13 max_dmdt=905 #211 t=1.97e-11 dt=3.05e-13 max_dmdt=891 #212 t=2e-11 dt=3.05e-13 max_dmdt=878 #213 t=2.03e-11 dt=3.05e-13 max_dmdt=867 #214 t=2.06e-11 dt=3.05e-13 max_dmdt=857 #215 t=2.09e-11 dt=3.05e-13 max_dmdt=847 #216 t=2.12e-11 dt=3.05e-13 max_dmdt=837 #217 t=2.15e-11 dt=3.05e-13 max_dmdt=827 #218 t=2.18e-11 dt=3.05e-13 max_dmdt=817 #219 t=2.22e-11 dt=3.05e-13 max_dmdt=807 #220 t=2.25e-11 dt=3.05e-13 max_dmdt=798 #221 t=2.28e-11 dt=3.05e-13 max_dmdt=788 #222 t=2.31e-11 dt=3.05e-13 max_dmdt=779 #223 t=2.34e-11 dt=3.05e-13 max_dmdt=769 #224 t=2.37e-11 dt=3.05e-13 max_dmdt=760 #225 t=2.4e-11 dt=3.05e-13 max_dmdt=751 #226 t=2.43e-11 dt=3.05e-13 max_dmdt=742 #227 t=2.46e-11 dt=3.05e-13 max_dmdt=733 #228 t=2.49e-11 dt=3.05e-13 max_dmdt=724 #229 t=2.52e-11 dt=3.05e-13 max_dmdt=716 #230 t=2.55e-11 dt=3.05e-13 max_dmdt=707 #231 t=2.58e-11 dt=3.05e-13 max_dmdt=699 #232 t=2.61e-11 dt=3.05e-13 max_dmdt=691 #233 t=2.64e-11 dt=3.05e-13 max_dmdt=684 #234 t=2.67e-11 dt=3.05e-13 max_dmdt=677 #235 t=2.7e-11 dt=3.05e-13 max_dmdt=672 #236 t=2.73e-11 dt=3.05e-13 max_dmdt=667 #237 t=2.76e-11 dt=3.05e-13 max_dmdt=662 #238 t=2.79e-11 dt=3.05e-13 max_dmdt=657 #239 t=2.82e-11 dt=3.05e-13 max_dmdt=653 #240 t=2.85e-11 dt=3.05e-13 max_dmdt=649 #241 t=2.89e-11 dt=3.05e-13 max_dmdt=645 #242 t=2.92e-11 dt=3.05e-13 max_dmdt=641 #243 t=2.95e-11 dt=3.05e-13 max_dmdt=637 #244 t=2.98e-11 dt=3.05e-13 max_dmdt=634 #245 t=3.01e-11 dt=3.05e-13 max_dmdt=630 #246 t=3.04e-11 dt=3.05e-13 max_dmdt=627 #247 t=3.07e-11 dt=3.05e-13 max_dmdt=623 #248 t=3.1e-11 dt=3.05e-13 max_dmdt=620 #249 t=3.13e-11 dt=3.05e-13 max_dmdt=616 #250 t=3.16e-11 dt=3.05e-13 max_dmdt=613 #251 t=3.19e-11 dt=3.05e-13 max_dmdt=609 #252 t=3.22e-11 dt=3.05e-13 max_dmdt=606 #253 t=3.25e-11 dt=3.05e-13 max_dmdt=602 #254 t=3.28e-11 dt=3.05e-13 max_dmdt=599 #255 t=3.31e-11 dt=3.05e-13 max_dmdt=595 #256 t=3.34e-11 dt=3.05e-13 max_dmdt=591 #257 t=3.37e-11 dt=3.05e-13 max_dmdt=587 #258 t=3.4e-11 dt=3.05e-13 max_dmdt=583 #259 t=3.43e-11 dt=3.05e-13 max_dmdt=579 #260 t=3.46e-11 dt=3.05e-13 max_dmdt=575 #261 t=3.49e-11 dt=3.05e-13 max_dmdt=570 #262 t=3.53e-11 dt=3.05e-13 max_dmdt=566 #263 t=3.56e-11 dt=3.05e-13 max_dmdt=561 #264 t=3.59e-11 dt=3.05e-13 max_dmdt=557 #265 t=3.62e-11 dt=3.05e-13 max_dmdt=552 #266 t=3.65e-11 dt=3.05e-13 max_dmdt=547 #267 t=3.68e-11 dt=3.05e-13 max_dmdt=542 #268 t=3.71e-11 dt=3.05e-13 max_dmdt=537 #269 t=3.74e-11 dt=3.05e-13 max_dmdt=532 #270 t=3.77e-11 dt=3.05e-13 max_dmdt=526 #271 t=3.8e-11 dt=3.05e-13 max_dmdt=521 #272 t=3.83e-11 dt=3.05e-13 max_dmdt=516 #273 t=3.86e-11 dt=3.05e-13 max_dmdt=510 #274 t=3.89e-11 dt=3.05e-13 max_dmdt=505 #275 t=3.92e-11 dt=3.05e-13 max_dmdt=499 #276 t=3.95e-11 dt=3.05e-13 max_dmdt=493 #277 t=3.98e-11 dt=3.05e-13 max_dmdt=488 #278 t=4.01e-11 dt=3.05e-13 max_dmdt=482 #279 t=4.04e-11 dt=3.05e-13 max_dmdt=477 #280 t=4.07e-11 dt=3.05e-13 max_dmdt=471 #281 t=4.1e-11 dt=3.05e-13 max_dmdt=466 #282 t=4.13e-11 dt=3.05e-13 max_dmdt=460 #283 t=4.16e-11 dt=3.05e-13 max_dmdt=455 #284 t=4.2e-11 dt=3.05e-13 max_dmdt=454 #285 t=4.23e-11 dt=3.05e-13 max_dmdt=454 #286 t=4.26e-11 dt=3.05e-13 max_dmdt=453 #287 t=4.29e-11 dt=3.05e-13 max_dmdt=452 #288 t=4.32e-11 dt=3.05e-13 max_dmdt=452 #289 t=4.35e-11 dt=3.05e-13 max_dmdt=451 #290 t=4.38e-11 dt=3.05e-13 max_dmdt=450 #291 t=4.41e-11 dt=3.05e-13 max_dmdt=449 #292 t=4.44e-11 dt=3.05e-13 max_dmdt=448 #293 t=4.47e-11 dt=3.05e-13 max_dmdt=446 #294 t=4.5e-11 dt=3.05e-13 max_dmdt=445 #295 t=4.53e-11 dt=3.05e-13 max_dmdt=444 #296 t=4.56e-11 dt=3.05e-13 max_dmdt=442 #297 t=4.59e-11 dt=3.05e-13 max_dmdt=441 #298 t=4.62e-11 dt=3.05e-13 max_dmdt=439 #299 t=4.65e-11 dt=3.05e-13 max_dmdt=438 #300 t=4.68e-11 dt=3.05e-13 max_dmdt=437 #301 t=4.71e-11 dt=3.05e-13 max_dmdt=436 #302 t=4.74e-11 dt=3.05e-13 max_dmdt=435 #303 t=4.77e-11 dt=3.05e-13 max_dmdt=434 #304 t=4.8e-11 dt=3.05e-13 max_dmdt=433 #305 t=4.84e-11 dt=3.05e-13 max_dmdt=432 #306 t=4.87e-11 dt=3.05e-13 max_dmdt=431 #307 t=4.9e-11 dt=3.05e-13 max_dmdt=430 #308 t=4.93e-11 dt=3.05e-13 max_dmdt=429 #309 t=4.96e-11 dt=3.05e-13 max_dmdt=428 #310 t=4.98e-11 dt=2.25e-13 max_dmdt=427 #311 t=5e-11 dt=2.25e-13 max_dmdt=426 #312 t=5.02e-11 dt=2.25e-13 max_dmdt=425 #313 t=5.05e-11 dt=2.25e-13 max_dmdt=424 #314 t=5.07e-11 dt=2.25e-13 max_dmdt=423 #315 t=5.09e-11 dt=2.25e-13 max_dmdt=423 #316 t=5.11e-11 dt=2.25e-13 max_dmdt=423 #317 t=5.14e-11 dt=2.25e-13 max_dmdt=422 #318 t=5.16e-11 dt=2.25e-13 max_dmdt=422 #319 t=5.18e-11 dt=2.25e-13 max_dmdt=421 #320 t=5.2e-11 dt=2.25e-13 max_dmdt=421 #321 t=5.23e-11 dt=2.25e-13 max_dmdt=420 #322 t=5.25e-11 dt=2.25e-13 max_dmdt=420 #323 t=5.27e-11 dt=2.25e-13 max_dmdt=419 #324 t=5.29e-11 dt=2.25e-13 max_dmdt=419 #325 t=5.32e-11 dt=2.25e-13 max_dmdt=418 #326 t=5.34e-11 dt=2.25e-13 max_dmdt=418 #327 t=5.36e-11 dt=2.25e-13 max_dmdt=417 #328 t=5.39e-11 dt=2.25e-13 max_dmdt=416 #329 t=5.41e-11 dt=2.25e-13 max_dmdt=416 #330 t=5.43e-11 dt=2.25e-13 max_dmdt=417 #331 t=5.45e-11 dt=2.25e-13 max_dmdt=419 #332 t=5.48e-11 dt=2.25e-13 max_dmdt=422 #333 t=5.5e-11 dt=2.25e-13 max_dmdt=425 #334 t=5.52e-11 dt=2.25e-13 max_dmdt=427 #335 t=5.54e-11 dt=2.25e-13 max_dmdt=430 #336 t=5.57e-11 dt=2.25e-13 max_dmdt=432 #337 t=5.59e-11 dt=2.25e-13 max_dmdt=435 #338 t=5.61e-11 dt=2.25e-13 max_dmdt=437 #339 t=5.63e-11 dt=2.25e-13 max_dmdt=439 #340 t=5.66e-11 dt=2.25e-13 max_dmdt=442 #341 t=5.68e-11 dt=2.25e-13 max_dmdt=444 #342 t=5.7e-11 dt=2.25e-13 max_dmdt=446 #343 t=5.72e-11 dt=2.25e-13 max_dmdt=449 #344 t=5.75e-11 dt=2.25e-13 max_dmdt=451 #345 t=5.77e-11 dt=2.25e-13 max_dmdt=453 #346 t=5.79e-11 dt=2.25e-13 max_dmdt=455 #347 t=5.81e-11 dt=2.25e-13 max_dmdt=457 #348 t=5.84e-11 dt=2.25e-13 max_dmdt=459 #349 t=5.86e-11 dt=2.25e-13 max_dmdt=461 #350 t=5.88e-11 dt=2.25e-13 max_dmdt=463 #351 t=5.9e-11 dt=2.25e-13 max_dmdt=465 #352 t=5.93e-11 dt=2.25e-13 max_dmdt=467 #353 t=5.95e-11 dt=2.25e-13 max_dmdt=468 #354 t=5.97e-11 dt=2.25e-13 max_dmdt=470 #355 t=5.99e-11 dt=2.25e-13 max_dmdt=472 #356 t=6.02e-11 dt=2.25e-13 max_dmdt=473 #357 t=6.04e-11 dt=2.25e-13 max_dmdt=475 #358 t=6.06e-11 dt=2.25e-13 max_dmdt=477 #359 t=6.08e-11 dt=2.25e-13 max_dmdt=478 #360 t=6.11e-11 dt=2.25e-13 max_dmdt=480 #361 t=6.13e-11 dt=2.25e-13 max_dmdt=481 #362 t=6.15e-11 dt=2.25e-13 max_dmdt=483 #363 t=6.17e-11 dt=2.25e-13 max_dmdt=484 #364 t=6.2e-11 dt=2.25e-13 max_dmdt=486 #365 t=6.22e-11 dt=2.25e-13 max_dmdt=487 #366 t=6.24e-11 dt=2.25e-13 max_dmdt=488 #367 t=6.26e-11 dt=2.25e-13 max_dmdt=490 #368 t=6.29e-11 dt=2.25e-13 max_dmdt=491 #369 t=6.31e-11 dt=2.25e-13 max_dmdt=492 #370 t=6.33e-11 dt=2.25e-13 max_dmdt=494 #371 t=6.35e-11 dt=2.25e-13 max_dmdt=495 #372 t=6.38e-11 dt=2.25e-13 max_dmdt=496 #373 t=6.4e-11 dt=2.25e-13 max_dmdt=498 #374 t=6.42e-11 dt=2.25e-13 max_dmdt=499 #375 t=6.44e-11 dt=2.25e-13 max_dmdt=500 #376 t=6.47e-11 dt=2.25e-13 max_dmdt=501 #377 t=6.5e-11 dt=3.43e-13 max_dmdt=502 #378 t=6.54e-11 dt=3.43e-13 max_dmdt=504 #379 t=6.57e-11 dt=3.43e-13 max_dmdt=506 #380 t=6.6e-11 dt=3.43e-13 max_dmdt=507 #381 t=6.64e-11 dt=3.43e-13 max_dmdt=509 #382 t=6.67e-11 dt=3.43e-13 max_dmdt=510 #383 t=6.71e-11 dt=3.43e-13 max_dmdt=511 #384 t=6.74e-11 dt=3.43e-13 max_dmdt=513 #385 t=6.78e-11 dt=3.43e-13 max_dmdt=514 #386 t=6.81e-11 dt=3.43e-13 max_dmdt=515 #387 t=6.86e-11 dt=5.15e-13 max_dmdt=517 #388 t=6.91e-11 dt=5.15e-13 max_dmdt=518 #389 t=6.96e-11 dt=5.15e-13 max_dmdt=520 #390 t=7.02e-11 dt=5.15e-13 max_dmdt=521 #391 t=7.07e-11 dt=5.15e-13 max_dmdt=523 #392 t=7.12e-11 dt=5.15e-13 max_dmdt=524 #393 t=7.17e-11 dt=5.15e-13 max_dmdt=525 #394 t=7.22e-11 dt=5.15e-13 max_dmdt=526 #395 t=7.27e-11 dt=5.15e-13 max_dmdt=527 #396 t=7.35e-11 dt=7.88e-13 max_dmdt=528 #397 t=7.43e-11 dt=7.88e-13 max_dmdt=529 #398 t=7.51e-11 dt=7.88e-13 max_dmdt=530 #399 t=7.59e-11 dt=7.88e-13 max_dmdt=531 #400 t=7.67e-11 dt=7.88e-13 max_dmdt=532 #401 t=7.75e-11 dt=7.88e-13 max_dmdt=532 #402 t=7.83e-11 dt=7.88e-13 max_dmdt=533 #403 t=7.9e-11 dt=7.88e-13 max_dmdt=533 #404 t=7.98e-11 dt=7.88e-13 max_dmdt=533 #405 t=8.06e-11 dt=7.88e-13 max_dmdt=533 #406 t=8.14e-11 dt=7.88e-13 max_dmdt=533 #407 t=8.22e-11 dt=7.88e-13 max_dmdt=533 #408 t=8.3e-11 dt=7.88e-13 max_dmdt=532 #409 t=8.38e-11 dt=7.88e-13 max_dmdt=532 #410 t=8.46e-11 dt=7.88e-13 max_dmdt=531 #411 t=8.53e-11 dt=7.88e-13 max_dmdt=531 #412 t=8.61e-11 dt=7.88e-13 max_dmdt=530 #413 t=8.69e-11 dt=7.88e-13 max_dmdt=529 #414 t=8.77e-11 dt=7.88e-13 max_dmdt=529 #415 t=8.85e-11 dt=7.88e-13 max_dmdt=528 #416 t=8.93e-11 dt=7.88e-13 max_dmdt=527 #417 t=9.01e-11 dt=7.88e-13 max_dmdt=526 #418 t=9.09e-11 dt=7.88e-13 max_dmdt=524 #419 t=9.17e-11 dt=7.88e-13 max_dmdt=523 #420 t=9.24e-11 dt=7.88e-13 max_dmdt=522 #421 t=9.32e-11 dt=7.88e-13 max_dmdt=521 #422 t=9.44e-11 dt=1.21e-12 max_dmdt=519 #423 t=9.56e-11 dt=1.21e-12 max_dmdt=517 #424 t=9.68e-11 dt=1.21e-12 max_dmdt=514 #425 t=9.81e-11 dt=1.21e-12 max_dmdt=512 #426 t=9.93e-11 dt=1.21e-12 max_dmdt=509 #427 t=1e-10 dt=1.21e-12 max_dmdt=507 #428 t=1.02e-10 dt=1.21e-12 max_dmdt=504 #429 t=1.03e-10 dt=1.21e-12 max_dmdt=501 #430 t=1.04e-10 dt=1.21e-12 max_dmdt=498 #431 t=1.05e-10 dt=1.21e-12 max_dmdt=495 #432 t=1.06e-10 dt=1.21e-12 max_dmdt=491 #433 t=1.08e-10 dt=1.21e-12 max_dmdt=488 #434 t=1.09e-10 dt=1.21e-12 max_dmdt=484 #435 t=1.1e-10 dt=1.21e-12 max_dmdt=481 #436 t=1.11e-10 dt=1.21e-12 max_dmdt=477 #437 t=1.13e-10 dt=1.21e-12 max_dmdt=473 #438 t=1.14e-10 dt=1.21e-12 max_dmdt=469 #439 t=1.15e-10 dt=1.21e-12 max_dmdt=465 #440 t=1.16e-10 dt=1.21e-12 max_dmdt=461 #441 t=1.17e-10 dt=1.21e-12 max_dmdt=457 #442 t=1.19e-10 dt=1.21e-12 max_dmdt=453 #443 t=1.2e-10 dt=1.21e-12 max_dmdt=449 #444 t=1.21e-10 dt=1.21e-12 max_dmdt=444 #445 t=1.22e-10 dt=1.21e-12 max_dmdt=440 #446 t=1.23e-10 dt=1.21e-12 max_dmdt=435 #447 t=1.25e-10 dt=1.21e-12 max_dmdt=431 #448 t=1.26e-10 dt=1.21e-12 max_dmdt=426 #449 t=1.27e-10 dt=1.21e-12 max_dmdt=421 #450 t=1.28e-10 dt=1.21e-12 max_dmdt=421 #451 t=1.29e-10 dt=1.21e-12 max_dmdt=424 #452 t=1.31e-10 dt=1.21e-12 max_dmdt=426 #453 t=1.32e-10 dt=1.21e-12 max_dmdt=428 #454 t=1.33e-10 dt=1.21e-12 max_dmdt=429 #455 t=1.34e-10 dt=1.21e-12 max_dmdt=431 #456 t=1.35e-10 dt=1.21e-12 max_dmdt=432 #457 t=1.37e-10 dt=1.21e-12 max_dmdt=432 #458 t=1.38e-10 dt=1.21e-12 max_dmdt=433 #459 t=1.39e-10 dt=1.21e-12 max_dmdt=433 #460 t=1.4e-10 dt=1.21e-12 max_dmdt=433 #461 t=1.41e-10 dt=1.21e-12 max_dmdt=433 #462 t=1.43e-10 dt=1.21e-12 max_dmdt=432 #463 t=1.44e-10 dt=1.21e-12 max_dmdt=431 #464 t=1.45e-10 dt=1.21e-12 max_dmdt=430 #465 t=1.46e-10 dt=1.21e-12 max_dmdt=429 #466 t=1.48e-10 dt=1.21e-12 max_dmdt=427 #467 t=1.49e-10 dt=1.21e-12 max_dmdt=425 #468 t=1.5e-10 dt=1.21e-12 max_dmdt=423 #469 t=1.51e-10 dt=1.21e-12 max_dmdt=421 #470 t=1.52e-10 dt=1.21e-12 max_dmdt=418 #471 t=1.54e-10 dt=1.21e-12 max_dmdt=416 #472 t=1.55e-10 dt=1.21e-12 max_dmdt=413 #473 t=1.56e-10 dt=1.21e-12 max_dmdt=410 #474 t=1.57e-10 dt=1.21e-12 max_dmdt=406 #475 t=1.58e-10 dt=1.21e-12 max_dmdt=403 #476 t=1.6e-10 dt=1.21e-12 max_dmdt=399 #477 t=1.61e-10 dt=1.21e-12 max_dmdt=395 #478 t=1.62e-10 dt=1.21e-12 max_dmdt=391 #479 t=1.63e-10 dt=1.21e-12 max_dmdt=386 #480 t=1.64e-10 dt=1.21e-12 max_dmdt=382 #481 t=1.66e-10 dt=1.21e-12 max_dmdt=377 #482 t=1.67e-10 dt=1.21e-12 max_dmdt=372 #483 t=1.68e-10 dt=1.21e-12 max_dmdt=367 #484 t=1.69e-10 dt=1.21e-12 max_dmdt=362 #485 t=1.7e-10 dt=1.21e-12 max_dmdt=356 #486 t=1.72e-10 dt=1.21e-12 max_dmdt=351 #487 t=1.73e-10 dt=1.21e-12 max_dmdt=345 #488 t=1.74e-10 dt=1.21e-12 max_dmdt=339 #489 t=1.75e-10 dt=1.21e-12 max_dmdt=333 #490 t=1.77e-10 dt=1.81e-12 max_dmdt=326 #491 t=1.79e-10 dt=1.81e-12 max_dmdt=316 #492 t=1.81e-10 dt=1.81e-12 max_dmdt=307 #493 t=1.82e-10 dt=1.81e-12 max_dmdt=297 #494 t=1.84e-10 dt=1.81e-12 max_dmdt=287 #495 t=1.86e-10 dt=1.81e-12 max_dmdt=277 #496 t=1.88e-10 dt=1.81e-12 max_dmdt=267 #497 t=1.9e-10 dt=1.81e-12 max_dmdt=257 #498 t=1.92e-10 dt=1.81e-12 max_dmdt=246 #499 t=1.93e-10 dt=1.81e-12 max_dmdt=236 #500 t=1.95e-10 dt=1.81e-12 max_dmdt=226 #501 t=1.97e-10 dt=1.81e-12 max_dmdt=219 #502 t=1.99e-10 dt=1.81e-12 max_dmdt=221 #503 t=2.01e-10 dt=1.81e-12 max_dmdt=223 #504 t=2.02e-10 dt=1.81e-12 max_dmdt=224 #505 t=2.04e-10 dt=1.81e-12 max_dmdt=224 #506 t=2.06e-10 dt=1.81e-12 max_dmdt=225 #507 t=2.08e-10 dt=1.81e-12 max_dmdt=225 #508 t=2.1e-10 dt=1.81e-12 max_dmdt=224 #509 t=2.11e-10 dt=1.81e-12 max_dmdt=224 #510 t=2.13e-10 dt=1.81e-12 max_dmdt=223 #511 t=2.15e-10 dt=1.81e-12 max_dmdt=222 #512 t=2.17e-10 dt=1.81e-12 max_dmdt=220 #513 t=2.19e-10 dt=1.81e-12 max_dmdt=218 #514 t=2.21e-10 dt=1.81e-12 max_dmdt=216 #515 t=2.22e-10 dt=1.81e-12 max_dmdt=214 #516 t=2.24e-10 dt=1.81e-12 max_dmdt=212 #517 t=2.26e-10 dt=1.81e-12 max_dmdt=209 #518 t=2.28e-10 dt=1.81e-12 max_dmdt=207 #519 t=2.3e-10 dt=1.81e-12 max_dmdt=204 #520 t=2.31e-10 dt=1.81e-12 max_dmdt=201 #521 t=2.33e-10 dt=1.81e-12 max_dmdt=197 #522 t=2.35e-10 dt=1.81e-12 max_dmdt=194 #523 t=2.37e-10 dt=1.81e-12 max_dmdt=191 #524 t=2.39e-10 dt=1.81e-12 max_dmdt=187 #525 t=2.4e-10 dt=1.81e-12 max_dmdt=184 #526 t=2.42e-10 dt=1.81e-12 max_dmdt=180 #527 t=2.44e-10 dt=1.81e-12 max_dmdt=176 #528 t=2.46e-10 dt=1.81e-12 max_dmdt=172 #529 t=2.48e-10 dt=1.81e-12 max_dmdt=168 #530 t=2.49e-10 dt=1.81e-12 max_dmdt=164 #531 t=2.51e-10 dt=1.81e-12 max_dmdt=160 #532 t=2.53e-10 dt=1.81e-12 max_dmdt=156 #533 t=2.55e-10 dt=1.81e-12 max_dmdt=152 #534 t=2.57e-10 dt=1.81e-12 max_dmdt=148 #535 t=2.59e-10 dt=1.81e-12 max_dmdt=144 #536 t=2.6e-10 dt=1.81e-12 max_dmdt=140 #537 t=2.62e-10 dt=1.81e-12 max_dmdt=136 #538 t=2.64e-10 dt=1.81e-12 max_dmdt=132 #539 t=2.67e-10 dt=2.74e-12 max_dmdt=127 #540 t=2.69e-10 dt=2.74e-12 max_dmdt=121 #541 t=2.72e-10 dt=2.74e-12 max_dmdt=115 #542 t=2.75e-10 dt=2.74e-12 max_dmdt=110 #543 t=2.78e-10 dt=2.74e-12 max_dmdt=104 #544 t=2.8e-10 dt=2.74e-12 max_dmdt=98.3 #545 t=2.83e-10 dt=2.74e-12 max_dmdt=92.9 #546 t=2.86e-10 dt=2.74e-12 max_dmdt=87.7 #547 t=2.89e-10 dt=2.74e-12 max_dmdt=82.8 #548 t=2.91e-10 dt=2.74e-12 max_dmdt=78 #549 t=2.94e-10 dt=2.74e-12 max_dmdt=77.7 #550 t=2.97e-10 dt=2.74e-12 max_dmdt=78.4 #551 t=3e-10 dt=2.74e-12 max_dmdt=78.9 #552 t=3.02e-10 dt=2.74e-12 max_dmdt=79.1 #553 t=3.05e-10 dt=2.74e-12 max_dmdt=79.1 #554 t=3.08e-10 dt=2.74e-12 max_dmdt=78.9 #555 t=3.11e-10 dt=2.74e-12 max_dmdt=78.5 #556 t=3.13e-10 dt=2.74e-12 max_dmdt=77.9 #557 t=3.16e-10 dt=2.74e-12 max_dmdt=77.1 #558 t=3.19e-10 dt=2.74e-12 max_dmdt=76.2 #559 t=3.22e-10 dt=2.74e-12 max_dmdt=75.1 #560 t=3.24e-10 dt=2.74e-12 max_dmdt=73.9 #561 t=3.27e-10 dt=2.74e-12 max_dmdt=72.5 #562 t=3.3e-10 dt=2.74e-12 max_dmdt=71.1 #563 t=3.32e-10 dt=2.74e-12 max_dmdt=69.5 #564 t=3.35e-10 dt=2.74e-12 max_dmdt=67.8 #565 t=3.38e-10 dt=2.74e-12 max_dmdt=66.1 #566 t=3.41e-10 dt=2.74e-12 max_dmdt=64.2 #567 t=3.43e-10 dt=2.74e-12 max_dmdt=62.3 #568 t=3.46e-10 dt=2.74e-12 max_dmdt=60.4 #569 t=3.49e-10 dt=2.74e-12 max_dmdt=58.4 #570 t=3.52e-10 dt=2.74e-12 max_dmdt=56.4 #571 t=3.54e-10 dt=2.74e-12 max_dmdt=54.3 #572 t=3.57e-10 dt=2.74e-12 max_dmdt=52.2 #573 t=3.6e-10 dt=2.74e-12 max_dmdt=50.1 #574 t=3.63e-10 dt=2.74e-12 max_dmdt=48 #575 t=3.65e-10 dt=2.74e-12 max_dmdt=45.9 #576 t=3.68e-10 dt=2.74e-12 max_dmdt=43.8 #577 t=3.71e-10 dt=2.74e-12 max_dmdt=41.7 #578 t=3.74e-10 dt=2.74e-12 max_dmdt=39.7 #579 t=3.76e-10 dt=2.74e-12 max_dmdt=37.7 #580 t=3.79e-10 dt=2.74e-12 max_dmdt=35.8 #581 t=3.82e-10 dt=2.74e-12 max_dmdt=34 #582 t=3.85e-10 dt=2.74e-12 max_dmdt=32.2 #583 t=3.87e-10 dt=2.74e-12 max_dmdt=31.5 #584 t=3.9e-10 dt=2.74e-12 max_dmdt=31.8 #585 t=3.93e-10 dt=2.74e-12 max_dmdt=32 #586 t=3.96e-10 dt=2.74e-12 max_dmdt=32.1 #587 t=3.98e-10 dt=2.74e-12 max_dmdt=32.1 #588 t=4.01e-10 dt=2.74e-12 max_dmdt=32.1 #589 t=4.04e-10 dt=2.74e-12 max_dmdt=32 #590 t=4.06e-10 dt=2.74e-12 max_dmdt=31.8 #591 t=4.09e-10 dt=2.74e-12 max_dmdt=31.5 #592 t=4.12e-10 dt=2.74e-12 max_dmdt=31.2 #593 t=4.15e-10 dt=2.74e-12 max_dmdt=30.8 #594 t=4.17e-10 dt=2.74e-12 max_dmdt=30.3 #595 t=4.2e-10 dt=2.74e-12 max_dmdt=29.8 #596 t=4.23e-10 dt=2.74e-12 max_dmdt=29.3 #597 t=4.26e-10 dt=2.74e-12 max_dmdt=28.7 #598 t=4.28e-10 dt=2.74e-12 max_dmdt=28.1 #599 t=4.31e-10 dt=2.74e-12 max_dmdt=27.4 #600 t=4.34e-10 dt=2.74e-12 max_dmdt=26.7 #601 t=4.37e-10 dt=2.74e-12 max_dmdt=26 #602 t=4.39e-10 dt=2.74e-12 max_dmdt=25.2 #603 t=4.42e-10 dt=2.74e-12 max_dmdt=24.4 #604 t=4.45e-10 dt=2.74e-12 max_dmdt=23.6 #605 t=4.48e-10 dt=2.74e-12 max_dmdt=22.8 #606 t=4.5e-10 dt=2.74e-12 max_dmdt=21.9 #607 t=4.53e-10 dt=2.74e-12 max_dmdt=21.1 #608 t=4.57e-10 dt=4.11e-12 max_dmdt=20 #609 t=4.61e-10 dt=4.11e-12 max_dmdt=18.8 #610 t=4.65e-10 dt=4.11e-12 max_dmdt=17.5 #611 t=4.69e-10 dt=4.11e-12 max_dmdt=16.3 #612 t=4.74e-10 dt=4.11e-12 max_dmdt=15.1 #613 t=4.78e-10 dt=4.11e-12 max_dmdt=14 #614 t=4.82e-10 dt=4.11e-12 max_dmdt=13 #615 t=4.86e-10 dt=4.11e-12 max_dmdt=12.9 #616 t=4.9e-10 dt=4.11e-12 max_dmdt=13.1 #617 t=4.94e-10 dt=4.11e-12 max_dmdt=13.1 #618 t=4.98e-10 dt=4.11e-12 max_dmdt=13.2 #619 t=5.02e-10 dt=4.11e-12 max_dmdt=13.1 #620 t=5.06e-10 dt=4.11e-12 max_dmdt=13 #621 t=5.11e-10 dt=4.11e-12 max_dmdt=12.8 #622 t=5.15e-10 dt=4.11e-12 max_dmdt=12.5 #623 t=5.19e-10 dt=4.11e-12 max_dmdt=12.2 #624 t=5.23e-10 dt=4.11e-12 max_dmdt=11.8 #625 t=5.27e-10 dt=4.11e-12 max_dmdt=11.4 #626 t=5.31e-10 dt=4.11e-12 max_dmdt=11 #627 t=5.35e-10 dt=4.11e-12 max_dmdt=10.6 #628 t=5.39e-10 dt=4.11e-12 max_dmdt=10.1 #629 t=5.44e-10 dt=4.11e-12 max_dmdt=9.56 #630 t=5.48e-10 dt=4.11e-12 max_dmdt=9.03 #631 t=5.52e-10 dt=4.11e-12 max_dmdt=8.5 #632 t=5.56e-10 dt=4.11e-12 max_dmdt=7.96 #633 t=5.6e-10 dt=4.11e-12 max_dmdt=7.43 #634 t=5.64e-10 dt=4.11e-12 max_dmdt=6.91 #635 t=5.68e-10 dt=4.11e-12 max_dmdt=6.42 #636 t=5.72e-10 dt=4.11e-12 max_dmdt=5.95 #637 t=5.76e-10 dt=4.11e-12 max_dmdt=5.52 #638 t=5.81e-10 dt=4.11e-12 max_dmdt=5.5 #639 t=5.85e-10 dt=4.11e-12 max_dmdt=5.56 #640 t=5.89e-10 dt=4.11e-12 max_dmdt=5.59 #641 t=5.93e-10 dt=4.11e-12 max_dmdt=5.59 #642 t=5.97e-10 dt=4.11e-12 max_dmdt=5.55 #643 t=6.01e-10 dt=4.11e-12 max_dmdt=5.49 #644 t=6.05e-10 dt=4.11e-12 max_dmdt=5.41 #645 t=6.09e-10 dt=4.11e-12 max_dmdt=5.3 #646 t=6.13e-10 dt=4.11e-12 max_dmdt=5.17 #647 t=6.18e-10 dt=4.11e-12 max_dmdt=5.02 #648 t=6.22e-10 dt=4.11e-12 max_dmdt=4.85 #649 t=6.26e-10 dt=4.11e-12 max_dmdt=4.67 #650 t=6.3e-10 dt=4.11e-12 max_dmdt=4.48 #651 t=6.34e-10 dt=4.11e-12 max_dmdt=4.28 #652 t=6.38e-10 dt=4.11e-12 max_dmdt=4.07 #653 t=6.42e-10 dt=4.11e-12 max_dmdt=3.85 #654 t=6.46e-10 dt=4.11e-12 max_dmdt=3.63 #655 t=6.5e-10 dt=4.11e-12 max_dmdt=3.4 #656 t=6.55e-10 dt=4.11e-12 max_dmdt=3.18 #657 t=6.59e-10 dt=4.11e-12 max_dmdt=2.97 #658 t=6.63e-10 dt=4.11e-12 max_dmdt=2.76 #659 t=6.67e-10 dt=4.11e-12 max_dmdt=2.56 #660 t=6.71e-10 dt=4.11e-12 max_dmdt=2.38 #661 t=6.75e-10 dt=4.11e-12 max_dmdt=2.26 #662 t=6.79e-10 dt=4.11e-12 max_dmdt=2.31 #663 t=6.83e-10 dt=4.11e-12 max_dmdt=2.33 #664 t=6.89e-10 dt=6.18e-12 max_dmdt=2.34 #665 t=6.96e-10 dt=6.18e-12 max_dmdt=2.33 #666 t=7.02e-10 dt=6.18e-12 max_dmdt=2.28 #667 t=7.08e-10 dt=6.18e-12 max_dmdt=2.22 #668 t=7.14e-10 dt=6.18e-12 max_dmdt=2.13 #669 t=7.2e-10 dt=6.18e-12 max_dmdt=2.02 #670 t=7.27e-10 dt=6.18e-12 max_dmdt=1.91 #671 t=7.33e-10 dt=6.18e-12 max_dmdt=1.78 #672 t=7.39e-10 dt=6.18e-12 max_dmdt=1.64 #673 t=7.45e-10 dt=6.18e-12 max_dmdt=1.5 #674 t=7.51e-10 dt=6.18e-12 max_dmdt=1.35 #675 t=7.57e-10 dt=6.18e-12 max_dmdt=1.22 #676 t=7.64e-10 dt=6.18e-12 max_dmdt=1.09 #677 t=7.7e-10 dt=6.18e-12 max_dmdt=0.979 #678 t=7.76e-10 dt=6.18e-12 max_dmdt=1 #679 t=7.82e-10 dt=6.18e-12 max_dmdt=1.01 #680 t=7.88e-10 dt=6.18e-12 max_dmdt=1.01 #681 t=7.95e-10 dt=6.18e-12 max_dmdt=0.994 #682 t=8.01e-10 dt=6.18e-12 max_dmdt=0.968 #683 t=8.07e-10 dt=6.18e-12 max_dmdt=0.933 #684 t=8.13e-10 dt=6.18e-12 max_dmdt=0.891 #685 t=8.19e-10 dt=6.18e-12 max_dmdt=0.843 #686 t=8.25e-10 dt=6.18e-12 max_dmdt=0.789 #687 t=8.32e-10 dt=6.18e-12 max_dmdt=0.732 #688 t=8.38e-10 dt=6.18e-12 max_dmdt=0.672 #689 t=8.44e-10 dt=6.18e-12 max_dmdt=0.612 #690 t=8.5e-10 dt=6.18e-12 max_dmdt=0.552 #691 t=8.56e-10 dt=6.18e-12 max_dmdt=0.496 #692 t=8.63e-10 dt=6.18e-12 max_dmdt=0.448 #693 t=8.69e-10 dt=6.18e-12 max_dmdt=0.42 #694 t=8.75e-10 dt=6.18e-12 max_dmdt=0.429 #695 t=8.81e-10 dt=6.18e-12 max_dmdt=0.432 #696 t=8.87e-10 dt=6.18e-12 max_dmdt=0.43 #697 t=8.93e-10 dt=6.18e-12 max_dmdt=0.422 #698 t=9e-10 dt=6.18e-12 max_dmdt=0.41 #699 t=9.06e-10 dt=6.18e-12 max_dmdt=0.394 #700 t=9.12e-10 dt=6.18e-12 max_dmdt=0.375 #701 t=9.18e-10 dt=6.18e-12 max_dmdt=0.353 #702 t=9.28e-10 dt=9.45e-12 max_dmdt=0.323 #703 t=9.37e-10 dt=9.45e-12 max_dmdt=0.283 #704 t=9.47e-10 dt=9.45e-12 max_dmdt=0.243 #705 t=9.56e-10 dt=9.45e-12 max_dmdt=0.21 #706 t=9.65e-10 dt=9.45e-12 max_dmdt=0.184 #707 t=9.75e-10 dt=9.45e-12 max_dmdt=0.189 #708 t=9.84e-10 dt=9.45e-12 max_dmdt=0.188 #709 t=9.94e-10 dt=9.45e-12 max_dmdt=0.181 #710 t=1e-09 dt=9.45e-12 max_dmdt=0.171 #711 t=1.01e-09 dt=9.45e-12 max_dmdt=0.158 #712 t=1.02e-09 dt=9.45e-12 max_dmdt=0.142 #713 t=1.03e-09 dt=9.45e-12 max_dmdt=0.125 #714 t=1.04e-09 dt=9.45e-12 max_dmdt=0.109 #715 t=1.05e-09 dt=9.45e-12 max_dmdt=0.0946 #716 t=1.06e-09 dt=9.45e-12 max_dmdt=0.0805 #717 t=1.07e-09 dt=9.45e-12 max_dmdt=0.0812 #718 t=1.08e-09 dt=9.45e-12 max_dmdt=0.0814 #719 t=1.09e-09 dt=9.45e-12 max_dmdt=0.0792 #720 t=1.1e-09 dt=9.45e-12 max_dmdt=0.0752 #721 t=1.11e-09 dt=9.45e-12 max_dmdt=0.0697 #722 t=1.12e-09 dt=9.45e-12 max_dmdt=0.0633 #723 t=1.13e-09 dt=9.45e-12 max_dmdt=0.0564 #724 t=1.14e-09 dt=9.45e-12 max_dmdt=0.0494 #725 t=1.14e-09 dt=9.45e-12 max_dmdt=0.0425 #726 t=1.15e-09 dt=9.45e-12 max_dmdt=0.0357 #727 t=1.16e-09 dt=9.45e-12 max_dmdt=0.0356 #728 t=1.18e-09 dt=1.42e-11 max_dmdt=0.0355 #729 t=1.19e-09 dt=1.42e-11 max_dmdt=0.0338 #730 t=1.21e-09 dt=1.42e-11 max_dmdt=0.0305 #731 t=1.22e-09 dt=1.42e-11 max_dmdt=0.0262 #732 t=1.23e-09 dt=1.42e-11 max_dmdt=0.0214 #733 t=1.25e-09 dt=1.42e-11 max_dmdt=0.0166 #734 t=1.26e-09 dt=1.42e-11 max_dmdt=0.0155 #735 t=1.28e-09 dt=1.42e-11 max_dmdt=0.0156 #736 t=1.29e-09 dt=1.42e-11 max_dmdt=0.0147 #737 t=1.31e-09 dt=1.42e-11 max_dmdt=0.0131 #738 t=1.32e-09 dt=1.42e-11 max_dmdt=0.0111 #739 t=1.33e-09 dt=1.42e-11 max_dmdt=0.00887
Plot the magnetisation components of the relaxed state.
[8]:
#NBVAL_IGNORE_OUTPUT plot_magnetisation([['m0.npy', 'mx'], ['m0.npy', 'my'], ['m0.npy', 'mz']])
The DW is at the maximum value of \(|m_z|\) or \(|m_y|\). Consequently, the domain wall position is:
[9]:
m0_z = np.load('m0.npy').reshape(-1, 3)[:, 2] x = np.arange(len(m0_z)) index_max = np.argmax(np.abs(m0_z)) print('Maximum |m_z| at x = %s' % x[index_max])
Maximum |m_z| at x = 124
Using the obtained domain wall equilibrium state, we now simulate its motion in presence of a spin-polarised current.
[10]:
#NBVAL_IGNORE_OUTPUT excite_system(mesh, 1.5e-9, 151)
We plot once again to compare the initial state with the ones after a SP current was applied.
[11]:
#NBVAL_IGNORE_OUTPUT # We can plot the m_x component for a number snapshots # to observe the DW motion # We will plot the 100th and 150th files (we can also compute # until the system reaches ~5 ns to improve the effect) plot_magnetisation([['m0.npy', 'mx'], ['dyn_npys/m_100.npy', 'mx'], ['dyn_npys/m_150.npy', 'mx']]) plt.xlim([0, 200])
(0, 200)