{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spin-polarised current driven skyrmion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Author**: Marijan Beg,  Weiwei Wang\n",
    "\n",
    "**Date**: 30 July 2016\n",
    "\n",
    "This notebook can be downloaded from the github repository, found [here](https://github.com/computationalmodelling/fidimag/blob/master/doc/ipynb/spin-polarised-current-driven-skyrmion.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial, a single magnetic skyrmion is driven by a spin-polarised current.\n",
    "\n",
    "Firstly, we define a function which will be subsequently used for plotting the z component of magnetisation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "def plot_magnetisation(m, mesh, title=None):\n",
    "    m.shape = (-1, 3)\n",
    "    mx = m[:, 0]\n",
    "    my = m[:, 1]\n",
    "    mz = m[:, 2]\n",
    "    nx, ny = mesh.nx, mesh.ny\n",
    "    mx.shape = (ny, nx)\n",
    "    my.shape = (ny, nx)\n",
    "    mz.shape = (ny, nx)\n",
    "    \n",
    "\n",
    "    #plt.imshow(mz, extent=extent)\n",
    "    #plt.xlabel('x (nm)')\n",
    "    #plt.ylabel('y (nm)')\n",
    "    \n",
    "    \n",
    "    fig = plt.figure(figsize=(8,8))\n",
    "    plt.axes().set_aspect('equal')\n",
    "    plt.quiver(mx[::3,::3], my[::3,::3], mz[::3,::3], pivot='mid', alpha=0.9, scale=18, width=0.005,  cmap=plt.get_cmap('jet'), edgecolors='None' )\n",
    "    if title is not None:\n",
    "        plt.title(title)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we create a finite difference mesh."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from fidimag.micro import Sim\n",
    "from fidimag.common import CuboidMesh\n",
    "from fidimag.micro import Zeeman, Demag, DMI, UniformExchange\n",
    "\n",
    "mesh = CuboidMesh(nx=51, ny=30, nz=1, dx=2.5, dy=2.5, dz=2, unit_length=1e-9, periodicity=(True, True, False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a simulation object that contains uniform exchange, DMI, and Zeeman energy contributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# PYTEST_VALIDATE_IGNORE_OUTPUT\n",
    "Ms = 8.6e5  # magnetisation saturation (A/m)\n",
    "A = 1.3e-11  # exchange stiffness (J/m)\n",
    "D = 4e-3  # DMI constant (J/m**2)\n",
    "H = (0, 0, 3.8e5)  # external magnetic field (A/m)\n",
    "alpha = 0.5  # Gilbert damping\n",
    "gamma = 2.211e5  # gyromagnetic ratio (m/As)\n",
    "\n",
    "sim  = Sim(mesh)  # create simulation object\n",
    "\n",
    "# Set parameters.\n",
    "sim.Ms = Ms\n",
    "sim.driver.alpha = alpha\n",
    "sim.driver.gamma = gamma\n",
    "sim.driver.do_precession = False\n",
    "\n",
    "# Add energies.\n",
    "sim.add(UniformExchange(A=A))\n",
    "sim.add(DMI(D))\n",
    "sim.add(Zeeman(H))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to get a skyrmion as a relaxed state, we need to initialise the system in an appropriate way. For that, we use the following function, and plot the initial state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def m_initial(coord):\n",
    "    # Extract x and y coordinates.\n",
    "    x = coord[0]\n",
    "    y = coord[1]\n",
    "    \n",
    "    # The centre of the circle\n",
    "    x_centre = 15*2.5\n",
    "    y_centre = 15*2.5\n",
    "    \n",
    "    # Compute the circle radius.\n",
    "    r = ((x-x_centre)**2 + (y-y_centre)**2)**0.5\n",
    "    \n",
    "    if r < 8.0:\n",
    "        return (0, 0, -1)\n",
    "    else:\n",
    "        return (0, 0, 1)\n",
    "    \n",
    "sim.set_m(m_initial)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can relax the system, save and plot the relaxed state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "sim.driver.relax(dt=1e-13, stopping_dmdt=0.1, max_steps=5000, save_m_steps=None, save_vtk_steps=None)\n",
    "np.save('m0.npy', sim.spin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Ly4Enb4UhT0DPy3yXn3zyKqRs9c0PCYX7XoDrhgQsMumll0j54IODj88aNox2L7wQsOUf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28d4559990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_magnetisation(sim.spin.copy(), mesh, title='t=0 ns')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the obtained relaxed state, we create a new smulation object and specify the driver to be 'llg_stt'. By applying a spin-polarised current of $J = 5 \\times 10^{12} \\,\\text{A/m}^{2}$ in the $x$ directions with $\\beta = 0.2$, we move a skyrmion in the simulated sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4eTIbJ9tzxnhOcjJbZs5ky8yZtuTtX7WKpNmzK51/wvdoi2/ZMqArVJnGF11E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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28d1ff4f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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eq1bhjoqyJ2jn17DubohoCJ5MiGwMEQ2C18983/K4xSlw1Wv7L//gz3BRB8vj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28d217a290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZCd9/b2nOEbmHD7Ppm2/YOHWqLXmp27axdeZMtto0Wj+0Zg0JP/5Y5vrTzmXF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\niIgP/j/4w+K6DQrarAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28d210d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PYTEST_VALIDATE_IGNORE_OUTPUT\n",
    "sim2  = Sim(mesh, driver='llg_stt')  # create simulation object\n",
    "\n",
    "# Set parameters.\n",
    "sim2.Ms = Ms\n",
    "sim2.alpha = alpha\n",
    "sim2.driver.gamma = gamma\n",
    "\n",
    "# Add energies.\n",
    "sim2.add(UniformExchange(A=A))\n",
    "sim2.add(DMI(D))\n",
    "sim2.add(Zeeman(H))\n",
    "\n",
    "sim2.driver.jx = -5e12\n",
    "sim2.alpha = 0.2\n",
    "sim2.driver.beta = 0.2\n",
    "\n",
    "sim2.set_m(np.load('m0.npy'))\n",
    "\n",
    "for t in [0, 0.1, 0.2]:\n",
    "    sim2.driver.run_until(t*1e-9)\n",
    "    plot_magnetisation(sim2.spin.copy(), mesh, title='t=%g ns'%t)"
   ]
  }
 ],
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