{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 04: Dzyaloshinskii-Moriya energy term\n",
    "\n",
    "> Interactive online tutorial:\n",
    "> [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/ubermag/oommfc/master?filepath=docs%2Fipynb%2Findex.ipynb)\n",
    "\n",
    "Dzyaloshinskii-Moriya energy density, depending on the crystallographic class, is computed as\n",
    "\n",
    "$$\\mathbf{w_\\text{dmi}} = \\left\\{\n",
    "\\begin{array}{ll}\n",
    "D \\mathbf{m} \\cdot (\\nabla \\times \\mathbf{m}), & \\text{for}\\,\\,T(O) \\\\\n",
    "D ( \\mathbf{m} \\cdot \\nabla m_{z} - m_{z} \\nabla \\cdot \\mathbf{m}), & \\text{for}\\,\\,C_{nv} \\\\\n",
    "D\\mathbf{m} \\cdot \\left( \\frac{\\partial \\mathbf{m}}{\\partial x} \\times \\hat{x} - \\frac{\\partial \\mathbf{m}}{\\partial y} \\times \\hat{y} \\right), & \\text{for}\\,\\,D_{2d} \\\\\n",
    "\\end{array}\n",
    "\\right. $$\n",
    "\n",
    "where $\\mathbf{m}$ is the normalised ($|\\mathbf{m}|=1$) magnetisation, and $D$ is the DM energy constant. DMI energy term tends to align neighbouring magnetic moments perpendicular to each other.\n",
    "\n",
    "In `oommfc`, $\\mathbf{m}$ is a part of the magnetisation field `system.m`. Therefore, only DMI energy constant $D$ should be provided as an input parameter to uniquely define the Exchange energy term. $D$ can be constant in space or spatially varying.\n",
    "\n",
    "## Spatially constant $D$\n",
    "\n",
    "Let us start by assembling a simple simple simulation where $D$ does not vary in space. The sample is a \"one-dimensional\" chain of magnetic moments. We are going to choose $C_{nv}$ as the crystallographic class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import oommfc as oc\n",
    "import discretisedfield as df\n",
    "import micromagneticmodel as mm\n",
    "%matplotlib inline\n",
    "\n",
    "p1 = (-10e-9, 0, 0)\n",
    "p2 = (10e-9, 1e-9, 1e-9)\n",
    "cell = (1e-9, 1e-9, 1e-9)\n",
    "region = df.Region(p1=p1, p2=p2)\n",
    "mesh = df.Mesh(region=region, cell=cell)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mesh is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f56f6c1486e14b16876d05662d326212",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mesh.k3d()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The system has a Hamiltonian, which consists of only DMI energy term."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = 1e-3  # Dzyaloshinksii-Moriya energy constant (J/m**2)\n",
    "system = mm.System(name='dmi_constant_D')\n",
    "system.energy = mm.DMI(D=D, crystalclass='Cnv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to minimise the system's energy using `oommfc.MinDriver` later. Therefore, we do not have to define the system's dynamics equation. Finally, we need to define the system's magnetisation (`system.m`). We are going to make it random with $M_\\text{s}=8\\times10^{5} \\,\\text{Am}^{-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import discretisedfield as df\n",
    "\n",
    "Ms = 8e5  # saturation magnetisation (A/m)\n",
    "\n",
    "def m_fun(pos):\n",
    "    \"\"\"Return random 3d vectors for initial random magnetisation\"\"\"\n",
    "    return [2*random.random()-1, 2*random.random()-1, 2*random.random()-1]\n",
    "\n",
    "system.m = df.Field(mesh, dim=3, value=m_fun, norm=Ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The magnetisation, we have set as initial values looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "42ff602464f341ce9479a6815cc55864",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.m.k3d_vectors(color_field=system.m.z)  # k3d plot\n",
    "system.m.plane('y').mpl()                     # matplotlib plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can minimise the system's energy by using `oommfc.MinDriver`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020/03/06 14:41: Running OOMMF (dmi_constant_D.mif) ... (1.0 s)\n"
     ]
    }
   ],
   "source": [
    "md = oc.MinDriver()\n",
    "md.drive(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We expect that now all magnetic moments are aligned orthogonally to each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "933ec01bd41c4c0485d2722ce44c8893",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.m.k3d_vectors(color_field=system.m.z)  # k3d plot\n",
    "system.m.plane('y').mpl()                     # matplotlib plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can delete the files created by `oommfc`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "md.delete(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spatially varying $D$\n",
    "\n",
    "In the case of DMI, there is only one way how a parameter can be made spatially varying - using a dictionary.\n",
    "\n",
    "In order to define a parameter using a dictionary, regions must be defined in the mesh. Regions are defined as a dictionary, whose keys are the strings and values are `discretisedfield.Region` objects, which take two corner points of the region as input parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "p1 = (-10e-9, 0, 0)\n",
    "p2 = (10e-9, 1e-9, 1e-9)\n",
    "cell = (1e-9, 1e-9, 1e-9)\n",
    "subregions = {'region1': df.Region(p1=(-10e-9, 0, 0), p2=(0, 1e-9, 1e-9)),\n",
    "              'region2': df.Region(p1=(0, 0, 0), p2=(10e-9, 1e-9, 1e-9))}\n",
    "region = df.Region(p1=p1, p2=p2)\n",
    "mesh = df.Mesh(region=region, cell=cell, subregions=subregions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The regions we have defined are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fbd0dcacc3dd430eab312f74d75e59be",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mesh.k3d_subregions()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us say there is no DMI energy ($D=0$) in region 1, whereas in region 2 $D=10^{-3} \\,\\text{Jm}^{-2}$. Unlike Zeeman and anisotropy energy terms, the DMI energy constant is defined between cells. Therefore, it is necessary to also define the value of $D$ between the two regions. This is achieved by adding another item to the dictionary with key `'region1:region2'`. The object `D` is now defined as a dictionary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = {'region1': 0, 'region2': 1e-3, 'region1:region2': 0.5e-3}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The system object is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "system = mm.System(name='dmi_dict_D')\n",
    "system.energy = mm.DMI(D=D, crystalclass='Cnv')\n",
    "system.m = df.Field(mesh, dim=3, value=m_fun, norm=Ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Its initial (and random) magnetisation is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cee4b9e61d98414ba959505aa1eb2156",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.m.k3d_vectors(color_field=system.m.z)\n",
    "system.m.plane('y').mpl()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After we minimise the energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020/03/06 14:41: Running OOMMF (dmi_dict_D.mif) ... (1.0 s)\n"
     ]
    }
   ],
   "source": [
    "md.drive(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The magnetisation is as we expected. The magnetisation remains random in region 1, and it is orthogonally aligned in region 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "013933b93a6e45dd9a6d5f8763b42d45",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system.m.k3d_vectors(color_field=system.m.z)\n",
    "system.m.plane('y').mpl()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "md.delete(system)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "013933b93a6e45dd9a6d5f8763b42d45": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_4a9bb1a2e30e434891a319709c071b53",
       "outputs": [
        {
         "data": {
          "application/vnd.jupyter.widget-view+json": {
           "model_id": "557a6d3bc8eb487c879d86bdbc7e72e7",
           "version_major": 2,
           "version_minor": 0
          },
          "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera=[2, -3, 0.2, 0.0, 0…"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "022e19fee5fb42ea8fca8fb5d3987888": {
      "model_module": "k3d",
      "model_module_version": "2.7.4",
      "model_name": "PlotModel",
      "state": {
       "_backend_version": "2.7.4",
       "_dom_classes": [],
       "_view_count": null,
       "antialias": 3,
       "auto_rendering": true,
       "axes": [
        "x (nm)",
        "y (nm)",
        "z (nm)"
       ],
       "axes_helper": 1,
       "background_color": 16777215,
       "camera": [
        16.707952969879074,
        -24.636929444760327,
        2.175795296317352,
        -0.04999999329447746,
        0.5,
        0.5,
        0,
        0,
        1
       ],
       "camera_animation": [],
       "camera_auto_fit": true,
       "camera_fov": 60,
       "camera_no_pan": false,
       "camera_no_rotate": false,
       "camera_no_zoom": false,
       "clipping_planes": [],
       "colorbar_object_id": -1,
       "fps": 25,
       "fps_meter": false,
       "grid": [
        -1,
        -1,
        -1,
        1,
        1,
        1
       ],
       "grid_auto_fit": true,
       "grid_visible": true,
       "height": 512,
       "layout": "IPY_MODEL_564112bc1f564f639770d691acc51d9c",
       "lighting": 1.5,
       "menu_visibility": true,
       "mode": "view",
       "name": null,
       "object_ids": [
        139841762281872
       ],
       "rendering_steps": 1,
       "screenshot": "",
       "screenshot_scale": 2,
       "snapshot": "",
       "time": 0,
       "voxel_paint_color": 0
      }
     },
     "043d0a3feaf54df49d39dea5030d7111": {
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