{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 04: Dzyaloshinskii-Moriya energy term\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",
    "\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": "d5a67821f40846e38523709c574f35d8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "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_z')"
   ]
  },
  {
   "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": "0179446af3f34fc48b031d70b767f02a",
       "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 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "system.m.k3d.vector(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": [
      "Running OOMMF (ExeOOMMFRunner) [2021/09/22 13:55]...  <1> mmarchive killed\n",
      " <2> mmarchive killed\n",
      "(1.3 s)\n"
     ]
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "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": "d9454cb4359e490e822954545cca0b0a",
       "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 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "system.m.k3d.vector(color_field=system.m.z)  # k3d plot\n",
    "system.m.plane('y').mpl()                     # matplotlib plot"
   ]
  },
  {
   "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": 8,
   "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": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "14177d1a0a794fb2ba3419d0d3544a8f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "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": 10,
   "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": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "system = mm.System(name='dmi_dict_D')\n",
    "system.energy = mm.DMI(D=D, crystalclass='Cnv_z')\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": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c93d64e5736e4ef1ae830be153ded9e9",
       "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 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "system.m.k3d.vector(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": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running OOMMF (ExeOOMMFRunner) [2021/09/22 13:55]...  <1> mmarchive killed\n",
      " <2> mmarchive killed\n",
      "(1.3 s)\n"
     ]
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0639b17ed43942d7b806d086e97d1c6f",
       "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 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "system.m.k3d.vector(color_field=system.m.z)\n",
    "system.m.plane('y').mpl()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "0179446af3f34fc48b031d70b767f02a": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_bfe3eb25bbb44630a1efd848d5214be5",
       "outputs": [
        {
         "data": {
          "application/vnd.jupyter.widget-view+json": {
           "model_id": "a2fe160c6bbc40838ff37c8fb6e12924",
           "version_major": 2,
           "version_minor": 0
          },
          "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera_animation=[], camer…"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "0639b17ed43942d7b806d086e97d1c6f": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_3356ecb317cf47b49a5c09cba8d69a6e",
       "outputs": [
        {
         "data": {
          "application/vnd.jupyter.widget-view+json": {
           "model_id": "20b8146d52c142c9be9f94a7f10b37b2",
           "version_major": 2,
           "version_minor": 0
          },
          "text/plain": "Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, background_color=16777215, camera_animation=[], camer…"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
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       },
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       }
      ],
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      "state": {
       "_view_count": null,
       "_view_module": null,
       "_view_module_version": "",
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       "colorLegend": false,
       "colors": {
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        "shape": [
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        ]
       },
       "compression_level": 0,
       "head_color": 255,
       "head_size": 1,
       "id": 140597839836400,
       "label_size": 1,
       "labels": [],
       "line_width": 0.01,
       "model_matrix": {
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        ]
       },
       "name": "Vectors #1",
       "origin_color": 255,
       "origins": {
        "dtype": "float32",
        "shape": [
         20,
         3
        ]
       },
       "type": "Vectors",
       "use_head": true,
       "vectors": {
        "dtype": "float32",
        "shape": [
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        ]
       },
       "visible": true
      }
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       },
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