{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial 07: Standard problem 3\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", "## Problem specification\n", "\n", "This problem is to calculate a single domain limit of a cubic magnetic particle. This is the size $L$ of equal energy for the so-called flower state (which one may also call a splayed state or a modified single-domain state) on the one hand, and the vortex or curling state on the other hand.\n", "\n", "Geometry:\n", "\n", "A cube with edge length, $L$, expressed in units of the intrinsic length scale, $l_\\text{ex} = \\sqrt{A/K_\\text{m}}$, where $K_\\text{m}$ is a magnetostatic energy density, $K_\\text{m} = \\frac{1}{2}\\mu_{0}M_\\text{s}^{2}$.\n", "\n", "Material parameters: \n", "\n", "- uniaxial anisotropy $K_\\text{u}$ with $K_\\text{u} = 0.1 K_\\text{m}$, and with the easy axis directed parallel to a principal axis of the cube (0, 0, 1),\n", "- exchange energy constant is $A = \\frac{1}{2}\\mu_{0}M_\\text{s}^{2}l_\\text{ex}^{2}$.\n", "\n", "More details about the standard problem 3 can be found in Ref. 1.\n", "\n", "## Simulation\n", "\n", "Firstly, we import all necessary modules." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import discretisedfield as df\n", "import micromagneticmodel as mm\n", "import oommfc as oc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following two functions are used for initialising the system's magnetisation [1]." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# Function for initiaising the flower state.\n", "def m_init_flower(pos):\n", " x, y, z = pos[0]/1e-9, pos[1]/1e-9, pos[2]/1e-9\n", " mx = 0\n", " my = 2*z - 1\n", " mz = -2*y + 1\n", " norm_squared = mx**2 + my**2 + mz**2\n", " if norm_squared <= 0.05:\n", " return (1, 0, 0)\n", " else:\n", " return (mx, my, mz)\n", "\n", "# Function for initialising the vortex state.\n", "def m_init_vortex(pos):\n", " x, y, z = pos[0]/1e-9, pos[1]/1e-9, pos[2]/1e-9\n", " mx = 0\n", " my = np.sin(np.pi/2 * (x-0.5))\n", " mz = np.cos(np.pi/2 * (x-0.5))\n", " \n", " return (mx, my, mz)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following function is used for convenience. It takes two arguments:\n", "\n", "- $L$ - the cube edge length in units of $l_\\text{ex}$, and\n", "- the function for initialising the system's magnetisation.\n", "\n", "It returns the relaxed system object.\n", "\n", "Please refer to other tutorials for more details on how to create system objects and drive them using specific drivers." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def minimise_system_energy(L, m_init):\n", " print(\"L={:9}, {} \".format(L, m_init.__name__), end=\"\")\n", " N = 16 # discretisation in one dimension\n", " cubesize = 100e-9 # cube edge length (m)\n", " cellsize = cubesize/N # discretisation in all three dimensions.\n", " lex = cubesize/L # exchange length.\n", " \n", " Km = 1e6 # magnetostatic energy density (J/m**3)\n", " Ms = np.sqrt(2*Km/mm.consts.mu0) # magnetisation saturation (A/m)\n", " A = 0.5 * mm.consts.mu0 * Ms**2 * lex**2 # exchange energy constant\n", " K = 0.1*Km # Uniaxial anisotropy constant\n", " u = (0, 0, 1) # Uniaxial anisotropy easy-axis\n", "\n", " p1 = (0, 0, 0) # Minimum sample coordinate.\n", " p2 = (cubesize, cubesize, cubesize) # Maximum sample coordinate.\n", " cell = (cellsize, cellsize, cellsize) # Discretisation.\n", " mesh = df.Mesh(p1=(0, 0, 0), p2=(cubesize, cubesize, cubesize),\n", " cell=(cellsize, cellsize, cellsize)) # Create a mesh object.\n", "\n", " system = mm.System(name='stdprob3')\n", " system.energy = mm.Exchange(A=A) + mm.UniaxialAnisotropy(K=K, u=u) + mm.Demag()\n", " system.m = df.Field(mesh, dim=3, value=m_init, norm=Ms)\n", "\n", " md = oc.MinDriver()\n", " md.drive(system, overwrite=True)\n", " \n", " return system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Relaxed magnetisation states\n", "\n", "Now, we show the magnetisation configurations of two relaxed states.\n", "\n", "**Vortex** state:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "L= 8, m_init_vortex Running OOMMF (ExeOOMMFRunner) [2020/06/14 11:19]... (5.4 s)\n" ] }, { "data": { "image/png": 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\n", 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