{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Micromagnetic standard problem 3\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": { "collapsed": true }, "outputs": [], "source": [ "import discretisedfield as df\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": { "collapsed": true }, "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": { "collapsed": true }, "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/oc.mu0) # magnetisation saturation (A/m)\n", " A = 0.5 * oc.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 = oc.Mesh(p1=(0, 0, 0), p2=(cubesize, cubesize, cubesize),\n", " cell=(cellsize, cellsize, cellsize)) # Create a mesh object.\n", "\n", " system = oc.System(name=\"stdprob3\")\n", " system.hamiltonian = oc.Exchange(A) + oc.UniaxialAnisotropy(K, u) + oc.Demag()\n", " system.m = df.Field(mesh, value=m_init, norm=Ms)\n", "\n", " md = oc.MinDriver()\n", " md.drive(system)\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 2017/9/25 14:43: Calling OOMMF (stdprob3/stdprob3.mif) ... [3.3s]\n" ] }, { "data": { "image/png": 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pRHN+20zuA34EIKXcAfiA6mKcmdJkyOqlUVMLhhPGAB7ho8xVpWTXNbmDptI1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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "system = minimise_system_energy(8, m_init_vortex)\n", "system.m.plot_plane(\"y\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Flower** state:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "L= 8, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.7s]\n" ] }, { "data": { "image/png": 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jBThWlVJmXMyrFuawyt63kF1AcXZYnH7pug7FWXnqa62UpVacF/NKmXFcR6Yz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\n3AAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "system = minimise_system_energy(8, m_init_flower)\n", "system.m.plot_plane(\"x\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Energy crossing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can plot the energies of both vortex and flower states as a function of cube edge length. This will give us an idea where the state transition occurrs." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "L= 8.0, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [2.5s]\n", "L= 8.0, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [0.8s]\n", "L= 8.25, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.9s]\n", "L= 8.25, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [0.8s]\n", "L= 8.5, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.6s]\n", "L= 8.5, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [0.8s]\n", "L= 8.75, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.6s]\n", "L= 8.75, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [0.8s]\n", "L= 9.0, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.9s]\n", "L= 9.0, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [0.8s]\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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tQoUKFXO5FRdx9r7giLNHw/nwoARjwBKIya7ZjUXzl5ufP4RGul4X4NfTfUGq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\nSqFqZCjDesTQJzb7QqemsFg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "L_array = np.linspace(8, 9, 5) # values of L for which the system is relaxed.\n", "\n", "vortex_energies = []\n", "flower_energies = []\n", "\n", "for L in L_array:\n", " vortex = minimise_system_energy(L, m_init_vortex)\n", " flower = minimise_system_energy(L, m_init_flower)\n", " \n", " vortex_energies.append(vortex.total_energy())\n", " flower_energies.append(flower.total_energy())\n", " \n", "# Plot the energy dependences.\n", "import matplotlib.pyplot as plt\n", "plt.plot(L_array, vortex_energies, 'o-', label='vortex')\n", "plt.plot(L_array, flower_energies, 'o-', label='flower')\n", "plt.xlabel('L (lex)')\n", "plt.ylabel('E')\n", "plt.xlim([8.0, 9.0])\n", "plt.grid()\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now know that the energy crossing occurrs between $8l_\\text{ex}$ and $9l_\\text{ex}$, so a bisection algorithm can be used to find the exact crossing." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "L= 8.0, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [2.7s]\n", "L= 8.0, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.1s]\n", "L= 9.0, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.7s]\n", "L= 9.0, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.0s]\n", "L= 8.5, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.9s]\n", "L= 8.5, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [0.8s]\n", "L= 8.25, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.8s]\n", "L= 8.25, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [0.8s]\n", "L= 8.375, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [1.8s]\n", "L= 8.375, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [0.8s]\n", "L= 8.4375, m_init_vortex 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [2.3s]\n", "L= 8.4375, m_init_flower 2017/9/25 14:44: Calling OOMMF (stdprob3/stdprob3.mif) ... [0.8s]\n", "The transition between vortex and flower states occurs at 8.4375*lex\n" ] } ], "source": [ "from scipy.optimize import bisect\n", "\n", "def energy_difference(L):\n", " vortex = minimise_system_energy(L, m_init_vortex)\n", " flower = minimise_system_energy(L, m_init_flower)\n", " \n", " return vortex.total_energy() - flower.total_energy()\n", "\n", "cross_section = bisect(energy_difference, 8, 9, xtol=0.1)\n", "\n", "print(\"The transition between vortex and flower states occurs at {}*lex\".format(cross_section))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "[1] µMAG Site Directory http://www.ctcms.nist.gov/~rdm/mumag.org.html" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }