{ "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, 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 2018/11/01 23:29: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (4.1 s)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "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 2018/11/01 23:29: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "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 2018/11/01 23:29: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (3.5 s)\n", "L= 8.0, m_init_flower 2018/11/01 23:29: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\n", "L= 8.25, m_init_vortex 2018/11/01 23:29: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (3.0 s)\n", "L= 8.25, m_init_flower 2018/11/01 23:29: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.9 s)\n", "L= 8.5, m_init_vortex 2018/11/01 23:29: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (2.7 s)\n", "L= 8.5, m_init_flower 2018/11/01 23:29: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\n", "L= 8.75, m_init_vortex 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (2.5 s)\n", "L= 8.75, m_init_flower 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\n", "L= 9.0, m_init_vortex 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (2.5 s)\n", "L= 9.0, m_init_flower 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ORZmuIrJCRDJFZECuY1nORaZOLzTla04N+Z09rBvXxEbz7qkhv1tsyK8xpvjzZAvkONBDVVsCrYA+ItIhV5mdwO3Aly7OT1PVVs5XPxfHfUZkmSBGD2zJl6eG/H7gGPJ78KgN+TXGFF8eSyDqkOp8G+h8aa4yO5wrF570VBwlSSfnkN/74+oxyTnkd8qq3aV69Igxpvjy6FQmIuIPLAfqA2+r6og8yn0MTFPV73LsywRWAZnAS6o6OY9zBwODAaKiolpPmHDhq4cVB7uOnGT8uuNsP3SSFpX8ubVpEJVCC57vU1NTCQsL82CEJYPVQzari2xWF9m6d+9e6KlMimQuLBGJBCYBD6rqOhfHP+bsBFJdVZNFpC4wB+ipqlvP9TnFYS4sd8o6qXyycAevznR8T8Mui+H2Ag75La3zHuVm9ZDN6iKb1UW2Yj8XlqqmAPFAn/M4J9n5dZvz3FI35s7fT7jzkjrMfKQr7etU4PlpG7j2nV/ZkGyz/BpjvM+To7CinC0PRCQU6AVsLOC55UUk2LldCegMbPBUrMVdjfJlGH97W8beEMvulDT62pBfY0wx4MkWSDVgroisAZYCs1R1moiMEpF+ACLSVkSSgIHA+yKy3nluY2CZiKwG5uLoAym1CQQcQ377tazOL4924/8udgz57f1GAr/akF9jjJd47El05+iqs247qerTObaXAmc9W6+qC4HmnoqtJIssE8QrA1rSPzaaJyau5aYPFjOgdQ3+dUVjypcN8nZ4xphSxJ5EL6E61avEdOeQ38k25NcY4wWWQEqwkEB//tmnET88eAk1yocy9OtV3PHxUnYdOObt0IwxpYAlEB/QuJpjlt9n+jZhyfYDXPZ6AjN2ZJB10lojxhjPsQTiI/z9hDs612HWo93oWK8iX208wTXv/Mr65EPeDs0Y46MsgfiY6MhQPrytDfe1DCY5JY1+//2VF39OJO2EDfk1xriXJRAfJCK0rxZwesjv+/O20efNBBZstiG/xhj3sQTiw04N+f3ynvb4iXDzh4sZNsFm+TXGuIclkFKgU71K/Dy0Cw90r8eUVTbk1xjjHpZASomQQH+G93YO+a1QhqFfr+L2j2zIrzGm8CyBlDKNq0Uw8b5OPNO3CUt3OIb8fjB/G5lZtiSLMeb8eGwqE1N8nRrye1nTqjw1eR3//jGRKauSeen/mrN5TyqjZ2wiOSWN6pGhDO8dQ//YaG+HbIwphiyBlGKnhvz+uPZPnp26gavGLsDfT8h0PoC4OyWNkRPXAlgSMcacxW5hlXIiwlUtqjP70W6EBvmfTh6npGVkMXqG7yzSZYxxH0sgBoByZQLzfNgwOSWtiKMxxpQElkDMadUjQ13ujwgNsE52Y8xZLIGY04b3jiE00P+MfX4Ch9IyueqtBSzdccBLkRljiiNPLmkbIiJLRGS1iKwXkedclOkqIitEJFNEBuQ6dpuIbHa+bvNUnCZb/9hoXry2OdGRoQiOTvYxA1vy3s2tOZyWwcD3FjFswmr2pR73dqjGmGLAk6OwjgM9VDVVRAKBBSLys6r+lqPMTuB24LGcJ4pIBeAZoA2gwHIRmaqqBz0Yr8GRRFyNuOrasBJvzdnCB/O3MWvDXwzv04gb29XC30+8EKUxpjjwWAtEHVKdbwOdL81VZodz6dvcN9h741hD/YAzacwC+ngqVpO/MkEBjOjTiJ+HdqFZdDmemryOa975ldW7UrwdmjHGSzz6HIiI+APLgfrA26q6uICnRgO7crxPcu5z9RmDgcEAUVFRxMfHFzpeX5KamuqxurinvtIiLJivNx6m/9u/0q1mAAMaBBEWVPxaI56sh5LG6iKb1YV7eDSBqGoW0EpEIoFJItJMVdcV4FRXv4lczvynquOAcQAxMTEaFxdX2HB9Snx8PJ6si+7AA+kZvD5rM58s2sGaA5k83qcRA1rXwK8Y3dbydD2UJFYX2awu3KNIRmGpagoQT8FvQyUBNXO8rwEkuzksc4HCQwJ5um8Tpj14CXUrleWf369h4PuLbBVEY0oJT47CinK2PBCRUKAXsLGAp88ALhOR8iJSHrjMuc8UQ42rRTDh3o6MHtCCHfuO0vetBTw7dT2H0zO8HZoxxoM82QKpBswVkTXAUhyd4tNEZJSI9AMQkbYikgQMBN4XkfUAqnoAeN553lJglHOfKab8/ISBbWoyZ1gcN7avxSeLdtBzzDwmr7R1R4zxVR7rA3GOrop1sf/pHNtLcdyecnX+eGC8p+IznlGuTCD/7t+cga1r8tSUdTz8zSq+XrqT569uRoMq4d4OzxjjRvYkuvGIljUjmXR/Z/7dvxmJfx7h8jfn8+LPiRw9nunt0IwxbmIJxHiMv59wc4eLmDOsG9fERvP+vG30em0eP6/9025rGeMDLIEYj6sYFszogS35bkhHyoUGct8XK7jto6Vs33fU26EZYy6AJRBTZNrUrsC0By/h6auasOKPg/R+PYHXZv1OeobraeSNMcWbJRBTpAL8/bjzkjrMGdaNy5tXZezszVz6+jzmbNzj7dCMMefJEojxisoRIbw5KJYv72lPcIA/d368jHs+XUbSwWPeDs0YU0CWQIxXdapXiZ8e6sKIPo1YsHkfvV6bx9tzt3A8025rGVPcWQIxXhcU4Md9cfX4ZVg34hpWZvSMTVz+xnwWbN7n7dCMMedgCcQUG9GRobx3S2s+vqMtWarc/OFiHvhyBX8dSvd2aMYYFyyBmGInLqYyMx7uyiO9GjJrwx56jonng/nbyLB12Y0pViyBmGIpJNCfob0a8Msj3WhftyL//jGRq8YuYMl2mxLNmOLCEogp1mpVLMOHt7Vh3C2tST2eyXXvL+LRCav4+4ity26Mt1kCMcWeiHBZ06rMerQr98fV44fVyfQYE8+ni3aQddKmRDHGWyyBmBKjTFAA/+zTiJ+HdqVFjXI8PWU9V7+9gJU7D3o7NGNKJUsgpsSpXzmMz+9qz1s3xPL3keNc++5CRk5cy8GjJ7wdmjGliidXJAwRkSUislpE1ovIcy7KBIvINyKyRUQWi0ht5/7aIpImIqucr/c8FacpmUSEvi2rM3tYHHd1rsOEZbvoMSaeb5bu5KTd1jKmSHiyBXIc6KGqLYFWQB8R6ZCrzF3AQVWtD7wOvJzj2FZVbeV8DSnIB4Yf2QqvN4M1E9wRvykBwoIDePKqJvz40CXUrxzGiO/XMuC9hbYuuzFFwGMJRB1SnW8Dna/cfxpeDXzi3P4O6CkicgGfCod2wQ8PWRIpZRpVdazLPmZgS/7Yf+z0uuzHMqw1YoyniCcX9hERf2A5UB94W1VH5Dq+DuijqknO91uB9kAYsB74HTgMPKmq8/P4jMHAYIDW1fxaLxscBkCWXzB/Ve1BZkDZfF/qF+iJb9+rUlNTCQsL83YYXnE0Q/l+8wnm7swkLFC5oXEIHav5c0F/m/iA0vwzkZvVRbbu3bsvV9U2hTnXownk9IeIRAKTgAdVdV2O/euB3rkSSDsgFQhT1f0i0hqYDDRV1cPn+pw21f31VAIBoExFSD8EJ/NZRjUgBELKnfkKjjh7X16vgBAoZr+c4uPjiYuL83YYXrU26RBDP1vItkMnaV+nAs/3b0bDUrwuu/1MZLO6yCYihU4gAe4OxhVVTRGReKAPsC7HoSSgJpAkIgFAOeCAOrLacee5y52JpSGwrMAfWq4mPLIOVCHjGKQfdiSTM14pjq/Hcx1LOwgHdzjPSYGsfEb3+Aflk3QiICQy7yQVVLbYJSBf0LxGOZ7sEMJfZerx8vSNXPHmfO66pA4P9WxA2eAi+dE3xqd57H+RiEQBGc7kEQr04sxOcoCpwG3AImAAMEdV1XnuAVXNEpG6QANgW4E/PDAUej59KhDHL+igshBRrXDfTEb62cnneO5klPN1GA4nZ7/PTDv39cXfRcI5tR3pOunkfAWFgZ+burPWTIDZo+BQEpSr4ajHFte559pe4CfCje1r0adZVV7+eSPvJ2xj6upknrqqCZc3q1rqb2sZcyE8+WdYNeATZz+IHzBBVaeJyChgmapOBT4EPhORLcABYJDz3K7AKBHJBLKAIapagEmQxNHycPcvvcAQxyu8SuHOzzzuSCrHD2e3elwlnZzv923Jbh2dSD339cUPgsPPSDpNU09AyoQCtIycx/38Hcnjh4cgw5nwTg1IgBKdRAAqlA3i5QEtuK5tDZ6cvJ77v1hBlwaVGHV1M+pUKuvt8IwpkTyWQFR1DRDrYv/TObbTgYEuynwPfH++n3kkvJ7jtlVxExAMYVGOV2FkZcDxIy6Sj6vbco6kE5q2B7YnZyeh/ARHwImjoLkWcspIgx+HQeqeHIkoIrt1dGpfQFDhvrci1vqiCvzwj8589tsfvDbzd3q/nsC93epyf1x9QoP8vR2eMSWK3QguCfwDoUwFx6uAluXsJDyZlaOfJ++kw2/vuL7Y8cMw88lzf2DOgQhnJZo8WkE5ywWFFVk/UIC/H3d0rsOVzavxn58SeWvOFiat3M2zfZvSq0khW5nGlEKWQEoDP38ILe94nUviD47bVrmVqwn3Lzq75XM6KaW43peyM3tfZj6LQom/I5Hkl2hc7nO2hPzP78e5ckQIbwyK5fq2tXh6yjru/nQZvRpX5pm+TalZocx5XcuY0sgSiMnW8+kz+0Age0BCcLjjVa5G4a6dke5MLqcSjYtbcWeMhjsMB7Zn7yvIbbjAsmclmsaH0iF16tl9PqcHJ0TQsXI5fryvNR8t/os352yh12vzeLBHfe7pWpfggAu8reVjgxKMyckSiMl26hebJ37hnRqIEFa5cOefzHL2A7lINDlvw+VsDaXuJfzIHtiwPt/ngYKAe/0CubtsBPszQ/gzPph1v4ZxUfVqVKpUOY9bcRFn7guOOHM0nA8PSjAGLIGY3FpcVzx/ufn5Q2ik43UelpzqC1J1/CI/IwHlGBXn3OeffpjK6Yfw3/83yXv2cOCPdfj/eZxycgy/jGP5fJpkj4YLjoD9WyAr18JXGWnw8z/BL+DM22+nklExfCjVmLxYAjGlgwgElXG8yP95oIpA2YwsxiVs4+25W/D3Ex7pUZvbW1ciMOOwi5aPi9bQ3vWuL552EL67w/Uxv8CzWzYhERCco9Vzxv7cZSIcgy6MKQKWQIzJQ0igPw/1bED/VtE898N6Xpi+lW9X7uH5q5vRvm7d/C/wejPXgxLCq8Etk1z3/ZzRT+T8um9v9nZ+zwQBBJY5e+BBcAQNDxyFjDln3obL2fo5tR0U7r4HU41PswRiTD5qVSzDh7e3ZdaGPTw7dT3Xj/uNa2KjGXlFIyqHh+R9Yl6DEi4dBZUbFy6Y3EOyXW7nahUdOwAHd1Dp8D7YG3/2bbWziOvEclar6BwtpMBQz9yKs0EJxYolEGMK6NImVbikfiX+O3cz4xK28cuGPTzWO4abO1yEv5+LX5aeGJRQ0CHZLiw81R90amaE06PhDufR+smxfXg37E3MTkx6Mp84A/O43RZ5jsR0ajuPW3E2KKHYsQRizHkIDfJneO9GXHtxDZ6Zsp5npq5nwrJdPN+/GRfXcvFLvTgOSrjQmRFUHbMWFKT1k3M7dWt2YjpxJP/POX0rzplY/lp79vNEGWnw8wjHg6iuEpafzS7gSedMICLyT1V9xbk9UFW/zXHsP6r6hKcDNKY4qhcVxmd3tePHtX/y/LQNXPvOQga1rcmIPo0oX7ZkTOtSaCIQHOZ4RVQv3DVO34o7V+sn5cz9eT2MmnYAvr7B9bGgsOwklOPrWf1BLso49odbEjqH/Fogg4BXnNsjgW9zHOsDWAIxpZaIcFWL6sTFVObNX35n/K87mL7+L0b0acT1bWri5+q2lnEozK24cw1KGPRldrI562uO1tCx/XBgO5WOFLQ/CMeggrOSS4TrviFXZXI/H+RD8ksgkse2q/fGlEphwQH868omDGhdk6cmr2PkxLV8s3QX/+7fjC17Uxk9YxPJKWlUjwxleO8Y+sdGezvkkulcgxKiLz6vS53VH3T8HC2h3Ino2D44sC37nPzWC4LsRHKuRJSzjyj3MU+MjHMOSGhdza91YS+RXwLRPLZdvTemVIupGs4393Zg0srd/OenRK56awH+fkLWScd/ld0paYycuBbAkki8tJmbAAAcJ0lEQVRheGJQwoX2B8GZ0/TkbO3k/Jqzb+j4YUjd63jQ9FSZfJOQ8yHVswYluPqae5YE57Gc6wblHpBQSPklkJYictgRPaHObed3wznGLxpTOokI115cg56Nq9DpxdkcPXHm9PhpGVmMnrHJEkhhFcdBCRc6TQ/kSEKHzp2Icg5WSP0L9v2efexkRj4fkmN49pG/ClA+f+dMIKpa6N4jEQkBEoBg5+d8p6rP5CoTDHwKtAb2A9er6g7nsZHAXTgWlHpIVWcUNhZjilq50ECO5UoepySnXNhffcYHXWgSUnUMMjjrllseiWj1l24J25PDeI8DPVQ1VUQCgQUi8rOq/pajzF3AQVWtLyKDcCx5e72INMHRgd8UqA78IiINVXOvdmRM8VU9MpTdLpJFSKA/fx5Ko1q5UC9EZXySiKM/KDC0YCun7pjvekDCefLY0AB1ODXvQqDzlbvf5GrgE+f2d0BPcSxSfTXwtaoeV9XtwBagnadiNcYThveOITTwzEZ8gJ9wIjOL7q/G8+Yvm0nLo5VijEf1fNqRbC6QR8eWiYi/iKwC9gKzVHVxriLRwC4AVc0EDuGYx+70fqck5z5jSoz+sdG8eG1zoiNDESA6MpRXB7Ykfnh3ejSqzOu//E7PMfFMXZ2Mqo1JMUWoxXXQd6xjsbgLIEXxgysikcAk4EFVXZdj/3qgt6omOd9vxdHSGAUsUtXPnfs/BH5yrpWe+9qDgcEAUVFRrSdMmODpb6dESE1NJSwszNtheF1xroeNB7L4MvEEO4+cpEGkHzc1DqJ2Oc89tFac66KoWV1k6969+3JVbVOYc4tkKhNVTRGReBwPH67LcSgJqAkkiUgAUA44kGP/KTWA5DyuPQ4YBxATE6On1wEv5eJzroleihXneogD7jmpfLtsF6/O3MRzv6Uz4OIaDO8Tc+5JGgupONdFUbO6cA+P3cISkShnywMRCQV6ARtzFZsK3ObcHgDMUUeTaCowSESCRaQO0ABY4qlYjfEWfz9hULtazHksjnu61GXyqt10Hx3Pu/FbOZ5p/SOmePNkH0g1YK6IrAGW4ugDmSYio0Skn7PMh0BFEdkCPAo8DqCq64EJwAZgOvCAjcAyviwiJJAnrmjMzEe60bFeJV6evpFLX0tg+rq/rH/EFFseu4WlqmuAWBf7n86xnQ4MzOP8F4AXPBWfMcVRnUpl+eC2Nszf/DfPT9vAkM+X07FuRZ7u24TG1SK8HZ4xZ/DNGb6MKeG6NIjip4e6MOrqpiT+dZgrx87niUlr2Z9agMn/jCkilkCMKaYC/P24tWNt4h+L49aOtflm6S7iXo3ng/nbOJGZz4JOxhQBSyDGFHORZYJ4tl9Tpg/tQmyt8vz7x0T6vJHA3I17vR2aKeUsgRhTQjSoEs4nd7Rl/O2OIft3fLyU28YvYcveAqzuZ4wHWAIxpgQREXo0qsL0h7vy5JWNWbHzIL3fmM+zU9dz6NiFz65qzPmwBGJMCRQU4MfdXeoS/1gc17etyaeLdtDt1bl8umgHmVnWP2KKhiUQY0qwimHB/Oea5vz4UBcaV43g6SnruWLsfBZs3uft0EwpYAnEGB/QuFoEX97Tnvduvpi0jCxu/nAxd3+yjB37jno7NOPDLIEY4yNEhD7NqjHrkW78s08Mi7bu49LX5/HiT4kcSbf+EeN+RTKZojGm6IQE+nN/XH0GXFyD0TM2MW7+Nr5fkUTfi6DLScXfT7wdovER1gIxxkdVjghh9MCWTHmgM7UrluWj9Sfo998FLN6239uhGR9hCcQYH9eiRiTfDunIkJbBHDx6guvH/cYDX6xg14Fj3g7NlHCWQIwpBUSEDtUCmD0sjkd6NWT2xj30fG0eY2Zu4ujxTG+HZ0ooSyDGlCKhQf4M7dWAOcPiuLxZVd6as4UeY+KZuCKJkydt2nhzfiyBGFMKVY8M5c1BsXx/X0eqRITw6ITVXPPuQlbsPOjt0EwJYgnEmFKs9UUVmHx/Z14d2JI/U9K49p2FPPz1Sv48lObt0EwJ4MklbWuKyFwRSRSR9SIy1EWZ8iIySUTWiMgSEWmW49gOEVkrIqtEZJmn4jSmtPPzEwa0rsHcx+J4oHs9flr3Fz1encfY2ZtJz7CFQE3ePNkCyQSGqWpjoAPwgIg0yVXmCWCVqrYAbgXezHW8u6q2UtU2HozTGAOUDQ5geO9GzH60G90bRfHarN/pOWYeP6xOtmV1jUseSyCq+qeqrnBuHwESgehcxZoAs51lNgK1RaSKp2IyxuSvZoUyvHNTa74e3IGI0EAe/Gol172/iHW7D3k7NFPMSFH8ZSEitYEEoJmqHs6x/z9AiKo+KiLtgIVAe1VdLiLbgYOAAu+r6rg8rj0YGAwQFRXVesKECR79XkqK1NRUwsLCvB2G11k9ZCtMXZxUJSEpk+83nyD1BFwSHcD/NQwkMrhkd5/az0W27t27Ly/sXR6PJxARCQPmAS+o6sRcxyJw3LaKBdYCjYC7VXW1iFRX1WQRqQzMAh5U1YRzfVZMTIxu2rTJI99HSRMfH09cXJy3w/A6q4dsF1IXh9MzeGv2Zj5euIPgAH8e6F6fOy+pTXCAv3uDLCL2c5FNRAqdQDz6Z4SIBALfA1/kTh4AqnpYVe9Q1VY4+kCigO3OY8nOr3uBSUA7T8ZqjMlbREgg/7qyCTMf6UaHuhV4efpGLn0tgRnr/7L+kVLMk6OwBPgQSFTV1/IoEykiQc63dwMJqnpYRMqKSLizTFngMmCdp2I1xhRMnUpl+eC2tnx6ZzuCA/y497Pl3PTBYjb+dTj/k43P8WQLpDNwC9DDORR3lYhcISJDRGSIs0xjYL2IbAQuB04N9a0CLBCR1cAS4EdVne7BWI0x56Frwyh+HtqF5/o1ZX3yYa54cz5PTl7LgaMnvB2aKUIem85dVRcA55w3WlUXAQ1c7N8GtPRQaMYYNwjw9+O2TrW5ulV13vhlM5/99gdTVyUztFdDbu14EYH+Jbuj3eTP/oWNMRckskwQz/ZryvShXWhZM5Lnp22g9xsJzN2019uhGQ+zBGKMcYsGVcL59M52fHhbG1Thjo+WcvtHS9iyN9XboRkPsQRijHEbEaFn4yrMeLgrT17ZmOU7DtLnjQSe+2E9h47Zsrq+xhKIMcbtggL8uLtLXeYOj2Ngm5p8vHAHca/O5bNFO8jMOunt8IybWAIxxnhMpbBgXry2OT8+2IWYquE8NWU9V45dwK9b9nk7NOMGlkCMMR7XpHoEX93TgXdvupijJzK56YPF3PPpMnbsO+rt0MwFsARijCkSIsLlzavxy6PdGN47hl+37OOy1xN48edEjqRb/0hJZAnEGFOkQgIdc2nFPxZHv1bVeX/eNrq/Oo9vlu4ky5bVLVEsgRhjvKJyRAivDmzJlAc6c1HFMoz4fi1Xv72AJdsPeDs0U0CWQIwxXtWyZiTfDenIm4NasT/1BNe9v4gHvlxB0sFj3g7N5MMSiDHG60SEq1tFM2dYHEN7NmB24h56jpnHmJmbOHYi09vhmTx4bC4sY4w5X6FB/jxyaUOub1uTl37eyFtztjBh2S4ev7wRV7eMZurqZEbP2ERyShrVI0MZ3juG/rG5Fzo1RcUSiDGm2KkeGcrYG2K5teNFPPfDBh75ZjWvz/qdPYePczzT8SDi7pQ0Rk5cC2BJxEvsFpYxpthqU7sCUx7ozOgBLUg6mHY6eZySlpHF6Bm2Cqm3WAIxxhRrfn7CwDY1yWvhw+SUtKINyJzmyRUJa4rIXBFJFJH1IjLURZnyIjJJRNaIyBIRaZbjWB8R2SQiW0TkcU/FaYwpGapHhrrcHxEawPHMrCKOxoBnWyCZwDBVbQx0AB4QkSa5yjwBrFLVFjjWRH8TQET8gbdxrFLYBLjBxbnGmFJkeO8YQgP9z9jnJ3AoLZOeY+YxZdVuTtqDiEXKYwlEVf9U1RXO7SNAIpC7p6sJMNtZZiNQW0SqAO2ALaq6TVVPAF8DV3sqVmNM8dc/NpoXr21OdGQoAkRHhvLada349M52hIcEMvTrVfR72yZqLEpFMgpLRGoDscDiXIdWA9fiWP+8HXARUANHotmVo1wS0N7jgRpjirX+sdEuR1xdUr8SU1bv5tUZv3PTB4vp1jCKxy9vRONqEV6IsvQQzatnyl0fIBIGzANeUNWJuY5F4LhtFQusBRoBdwMNgd6qerez3C1AO1V90MX1BwODAaKiolpPmDDBg99NyZGamkpYWJi3w/A6q4dspaEuTmQps3dmMm3bCY5lQKfqAVzbIJCKoWfebCkNdVFQ3bt3X66qbQpzrkcTiIgEAtOAGar6Wj5lBdgOtACaAs+qam/nsZEAqvriua4RExOjmzbZkD6A+Ph44uLivB2G11k9ZCtNdXHoWAbvxG/ho4U7ALijc23u71afcmUCgdJVF/kRkUInEE+OwhLgQyAxr+QhIpEiEuR8ezeQoKqHgaVAAxGp4zw+CJjqqViNMb6lXJlARl7RmLmPxXFVi2qMS9hG19Fz+V/CNtIzbMSWu3iyD6QzcAuwVkRWOfc9AdQCUNX3gMbApyKSBWwA7nIeyxSRfwAzAH9gvKqu92CsxhgfdKqj/e5L6vLy9I288FMiHy/cwZW1TtL1pOLnJ94OsUTzWAJR1QXAOf91VHUR0CCPYz8BP3kgNGNMKdOkegSf3NmOX7fs48WfExm35jAL/l7AyCsa0aVBlLfDK7HsSXRjTKnRuX4lpj5wCfe2COZwega3fLiEWz5czLrdh7wdWolkCcQYU6r4+Qkdqwcwe1g3nryyMWt3H+KqtxbwyDerbA2S82QJxBhTKgUH+HN3l7rMG96d++Lq8dPaP+nx6jxe+HEDKcdOeDu8EsESiDGmVCsXGsiIPo2Y+1gcV7eqzgcLttP1lbm8P2+rjdjKhyUQY4zBMVnj6IEt+XloF1pfVJ4Xf95Ij1fj+X55Elk2x5ZLlkCMMSaHRlUj+OiOdnx5T3sqhQcz7NvVXDl2PvGb9uLpmTtKGksgxhjjQqd6lZh8f2feuiGWoycyuf2jpdxsI7bOYAnEGGPy4Ocn9G1ZndmPxvFM3yZsSD7MVW8tYOjXK9l1wEZsWQIxxph8BAX4cUfnOsz7Z3ce6F6PGev/oueYeTw/bQMHj5beEVuWQIwxpoAiQgIZ3rsR8Y9155rYaD76dTtdR8/lnfgtpXLEliUQY4w5T1XLhfDygBZMf7gr7WpX4JXpm+j+ajwTlu0qVSO2LIEYY0whNawSzoe3t+XrwR2oHBHCP79bwxVvzmfuxtIxYssSiDHGXKAOdSsy+f5OvH3jxRzPzOKOj5dy4/8WsyYpxduheZQlEGOMcQMR4coW1Zj5SDee69eU3/ccod9/f+XBr1ayc79vjtiyBGKMMW4UFODHbZ1qEz88jgd71OeXDXvo+Vo8z05dzwEfG7FlCcQYYzwgPCSQYZfFMG94HANa1+TTRTvo9spc3p67hbQTvjFiy5NL2tYUkbkikigi60VkqIsy5UTkBxFZ7SxzR45jWSKyyvmy5WyNMSVS5YgQXry2OTMf6UqHehUZPWMTca/O5ZulO8nMOunt8C6IJ1sgmcAwVW0MdAAeEJEmuco8AGxQ1ZZAHDAmxxrpaarayvnq58E4jTHG4+pXDud/t7bh2yEdqR4Zyojv13L5m/OZnbinxI7Y8lgCUdU/VXWFc/sIkAhE5y4GhIuIAGHAARyJxxhjfFLb2hWYeF8n3r3pYjJPKnd9sozrx/3Gyp0HvR3aeZOiyHwiUhtIAJqp6uEc+8OBqUAjIBy4XlV/dB7LBFbhSCgvqerkPK49GBgMEBUV1XrChAme+0ZKkNTUVMLCwrwdhtdZPWSzushWXOoi86SSkJTJ5C0nOHwC2lb1Z0CDIKqULbru6e7duy9X1TaFOdfjCUREwoB5wAuqOjHXsQFAZ+BRoB4wC2ipqodFpLqqJotIXWAO0FNVt57rs2JiYnTTpk0e+T5Kmvj4eOLi4rwdhtdZPWSzushW3Ooi9Xgm/0vYxv/mb+NE5klual+LB3s2oFJYsMc/W0QKnUA8muZEJBD4Hvgid/JwugOYqA5bgO04WiOoarLz6zYgHoj1ZKzGGOMtYcEBPHJpQ+KHx3F925p8vngn3V6Zy1uzN3PsRPG9q+/JUVgCfAgkqupreRTbCfR0lq8CxADbRKS8iAQ791fC0UrZ4KlYjTGmOKgcHsIL1zhGbF3SoBJjZv1O3Oh4vlxcPEdsebIF0hm4BeiRYzjuFSIyRESGOMs8D3QSkbXAbGCEqu4DGgPLRGQ1MBdHH4glEGNMqVAvKoz3b2nDd0M6UrNCGZ6YtJbebyQwc/1fxWrEVoCnLqyqCwDJp0wycJmL/QuB5h4KzRhjSoQ2tSvw3ZCOzNywh5enb2TwZ8tpW7s8I69ozMW1yns7PHsS3RhjijMRoXfTqsx8uCsvXNOMHfuPce07C7nv8+Vs+zvVq7F5rAVijDHGfQL8/bip/UX0bxXNB/O3My5hKzM37OHGdrV4qGcDosI9P2IrN2uBGGNMCVI2OIChvRoQP7w7N7WvxVdLdhI3ei5v/PI7R48X7YgtSyDGGFMCRYUHM+rqZsx6tBvdYqJ445fNdBsdz+e//UFGEY3YsgRijDElWJ1KZXnnptZMvL8TdSuV5cnJ6+j9RgLT13l+xJYlEGOM8QEX1yrPN/d24H+3tsFPhCGfL2fAe4tY/scBj32mJRBjjPERIsKlTaowfWgXXry2ObsOHOP/3l3E4E+XsWWv+0dsWQIxxhgfE+Dvxw3tahE/PI7HLmvIwq376f1GAk9MWsveI+nu+xy3XckYY0yxUiYogH/0aMAN7Wrx1pwtfP7bH0xeuZu7u9SlerkQ3pqzhaCq9VsX9vqWQIwxxsdVDAvm2X5Nub1TbUbP3MTY2Zvdcl27hWWMMaVE7UplefvGi4ly0zTxlkCMMaaU2Zd63C3XsQRijDGlTPXIULdcxxKIMcaUMsN7xxAa6H/B17FOdGOMKWX6x0YDMHrGJv68gOt4ckXCmiIyV0QSRWS9iAx1UaaciPwgIqudZe7Icew2EdnsfN3mqTiNMaY06h8bza+P9+DEX1uWF/YanmyBZALDVHWFiIQDy0VkVq6VBR8ANqhqXxGJAjaJyBdAGPAM0AZQ57lTVfWgB+M1xhhzHjzWAlHVP1V1hXP7CJAIROcuBoQ7108PAw7gSDy9gVmqesCZNGYBfTwVqzHGmPNXJH0gIlIbiAUW5zr0X2AqkAyEA9er6kkRiQZ25SiXxNnJ59S1BwODAaKiooiPj3dn6CVWamqq1QVWDzlZXWSzunAPjycQEQkDvgceVtXDuQ73BlYBPYB6wCwRmY/rtdRdzkusquOAcQAxMTEaFxfnpshLtvj4eKwurB5ysrrIZnXhHh4dxisigTiSxxeqOtFFkTuAieqwBdgONMLR4qiZo1wNHK0UY4wxxYR4asERZ7/GJ8ABVX04jzLvAntU9VkRqQKsAFoCJ4HlwMXOoiuA1qp6zontReQIsMlN30JJVwnY5+0gigGrh2xWF9msLrLFqGp4YU705C2szsAtwFoRWeXc9wRQC0BV3wOeBz4WkbU4bluNUNV9ACLyPLDUed6o/JKH0yZVbePG76HEEpFlVhdWDzlZXWSzusgmIssKe67HEoiqLsB1X0bOMsnAZXkcGw+M90Boxhhj3MCmMjHGGFMovpZAxnk7gGLE6sLB6iGb1UU2q4tsha4Lj3WiG2OM8W2+1gIxxhhTRCyBGGOMKZQSl0BE5BHnzL3rROQrEQnJdTxYRL4RkS0istg5jYpPKkBdPCoiG0RkjYjMFpGLvBWrp+VXFznKDRARFRGfHcJZkLoQkeucPxvrReRLb8RZFArwf6SWc9bwlc7/J1d4K1ZPE5GhznpYLyJnPZsnDmOdvzvXiMjFrq5zBlUtMS8c82FtB0Kd7ycAt+cqcz/wnnN7EPCNt+P2Yl10B8o4t+8rzXXh3B8OJAC/AW28HbcXfy4aACuB8s73lb0dtxfrYhxwn3O7CbDD23F7qC6aAeuAMjge3/gFaJCrzBXAzzgev+gALM7vuiWuBYLjmw8VkQAclZF7ipOrcTwBD/Ad0NP5VLwvOmddqOpcVT3mfPsbjilhfFV+PxfgeHD1FSC9KAPzgvzq4h7gbXUuj6Cqe4s4vqKUX10oEOHcLufiuK9oDPymqsdUNROYB1yTq8zVwKfq8BsQKSLVznXREpVAVHU38CqwE/gTOKSqM3MVOz2Tr7OiDgEVizLOolDAusjpLhx/XficgtSFiMQCNVV1mhdCLDIF/LloCDQUkV9F5DcR8cmlEgpYF88CN4tIEvAT8GCRBll01gFdRaSiiJTB0dqomatMgWdBP6VEJRARKY8jS9YBqgNlReTm3MVcnOpzY5ULWBenyt6MY3Gu0UUXYdHJry5ExA94HRjmnQiLTgF/LgJw3MaKA24APhCRyKKMsygUsC5uAD5W1Ro4fql+5vx58Smqmgi8jGNtpenAahxrL+V03r87S1pF9QK2q+rfqpoBTAQ65SpzeiZfZ7O1HI6FqnxNQeoCEekF/Avop6rHizjGopJfXYTjuAccLyI7cNzfneqjHekF/T8yRVUzVHU7jglIGxRxnEWhIHVxF46+EVR1ERCCY6JFn6OqH6rqxaraFcfvxM25ipz3LOglLYHsBDqISBlnv0ZPHCsd5jQVOLWG+gBgjjp7iHxMvnXhvG3zPo7k4cv3uc9ZF6p6SFUrqWptVa2Noz+on6oWehK5Yqwg/0cm4xhggYhUwnFLa1uRRlk0ClIXO537EZHGOBLI30UaZRERkcrOr7WAa4GvchWZCtzqHI3VAcctvz/Pdc0SlUBUdTGOjvEVwFoc8Y8TkVEi0s9Z7EOgooh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" ] }, "metadata": { "needs_background": "light" }, "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 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (3.3 s)\n", "L= 8.0, m_init_flower 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\n", "L= 9.0, m_init_vortex 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (2.5 s)\n", "L= 9.0, m_init_flower 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\n", "L= 8.5, m_init_vortex 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (2.7 s)\n", "L= 8.5, m_init_flower 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\n", "L= 8.25, m_init_vortex 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (3.1 s)\n", "L= 8.25, m_init_flower 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.7 s)\n", "L= 8.375, m_init_vortex 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (2.8 s)\n", "L= 8.375, m_init_flower 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\n", "L= 8.4375, m_init_vortex 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (2.7 s)\n", "L= 8.4375, m_init_flower 2018/11/01 23:30: Running OOMMF (stdprob3/drive-0/stdprob3.mif) ... (1.8 s)\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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }