{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial 10: FMR standard problem\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", "We choose a cuboidal thin film permalloy sample measuring $120 \\times 120 \\times 10 \\,\\text{nm}^{3}$. The choice of a cuboid is important as it ensures that the finite difference method employed by OOMMF does not introduce errors due to irregular boundaries that cannot be discretized well. We choose the thin film geometry to be thin enough so that the variation of magnetization dynamics along the out-of-film direction can be neglected. Material parameters based on permalloy are:\n", "\n", "- exchange energy constant $A = 1.3 \\times 10^{-11} \\,\\text{J/m}$,\n", "- magnetisation saturation $M_\\text{s} = 8 \\times 10^{5} \\,\\text{A/m}$,\n", "- Gilbert damping $\\alpha = 0.008$.\n", "\n", "An external magnetic bias field with magnitude $80 \\,\\text{kA/m}$ is applied along the direction $e = (1, 0.715, 0)$. We choose the external magnetic field direction slightly off the sample diagonal in order to break the system’s symmetry and thus avoid degenerate eigenmodes. First, we initialize the system with a uniform out-of-plane magnetization $m_{0} = (0, 0, 1)$. The system is allowed to relax for $5 \\,\\text{ns}$, which was found to be sufficient time to obtain a well-converged equilibrium magnetization configuration. We refer to this stage of simulation as the relaxation stage, and its final relaxed magnetization configuration is saved to serve as the initial configuration for the next dynamic stage. Because we want to use a well defined method that is supported by all simulation tools, we minimize the system’s energy by integrating the LLG equation with a large, quasistatic Gilbert damping $\\alpha = 1$ for $5 \\,\\text{ns}$. In the next step (dynamic stage), a simulation is started using the equilibrium magnetisation configuration from the relaxation stage as the initial configuration. Now, the direction of an external magnetic field is altered to $e = (1, 0.7, 0)$. This simulation stage runs for $T = 20 \\,\\text{ns}$ while the (average and spatially resolved) magnetization $M(t)$ is recorded every $\\Delta t = 5 \\,\\text{ps}$. The Gilbert damping in this dynamic simulation stage is $\\alpha = 0.008$.\n", "\n", "Details of this standard problem specification can be found in Ref. 1.\n", "\n", "## Relaxation stage\n", "\n", "Firstly, all required modules are imported." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [], "source": [ "import oommfc as oc\n", "import discretisedfield as df\n", "import micromagneticmodel as mm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we specify all simulation parameters." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "lx = ly = 120e-9 # x and y dimensions of the sample(m)\n", "lz = 10e-9 # sample thickness (m)\n", "dx = dy = dz = 5e-9 # discretisation in x, y, and z directions (m)\n", "\n", "Ms = 8e5 # saturation magnetisation (A/m)\n", "A = 1.3e-11 # exchange energy constant (J/m)\n", "H = 8e4 * np.array([0.81345856316858023, 0.58162287266553481, 0.0])\n", "alpha = 0.008 # Gilbert damping\n", "gamma0 = 2.211e5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the system object can be created and mesh, magnetisation, hamiltonian, and dynamics are specified." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "mesh = df.Mesh(p1=(0, 0, 0), p2=(lx, ly, lz), cell=(dx, dy, dz))\n", "\n", "system = mm.System(name='stdprobfmr')\n", "\n", "system.energy = mm.Exchange(A=A) + mm.Demag() + mm.Zeeman(H=H)\n", "system.dynamics = mm.Precession(gamma0=gamma0) + mm.Damping(alpha=alpha)\n", "system.m = df.Field(mesh, dim=3, value=(0, 0, 1), norm=Ms)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the system is relaxed." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020/03/09 10:55: Running OOMMF (stdprobfmr.mif) ... (1.0 s)\n" ] } ], "source": [ "md = oc.MinDriver()\n", "md.drive(system)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now load the relaxed state to the Field object and plot the $z$ slice of magnetisation." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "system.m.plane('z', n=(10, 10)).mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dynamic stage" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the dynamic stage, we use the relaxed state from the relaxation stage." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Change external magnetic field.\n", "H = 8e4 * np.array([0.81923192051904048, 0.57346234436332832, 0.0])\n", "system.energy.zeeman.H = H" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we run the multiple stage simulation using `TimeDriver`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020/03/09 10:55: Running OOMMF (stdprobfmr.mif) ... (136.8 s)\n" ] } ], "source": [ "T = 20e-9\n", "n = 4000\n", "\n", "td = oc.TimeDriver()\n", "td.drive(system, t=T, n=n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Postprocessing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the obtained vector field samples, we can compute the average of magnetisation $y$ component and plot its time evolution. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "t = system.table['t'].values\n", "my = system.table['mx'].values\n", "\n", "# Plot time evolution.\n", "plt.figure(figsize=(8, 6))\n", "plt.plot(t, my)\n", "plt.xlabel('t (ns)')\n", "plt.ylabel('my average')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the $$ time evolution, we can compute and plot its Fourier transform." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import scipy.fftpack\n", "\n", "psd = np.log10(np.abs(scipy.fftpack.fft(my))**2)\n", "f_axis = scipy.fftpack.fftfreq(4000, d=20e-9/4000)\n", "\n", "plt.plot(f_axis/1e9, psd)\n", "plt.xlim([6, 12])\n", "plt.xlabel('f (GHz)')\n", "plt.ylabel('Psa (a.u.)')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "[1] A. Baker, M. Beg, G. Ashton, M. Albert, D. Chernyshenko, W. Wang, S. Zhang, M.-A. Bisotti, M. Franchin, C.L. Hu, R. Stamps, T. Hesjedal, and H. Fangohr, *J. Magn. Magn. Mater.* **421**, 428 (2017)." ] } ], "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": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 4 }