{ "cells": [ { "cell_type": "markdown", "id": "abd7e6a2-d9b9-452d-9552-510f4536a916", "metadata": {}, "source": [ "# Nonreciprocal dispersion of a synthetic antiferromagnet\n", "This example shows how to calculate dispersion of synthetic antiferromagnet. It uses method `SWT.DoubleLayerNumeric.GetPhisSAFM()` to find the equilibribrium state of the coupled magnetization vectors and then the method `SWT.DoubleLayerNumeric.GetDispersion()` which numerically calculates eigenvalues of the system matrix, constructed from the provided input values. The individual elements of the matrix represent magnetic interactions within the system. The eigenvalues then represent angular frequencies of the spin wave modes. *(The eigenvectors can provide spin-wave amplitudes but this is not implemented in this example.)* \n", "This calculation is described in detail in the supplementary material of [Gallardo et al., *Phys. Rev. Applied* **12**, 034012 (2019)](https://doi.org/10.1103/PhysRevApplied.12.034012). It was also used in the work [Wojewoda et al., *Appl. Phys. Lett.* **125**, 132401 (2024)](https://doi.org/10.1063/5.0218478)." ] }, { "cell_type": "code", "execution_count": 2, "id": "e8061284-2087-4c9c-a1ed-071c74313c6c", "metadata": {}, "outputs": [], "source": [ "# necessary imports\n", "import SpinWaveToolkit as SWT\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import warnings" ] }, { "cell_type": "code", "execution_count": 3, "id": "a5e42367-7449-4e39-9634-d14fd75a69ed", "metadata": {}, "outputs": [], "source": [ "kxi = np.linspace(-100e6, 100e6, 200) #define numpy array with k-vectors we want to calculate\n", "lxi = 2*np.pi/(kxi*1e-6) #for convenience prepare also numpy array with wavelengths" ] }, { "cell_type": "code", "execution_count": 4, "id": "2bb883b3-6128-4f4a-8fe9-0426adb10c5a", "metadata": {}, "outputs": [], "source": [ "# Define some variables here to have them easilly accessible on one place\n", "\n", "# Material\n", "Ms = 1329e3 # Saturation magnetization in A/m\n", "Aex = 15e-12 # Exchange stiffness in J/m\n", "alpha = 40e-4 # Damping constant in -\n", "gamma = 30*2*np.pi*1e9 # Gyromagnetic ratio in rad/s\n", "\n", "# Geometry\n", "d = 10e-9 # thickness of the first layer in m \n", "s=0.6e-9 # thickness of the spacer in m\n", "d2=10e-9 # thickness of the second layer in m\n", "\n", "# RKKY coupling\n", "Jbl = -0.67e-3 # Bilinear RKKY coupling strength\n", "Jbq = -0.28e-3 # Biquadratic RKKX coupling strength\n", "\n", "# Anisotropy\n", "Ku = 1.5e3 # in plane anisotropy in the first SAF layer\n", "Ku2 = Ku # the second layer has the same anisotropy as the first\n", "phiAnis1 = 90 # in plane angle of the anisotropy direction in the first SAF layer, here in degrees \n", "phiAnis2 = -phiAnis1 # in plane angle of the anisotropy direction in the second SAF layer, here in degrees\n", "phiInit1= -45 # initial angle of magnetization in the first layer from which we start to look for the equilibrium state\n", "phiInit2= 45 # initial angle of magnetization in the second layer from which we start to look for the equilibrium state\n", "\n", "# External field\n", "Bext = 100e-3 # applied magnetic field in T\n", "phiBext = 0 # in plane angle of the applied magnetic field, here in degrees" ] }, { "cell_type": "code", "execution_count": 5, "id": "f842bcd4-47f1-4133-b34d-8a78ffd3a226", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "# Define material class\n", "CFB = SWT.Material(Ms = Ms, Aex = Aex, alpha = alpha, gamma=gamma)\n", "# Plug all necessary variables into the SWT.Dispersion characteristic class \n", "SAF = SWT.DoubleLayerNumeric(kxi=kxi, theta=np.deg2rad(90), phi=np.deg2rad(phiBext), \n", " Bext=Bext, material=CFB, \n", " Ku=Ku, Ku2=Ku2, Jbl=Jbl, Jbq=Jbq, d=d, s=s, d2=d2, \n", " phiAnis1=np.deg2rad(phiAnis1), phiAnis2=np.deg2rad(phiAnis2), \n", " phiInit1=np.deg2rad(phiInit1), phiInit2=np.deg2rad(phiInit2))" ] }, { "cell_type": "markdown", "id": "5c9f661b-6312-4f8d-bf53-c50a619a78e5", "metadata": {}, "source": [ "## Find equilibrium state of the two coupled magnetization vectors\n", "SpinWaveToolkit looks for the equilibrium state (minimizes the total energy) of the two coupled magnetizations vectors. The angle of these vectors is then used to calculate the dispersion. Sometimes the minimization procedure can give strange results and it is better to check if the magnetization angles are as expected." ] }, { "cell_type": "code", "execution_count": 6, "id": "c183440d-3de4-4465-ae51-dd7acae1ab30", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now we can have a look at the equilibrium canted state. First we get the angles of the magnetization in both layers\n", "phi1, phi2 = SAF.GetPhis()\n", "\n", "#And then we can plot them to see if the minimization angle with arrow\n", "def plot_angle_arrow(angle, color, radius=1):\n", " x = np.cos(np.deg2rad(angle))\n", " y = np.sin(np.deg2rad(angle))\n", " ax = plt.gca()\n", " ax.plot([0, x], [0, y], linewidth=0) # Plot line from origin to point\n", " ax.annotate('', xy=(x, y), xytext=(0, 0),\n", " arrowprops=dict(arrowstyle=\"-|>,head_length=0.7,head_width=0.5\", \n", " color=color)) # Plot arrow\n", " ax.text(0.5*x, 0.5*y, \"{:.1f}°\".format(angle), ha='center', va='center', \n", " bbox=dict(facecolor='white', edgecolor='black', boxstyle='round,pad=0.2')) # Angle label rounded to one decimal place\n", "\n", "# Make plot with arrows representing all important angles\n", "plt.figure(figsize=(3, 3))\n", "plt.title('$B_{ext}$ (green) \\n$K_u$ (blue) \\n$M_1$ and $M_2$ (red)')\n", "plt.gca().set_aspect('equal', adjustable='box') # make sure aspect ratio is 1:1 so angles are not distorted\n", "plt.xlim(-0.5, 1)\n", "plt.grid(True)\n", "plot_angle_arrow(phiAnis1, 'blue') # Anisotropy\n", "plot_angle_arrow(phiAnis2, 'blue')\n", "plot_angle_arrow(np.rad2deg(phi1), 'red')\n", "plot_angle_arrow(np.rad2deg(phi2), 'red')\n", "plot_angle_arrow(phiBext, 'green') # External field\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9861b9a8-fac4-4df6-a38d-a498329fa034", "metadata": {}, "source": [ "## Get dispersion relation and plot it\n", "If the equilibribrium magnetization is OK, we can now call `SAF.GetDispersion()` method to get the acoustic and optic mode of the dispersion. We can also plot the dispersion together with description summarizing parameters used for the calculation." ] }, { "cell_type": "code", "execution_count": 7, "id": "9d7d4208-c0ad-49fb-9b59-0d45f6735bf9", "metadata": {}, "outputs": [], "source": [ "f = SAF.GetDispersion()[0]/(2e9*np.pi) # (GHz) neglecting eigenvectors\n", "SAF1 = f[0] #acoustic mode\n", "SAF2 = f[1] #optic mode" ] }, { "cell_type": "code", "execution_count": 8, "id": "0d300165-9a19-440e-b4fd-ff56596f7df4", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib.ticker import FuncFormatter # this is needed to recalculate second axis into wavelengths\n", "warnings.filterwarnings('ignore') #suppress division by zero warning\n", "\n", "plt.figure()\n", "plt.grid(True)\n", "\n", "# Plot dispersions with legends\n", "plt.plot(kxi*1e-6, SAF2, label = 'optic mode');\n", "plt.plot(kxi*1e-6, SAF1, label = 'acoustic mode');\n", "plt.legend()\n", "\n", "# Add tithe and axis labels\n", "plt.title('Dispersion relation of synthetic antiferromagnet\\n')\n", "plt.xlabel('k-vector (rad/um)')\n", "plt.ylabel('Frequency (GHz)')\n", "\n", "# Add some marker lines\n", "plt.axhline(11, color='red', linestyle='--')\n", "plt.axvline(-70, color='red', linestyle='--')\n", "\n", "# Add second x-axis with wavelength in nanometers\n", "def custom_formatter(x, pos):\n", " return \"{:.0f}\".format((2*np.pi/(x))*1000)\n", "plt2 = plt.twiny()\n", "plt2.spines['top'].set_visible(True)\n", "plt2.xaxis.set_major_formatter(FuncFormatter(custom_formatter))\n", "plt.xlabel('Wavelength (nm)')\n", "\n", "# Need to reset the axis limits\n", "plt.xlim(min(kxi*1e-6), max(kxi*1e-6))\n", "\n", "# Add info text below the plot so we always know what is plotted\n", "info_text = (\n", " 'Material param: $M_s$ = %.1d kA/m, $A_{ex}$ = %.1f pJ/m, $\\\\alpha$ = %.1e, $\\\\gamma$ = %.1f GHz/T \\n'\n", " 'Thicknesses: $d$ = %.1d nm, $s$ = %.1f nm, $d_2$ = %.1d nm\\n'\n", " 'Coupling: $J_{bl}$ = %.2f mJ/m$^2$, $J_{bq}$ = %.2f mJ/m$^2$\\n'\n", " 'Anisotropy: $K_u$ = %.1d J/m$^3$, $K_{u2}$ = %.1d J/m$^3$\\n'\n", " 'Angles: $\\phi_{Bext}$ = %.1f°, $\\phi_{M1}$ = %.1f°, $\\phi_{M2}$ = %.1f°, $\\phi_{Anis1}$ = %.1f°, $\\phi_{Anis2}$ = %.1f°'\n", ") % (Ms/1e3, Aex*1e12, alpha, gamma/2/np.pi/1e9, d*1e9, s*1e9, d2*1e9, Jbl*1e3, Jbq*1e3, Ku, Ku2, phiBext, np.rad2deg(phi1), np.rad2deg(phi1), phiAnis1, phiAnis2)\n", "plt.figtext(0.1, -0.2, info_text, ha='left', fontsize=8)\n", "\n", "# show the plot\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "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": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 5 }