{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise 01: Domain wall pair conversion\n", "\n", "We want to simulate a domain wall conversion in a two-dimensional thin film sample with:\n", "\n", "- exchange energy constant $A = 15 \\,\\text{pJ}\\,\\text{m}^{-1}$,\n", "- Dzyaloshinskii-Moriya energy constant $D = 3 \\,\\text{mJ}\\,\\text{m}^{-2}$,\n", "- uniaxial anisotropy constant $K = 0.5 \\,\\text{MJ}\\,\\text{m}^{-3}$ with $\\hat{\\mathbf{u}} = (0, 0, 1)$ in the out of plane direction,\n", "- gyrotropic ratio $\\gamma = 2.211 \\times 10^{5} \\,\\text{m}\\,\\text{A}^{-1}\\,\\text{s}^{-1}$, and\n", "- Gilbert damping $\\alpha=0.3$.\n", "\n", "Please carry out the following steps:\n", "\n", "1. Create the following geometry with discretisation cell size $(2 \\,\\text{nm}, 2 \\,\\text{nm}, 2 \\,\\text{nm})$.\n", " \n", " \n", "\n", "2. Initialise the magnetisation so that when relaxes, a domain pair is present in the narrower part of the geometry.\n", "\n", "3. Relax the system. Is a domain wall pair contained in the constrained part?\n", "\n", "4. Apply the spin polarised current in the positive $x$ direction with velocity $\\mathbf{u} = (400, 0, 0) \\,\\text{m}\\,\\text{s}^{-1}$, with $\\beta=0.5$.\n", "\n", "5. Evolve the system over $0.2 \\,\\text{ns}$. What did you get? [1]\n", "\n", "#### References\n", "\n", "[1] Zhou, Y., & Ezawa, M. (2014). A reversible conversion between a skyrmion and a domain-wall pair in a junction geometry. *Nature Communications* **5**, 8. https://doi.org/10.1038/ncomms5652\n", "\n", "\n", "## Solution" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "4a2a37f898304e71a78e0b9eb773292d", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# NBVAL_IGNORE_OUTPUT\n", "import oommfc as oc\n", "import discretisedfield as df\n", "import micromagneticmodel as mm\n", "\n", "Ms = 5.8e5 # saturation magnetisation (A/m)\n", "A = 15e-12 # exchange energy constant (J/)\n", "D = 3e-3 # Dzyaloshinkii-Moriya energy constant (J/m**2)\n", "K = 0.5e6 # uniaxial anisotropy constant (J/m**3)\n", "u = (0, 0, 1) # easy axis\n", "gamma0 = 2.211e5 # gyromagnetic ratio (m/As)\n", "alpha = 0.3 # Gilbert damping\n", "\n", "system = mm.System(name='dw_pair_conversion')\n", "system.energy = mm.Exchange(A=A) + mm.DMI(D=D, crystalclass=\"Cnv_z\") + mm.UniaxialAnisotropy(K=K, u=u)\n", "system.dynamics = mm.Precession(gamma0=2.211e5) + mm.Damping(alpha=alpha)\n", "\n", "p1 = (0, 0, 0)\n", "p2 = (150e-9, 50e-9, 2e-9)\n", "cell = (2e-9, 2e-9, 2e-9)\n", "\n", "region = df.Region(p1=p1, p2=p2)\n", "mesh = df.Mesh(region=region, cell=cell)\n", "\n", "def Ms_fun(pos):\n", " x, y, z = pos\n", " if x < 50e-9 and (y < 15e-9 or y > 35e-9):\n", " return 0\n", " else:\n", " return Ms\n", " \n", "def m_init(pos):\n", " x, y, z = pos\n", " if 30e-9 < x < 40e-9:\n", " return (0.1, 0.1, -1)\n", " else:\n", " return (0.1, 0.1, 1)\n", " \n", "system.m = df.Field(mesh, dim=3, value=m_init, norm=Ms_fun)\n", "\n", "system.m.z.plane('z').k3d.scalar(filter_field=system.m.norm)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running OOMMF (ExeOOMMFRunner) [2021/09/22 13:57]... <1> mmarchive killed\n", " <2> mmarchive killed\n", "(1.5 s)\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "af8badc16d1e478682a80fa34310ee49", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# NBVAL_IGNORE_OUTPUT\n", "md = oc.MinDriver()\n", "md.drive(system)\n", "\n", "system.m.z.plane('z').k3d.scalar(filter_field=system.m.norm)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "ux = 400 # velocity in x direction (m/s)\n", "beta = 0.5 # non-adiabatic STT parameter\n", "\n", "system.dynamics += mm.ZhangLi(u=ux, beta=beta)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running OOMMF (ExeOOMMFRunner) [2021/09/22 13:57]... <1> mmarchive killed\n", " <2> mmarchive killed\n", " <3> mmarchive killed\n", "(5.1 s)\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c7616afe8f1d4b83be0a80e78afc55c2", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# NBVAL_IGNORE_OUTPUT\n", "td = oc.TimeDriver()\n", "td.drive(system, t=0.2e-9, n=200)\n", "\n", "system.m.z.plane('z').k3d.scalar(filter_field=system.m.norm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a result, we got a skyrmion formed in the wider region." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "249d8672bd254ed48565b21d938dc86c": { 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