{ "cells": [ { "cell_type": "markdown", "id": "c8845bf4", "metadata": {}, "source": [ "# Table FFT\n", "`ubermagtable` has the functionality to Fourier transform table data. This can be useful for trying to look at phenomena such as ferromagnetic resonance. " ] }, { "cell_type": "markdown", "id": "0d863c14", "metadata": {}, "source": [ "To give an example of the Fourier transform functionality, a system with a single macrospin has been created. This system has the initial magnetisation along the $x$ direction with an external magnetic field applied along the $z$ direction. We can then use a time driver to evolve the state with a dynamics equation which includes precession and damping. The following code is used to generate data (using the full range of packages available in Ubermag):\n", "\n", "```python\n", "import oommfc as mc\n", "import discretisedfield as df\n", "import micromagneticmodel as mm\n", "\n", "# Define a macrospin mesh (i.e. one discretisation cell).\n", "p1 = (0, 0, 0) # first point of the mesh domain (m)\n", "p2 = (1e-9, 1e-9, 1e-9) # second point of the mesh domain (m)\n", "n = (1, 1, 1) # discretisation cell size (m)\n", "\n", "Ms = 8e6 # magnetisation saturation (A/m)\n", "H = (0, 0, 2e6) # external magnetic field (A/m)\n", "gamma0 = 2.211e5 # gyromagnetic ratio (m/As)\n", "alpha = 0.1 # Gilbert damping\n", "\n", "region = df.Region(p1=p1, p2=p2)\n", "mesh = df.Mesh(region=region, n=n)\n", "\n", "system = mm.System(name='macrospin')\n", "system.energy = mm.Zeeman(H=H)\n", "system.dynamics = mm.Precession(gamma0=gamma0) + mm.Damping(alpha=alpha)\n", "system.m = df.Field(mesh, dim=3, value=(1, 0, 0), norm=Ms)\n", "\n", "td = mc.TimeDriver()\n", "td.drive(system, t=0.1e-9, n=200)\n", "```\n", "\n", "However, `ubermagtable` can be used indepentently of most other packages in Ubermag. Therefore, in this example we assume that we already have an `odt` file that we can load from disk using only `ubermagtable`. (When using the full range of Ubermag packages this is generally done automatically in the background and the table made available as `system.table`)." ] }, { "cell_type": "code", "execution_count": 1, "id": "db01a9c1-2936-44dd-8579-9737be7f0e68", "metadata": {}, "outputs": [], "source": [ "import os\n", "\n", "import numpy as np\n", "\n", "import ubermagtable" ] }, { "cell_type": "markdown", "id": "9676fd34-6d8c-48cf-a91e-831396a14fc5", "metadata": {}, "source": [ "There is a pre-computed file under `./macrospin/drive-0/macrospin.odt` (obtained with the code shown above):" ] }, { "cell_type": "code", "execution_count": 2, "id": "05567b49-86c5-4b91-b579-d99b5352ae16", "metadata": {}, "outputs": [], "source": [ "odtfile = os.path.join(\".\", \"macrospin\", \"drive-0\", \"macrospin.odt\")\n", "table = ubermagtable.Table.fromfile(odtfile, x=\"t\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "f78b26a0-8cf1-4457-8485-339c727db402", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", " | E | \n", "E_calc_count | \n", "max_dm/dt | \n", "dE/dt | \n", "delta_E | \n", "E_zeeman | \n", "iteration | \n", "stage_iteration | \n", "stage | \n", "mx | \n", "my | \n", "mz | \n", "last_time_step | \n", "t | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | \n", "-4.400762e-22 | \n", "37.0 | \n", "25204.415522 | \n", "-8.798712e-10 | \n", "-3.269612e-22 | \n", "-4.400762e-22 | \n", "6.0 | \n", "6.0 | \n", "0.0 | \n", "0.975901 | \n", "0.217115 | \n", "0.021888 | \n", "3.715017e-13 | \n", "5.000000e-13 | \n", "
1 | \n", "-8.797309e-22 | \n", "44.0 | \n", "25186.311578 | \n", "-8.786077e-10 | \n", "-4.396547e-22 | \n", "-8.797309e-22 | \n", "8.0 | \n", "1.0 | \n", "1.0 | \n", "0.904810 | \n", "0.423562 | \n", "0.043754 | \n", "5.000000e-13 | \n", "1.000000e-12 | \n", "
2 | \n", "-1.318544e-21 | \n", "51.0 | \n", "25156.186455 | \n", "-8.765071e-10 | \n", "-4.388134e-22 | \n", "-1.318544e-21 | \n", "10.0 | \n", "1.0 | \n", "2.0 | \n", "0.790286 | \n", "0.609218 | \n", "0.065579 | \n", "5.000000e-13 | \n", "1.500000e-12 | \n", "
3 | \n", "-1.756100e-21 | \n", "58.0 | \n", "25114.112032 | \n", "-8.735776e-10 | \n", "-4.375555e-22 | \n", "-1.756100e-21 | \n", "12.0 | \n", "1.0 | \n", "3.0 | \n", "0.638055 | \n", "0.765021 | \n", "0.087341 | \n", "5.000000e-13 | \n", "2.000000e-12 | \n", "
4 | \n", "-2.191985e-21 | \n", "65.0 | \n", "25060.188355 | \n", "-8.698302e-10 | \n", "-4.358857e-22 | \n", "-2.191985e-21 | \n", "14.0 | \n", "1.0 | \n", "4.0 | \n", "0.455710 | \n", "0.883427 | \n", "0.109020 | \n", "5.000000e-13 | \n", "2.500000e-12 | \n", "
... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
195 | \n", "-2.009865e-20 | \n", "1402.0 | \n", "690.438568 | \n", "-6.602614e-13 | \n", "-3.374608e-25 | \n", "-2.009865e-20 | \n", "396.0 | \n", "1.0 | \n", "195.0 | \n", "0.013011 | \n", "-0.024099 | \n", "0.999625 | \n", "5.000000e-13 | \n", "9.800000e-11 | \n", "
196 | \n", "-2.009897e-20 | \n", "1409.0 | \n", "675.493807 | \n", "-6.319876e-13 | \n", "-3.230101e-25 | \n", "-2.009897e-20 | \n", "398.0 | \n", "1.0 | \n", "196.0 | \n", "0.017545 | \n", "-0.020251 | \n", "0.999641 | \n", "5.000000e-13 | \n", "9.850000e-11 | \n", "
197 | \n", "-2.009928e-20 | \n", "1416.0 | \n", "660.872303 | \n", "-6.049242e-13 | \n", "-3.091780e-25 | \n", "-2.009928e-20 | \n", "400.0 | \n", "1.0 | \n", "197.0 | \n", "0.021059 | \n", "-0.015612 | \n", "0.999656 | \n", "5.000000e-13 | \n", "9.900000e-11 | \n", "
198 | \n", "-2.009958e-20 | \n", "1423.0 | \n", "646.567078 | \n", "-5.790193e-13 | \n", "-2.959381e-25 | \n", "-2.009958e-20 | \n", "402.0 | \n", "1.0 | \n", "198.0 | \n", "0.023428 | \n", "-0.010435 | \n", "0.999671 | \n", "5.000000e-13 | \n", "9.950000e-11 | \n", "
199 | \n", "-2.009986e-20 | \n", "1430.0 | \n", "632.571305 | \n", "-5.542233e-13 | \n", "-2.832649e-25 | \n", "-2.009986e-20 | \n", "404.0 | \n", "1.0 | \n", "199.0 | \n", "0.024591 | \n", "-0.004988 | \n", "0.999685 | \n", "5.000000e-13 | \n", "1.000000e-10 | \n", "
200 rows × 14 columns
\n", "