{
"cells": [
{
"cell_type": "markdown",
"id": "748dc020",
"metadata": {},
"source": [
"# Double layers of Py / CoFeB\n",
"\n",
"Here, we calculate the dispersion of the Damon-Eshbach (DE) modes in a bilayer made of two different materials. In this system, mirror symmetries are broken, and the dipolar interaction induces a dispersion asymmetry. For more details, see Grassi *et al.* in Ref. 1. For the present case, we consider a bilayer with 25 nm permalloy and 25 nm CoFeB (without any nonmagnetic spacer). \n",
"\n",
"## Sample creation\n",
"\n",
"This can be modeled using the monolayer geometry and by setting inhomogenous material parameters. We start by creating the sample"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "3e649e39-7895-47d7-8aae-98e7549ec296",
"metadata": {},
"outputs": [],
"source": [
"import tetrax as tx\n",
"import numpy as np\n",
"\n",
"t1_Py = 25\n",
"t2_CoFeB = 25\n",
"total_thickness = t1_Py + t2_CoFeB\n",
"res = 2.0\n",
"\n",
"\n",
"dlayer_50 = tx.Sample(\n",
" tx.geometries.layer.monolayer(total_thickness, res),\n",
" name=\"Py25CoFeB25\"\n",
")\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "4c4e9dce",
"metadata": {},
"source": [
"and set the material parameters in both layers."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "c514ace3",
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"dlayer_50.gamma = 29.2 * 2 * np.pi * 1e9\n",
"\n",
"Msat_Py = 845e3\n",
"Msat_CoFeB = 1270e3\n",
"middle = -(total_thickness)/2 + t1_Py\n",
"Msat_ = np.piecewise(dlayer_50.xyz.x, [dlayer_50.xyz.y <= middle, dlayer_50.xyz.y > middle], [Msat_Py,Msat_CoFeB])\n",
"dlayer_50.material[\"Msat\"] = Msat_\n",
"\n",
"A_Py = 12.8e-12\n",
"A_CoFeB = 17e-12\n",
"Aex_ = np.piecewise(dlayer_50.xyz.x, [dlayer_50.xyz.y <= middle, dlayer_50.xyz.y > middle], [A_Py,A_CoFeB])\n",
"dlayer_50.material[\"Aex\"] = Aex_"
]
},
{
"cell_type": "markdown",
"id": "e7494f8a",
"metadata": {},
"source": [
"Here, the `piecewise` function of the *NumPy* package creates a staircase dependent on the material parameters (which are piecewise constant)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6f5778d1",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/attilak/micromag/tetrax-tests/fresh_environement_test/venv/lib/python3.13/site-packages/traittypes/traittypes.py:97: UserWarning: Given trait value dtype \"float32\" does not match required type \"float32\". A coerced copy has been created.\n",
" warnings.warn(\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "2337404fd23a492c80aa99f239f791aa",
"version_major": 2,
"version_minor": 0
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"text/plain": [
"Plot(antialias=3, axes=['x', 'y', 'z'], axes_helper=1.0, axes_helper_colors=[16711680, 65280, 255], background…"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dlayer_50.mag = (1,0,0)\n",
"dlayer_50.show()"
]
},
{
"cell_type": "markdown",
"id": "55b76ff1",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "598d6bd1-e7fb-45d2-a34e-c7a7cfc4bab8",
"metadata": {},
"source": [
"We see that the difference in saturation magnetization `Msat` between the two layers is visualized as different arrow lengths in the 3D plot. Note, that ```dlayer_50.mag``` is still a unitary vector field $\\mathbf{m}(\\mathbf{r})$ of length 1 everywhere. The scaled magnetization vector $M_\\mathrm{s}(\\mathbf{r})\\mathbf{m}(\\mathbf{r})$ can be obtained as ```dlayer_50.mag_full```. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "2bb1a537-b119-4846-935d-7d2f166a8382",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"MeshVector([[ 845000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [ 845000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.],\n",
" [1270000., 0., 0.]])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dlayer_50.mag_full"
]
},
{
"cell_type": "markdown",
"id": "3d6cf8a1-9ea7-44b7-a3e9-eb4e44156376",
"metadata": {},
"source": [
"The vectors displayed in the 3D plot are simply `dlayer_50.mag_full / dlayer_50.material[\"Msat\"].average`."
]
},
{
"cell_type": "markdown",
"id": "cef7c011",
"metadata": {},
"source": [
"## Dispersion calculation for the first N=5 Damon-Eshbach modes\n",
"\n",
"To calculate the first 5 DE modes, we apply an external field perpendicular to the propagation ($z$) direction. A homogeneous magnetization in the same direction can be assumed as the equilibrium. So we do not need to relax anymore."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b092cb0f",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|███████████████████| 41/41 [00:01<00:00, 34.14it/s]\n"
]
}
],
"source": [
"dlayer_50.external_field = (30e-3,0,0)\n",
"dlayer_50.mag = (1,0,0)\n",
"\n",
"spectrum = tx.experiments.eigenmodes(dlayer_50, kmin=-50e6,kmax=50e6,num_k=81, num_cpus=-1,num_modes=5)"
]
},
{
"cell_type": "markdown",
"id": "379039ff-a79a-4fe7-b98d-ac268f79329c",
"metadata": {},
"source": [
"Plotting the spectrum shows hybridization and dispersion asymmetry of the lowest two modes."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "1f2800ea-fa30-4705-be65-f394422357e2",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
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"data": {
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""
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"source": [
"spectrum.plot(fscale=\"G\", kscale=\"u\", n=[0,1], renderer=\"notebook\") # remove the renderer argument when running on your computer"
]
},
{
"cell_type": "markdown",
"id": "fde7270c-7f71-48aa-a1de-fb971f7bd9a0",
"metadata": {},
"source": [
"## References\n",
"\n",
"1. Grassi et al. \"Slow-Wave-Based Nanomagnonic Diode\", [Physical Review Applied 14, 024047](https://doi.org/10.1103/PhysRevApplied.14.024047) (2020)"
]
}
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