{ "cells": [ { "cell_type": "markdown", "id": "cc27231c", "metadata": {}, "source": [ "# Static magnetization equilibrium and hysteresis loops\n", "In this example, we show how to use our `MacrospinEquilibrium` class to calculate static direction of magnetization in simple systems. The output can then be used in `SingleLayerNumeric` *(other classes don't work for partially OOP magnetization, yet)*. Eventually, it can also be used to calculate hysteresis loops or field-swept ferromagnetic resonance frequencies in films with some uniaxial anisotropies (`### make an example on the FMR sweep and reference it here`).\n", "\n", "*Note: It is based on a single macrospin model, so do not expect it to be super exact for thick films, waveguides, etc.*\n", "\n", "## Basic usage and application to `SingleLayer`\n", "\n", "We start with importing the needed modules and simple system definition. By default, the class assumes a thin film in the laboratory frame of coordinates, i.e. *x,y* are in-plane (IP) of the film, *z* out-of-plane (OOP) (later we will also assume that spin waves propagate along *x*). We will now use the saturation magnetization of NiFe and apply magnetic field 40° from film normal." ] }, { "cell_type": "code", "execution_count": 1, "id": "358c3f10", "metadata": {}, "outputs": [], "source": [ "# import modules\n", "import numpy as np # for vectorization\n", "import matplotlib.pyplot as plt # for plotting\n", "import SpinWaveToolkit as SWT" ] }, { "cell_type": "code", "execution_count": null, "id": "7d9a4bf5", "metadata": {}, "outputs": [], "source": [ "# initiate the class\n", "maceq = SWT.MacrospinEquilibrium(\n", " Ms=SWT.NiFe.Ms, # saturation magnetization of built-in NiFe\n", " Bext=0.5, # (T) external field\n", " theta_H=np.deg2rad(40), # (rad) polar angle of external field\n", " phi_H=np.deg2rad(1e-4), # (rad) azimuthal angle of external field\n", " # Without specifying `theta` and `phi`, the initial state of magnetization\n", " # will be in the direction of the field.\n", ")" ] }, { "cell_type": "markdown", "id": "0b406501", "metadata": {}, "source": [ "You could notice the small angle of `phi_H`. This is because the model can get stuck, so slight \"kick\" around the exact value may help you reach the better results.\n", "\n", "Now, to get the equilibrium angle we just use the `maceq.minimize()` method. The output is then stored in the `maceq.M` attribute as a dictionary." ] }, { "cell_type": "code", "execution_count": null, "id": "11fedd93", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Minimum successfully found.\n", "theta = 1.281 rad = 73.40°, phi = 0.000 rad = 0.00°,\n" ] } ], "source": [ "maceq.minimize()\n", "print(*[f\"{key} = {maceq.M[key]:.3f} rad = {np.rad2deg(maceq.M[key]):.2f}°,\"\n", " for key in maceq.M.keys()])" ] }, { "cell_type": "markdown", "id": "85b0e158", "metadata": {}, "source": [ "You see, that the interplay between the demagnetization field and external field resulted in the static magnetization direction of about 73.4°. This can be now used for dispersion relation calculations. To do this, we will now just use the `maceq` object and built-in NiFe parameters." ] }, { "cell_type": "code", "execution_count": 4, "id": "94639c6b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k = np.linspace(1, 50e6, 200)\n", "sl = SWT.SingleLayer(material=SWT.NiFe, d=50e-9, kxi=k, **maceq.M, **maceq.Bext)\n", "\n", "for i in range(3):\n", " plt.plot(k*1e-6, sl.GetDispersion(i)/(2e9*np.pi), \"-\", label=f\"$n=${i}\")\n", "plt.xlabel(\"wavenumber (rad/µm)\")\n", "plt.ylabel(\"frequency (GHz)\")\n", "plt.legend(loc=\"upper right\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "70ea9af2", "metadata": {}, "source": [ "## Calculation of effective field\n", "It's also possible to calculate the effective field $\\mu_0H_{\\mathrm{eff}}$ (here denoted as `Heff`). To do this, use the `maceq.getHeff()` method." ] }, { "cell_type": "code", "execution_count": 5, "id": "c3704b36", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "theta = 1.281 rad, phi = 0.000 rad, Heff = 0.335 T\n" ] } ], "source": [ "Heff_data = maceq.getHeff()\n", "print(\"theta = {:.3f} rad, phi = {:.3f} rad, Heff = {:.3f} T\".format(*Heff_data))" ] }, { "cell_type": "markdown", "id": "55ab43b5", "metadata": {}, "source": [ "The resulting direction angles of Heff are the same as for M, which complies with the condition of equilibrium (effective field parallel to static magnetization). However, this method can be called at any time, even before the system is minimized. For example, by setting the magnetization angles to some non-equilibrium value, one can explore the direction and magnitude of the effective field." ] }, { "cell_type": "markdown", "id": "67d4af92", "metadata": {}, "source": [ "## Adding anisotropy\n", "It is quite common to encounter magnetic systems with anisotropic behaviour. Here, we currently implement only uniaxial anisotropy, which can be set in any direction in the laboratory frame using the `theta` and `phi` angles. You can add as many anisotropies as you like, but one or two is usually enough. It is done by calling the `add_uniaxial_anisotropy()` method with `Ku > 0` for easy-axis and `Ku < 0` for easy plane. However, sometimes it is more useful to define the anisotropy using the anisotropy field `Bani`. In this case the `Ku` input is ignored in favor of the `Bani` parameter, which is recalculated to `Ku` internally." ] }, { "cell_type": "code", "execution_count": 6, "id": "137d7121", "metadata": {}, "outputs": [], "source": [ "maceq.add_uniaxial_anisotropy(\n", " name=\"anisotropy0\", # name to be used in the dictionary of anisotropies\n", " Ku=0, # (J/m^3) uniaxial anisotropy stength, here unused because we use Bani\n", " theta=np.pi/2, # (rad) polar angle of anisotropy axis, here IP\n", " phi=0, # (rad) azimuthal angle of anisotropy axis\n", " Bani=20e-3, # (T) anisotropy field µ_0*H_ani\n", ")" ] }, { "cell_type": "markdown", "id": "981e4983", "metadata": {}, "source": [ "Now, you can either update the parameters of this anisotropy if you use the same name in this method or add another anisotropy with different name. All anisotropies are saved as a dictionary under the `maceq.anis` attribute with names being the dict keys. Each value is then another dictionary consisting of the set values of `Ku`, `theta`, `phi`, and a corresponding anisotropy tensor in the lab frame `Na`." ] }, { "cell_type": "code", "execution_count": 7, "id": "c8688d61", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'Ku': 8000.0,\n", " 'theta': 1.5707963267948966,\n", " 'phi': 0,\n", " 'Na': array([[-1.98943679e-02, -0.00000000e+00, -1.21817870e-18],\n", " [-0.00000000e+00, -0.00000000e+00, -0.00000000e+00],\n", " [-1.21817870e-18, -0.00000000e+00, -7.45919322e-35]])}" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "maceq.anis[\"anisotropy0\"]" ] }, { "cell_type": "markdown", "id": "ace31340", "metadata": {}, "source": [ "The tensor is currently used for the energy evaluations and is calculated only when the method `add_uniaxial_anisotropy()` is called. Therefore to change the parameters, e.g. the theta angle, it is recommended to use rather the `add_uniaxial_anisotropy()` method instead of dictionary assignment.\n", "\n", "We chose the representation in the form of the tensor, since it can be used like this in the dispersion calculations with the `SingleLayer` class by supplying the tensor as the `Na` parameter." ] }, { "cell_type": "markdown", "id": "e6d0f2c8", "metadata": {}, "source": [ "## Hysteresis loops\n", "With this macrospin model, we can also simulate hysteresis loops, similarly to e.g. the Stoner-Wohlfarth model.\n", "\n", "So far we have created the system as a thin film with IP uniaxial anisotropy. To get the hysteresis loops, we will sweep the values of `maceq.Bext` dictionary and calculate a new equilibrium at each field value, while the starting value of magnetization direction will be the one calculated at the previous field point. We can either code this ourselves or use the built-in method `hysteresis()` of the `MacrospinEquilibrium` class.\n", "\n", "We will illustrate this also while sweeping the IP angle of external field, changing from the easy-axis direction to the hard-axis direction." ] }, { "cell_type": "code", "execution_count": null, "id": "3595afa8", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|##########| 499/499 [00:02<00:00, 248.32it/s]\n", "100%|##########| 499/499 [00:01<00:00, 304.11it/s]\n", "100%|##########| 499/499 [00:01<00:00, 283.54it/s]\n", "100%|##########| 499/499 [00:01<00:00, 293.03it/s]\n", "100%|##########| 499/499 [00:01<00:00, 272.29it/s]\n", "100%|##########| 499/499 [00:01<00:00, 258.39it/s]\n", "100%|##########| 499/499 [00:01<00:00, 272.66it/s]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nb, na = 200, 7 # number of field points and IP angle points\n", "bexts = np.linspace(-0.05, 0.05, nb) # field range vector\n", "# now we use the range vector to create the full loop (0->max->min->max)\n", "bexts = np.concatenate((bexts[nb//2+1:], -bexts, bexts))\n", "nb = len(bexts) # ...and update the number of field points\n", "\n", "btheta = np.deg2rad(90)+1e-5 # (rad) fixed value of field's theta\n", "bphis_deg = np.linspace(0, 90, na)+1e-3 # (deg) sweep vector of IP angle\n", "bphis = np.deg2rad(bphis_deg) # same in radians\n", "\n", "# We also need unit vectors of field to convert the magnetization components\n", "# to projections in the field direction.\n", "bs = SWT.sphr2cart(btheta, bphis)\n", "\n", "thetas, phis = np.zeros((na, nb)), np.zeros((na, nb)) # preallocate\n", "for i in range(na): # calculate loops at each `bphis`\n", " thetas[i], phis[i] = maceq.hysteresis(\n", " bexts, btheta, bphis[i],\n", " # The default \"Nelder-Mead\" method usually works best, but it can be\n", " # changed manually through the `scipy_kwargs` dirtionary.\n", " scipy_kwargs={\"method\": \"L-BFGS-B\"},\n", " )\n", "ms = SWT.sphr2cart(thetas, phis) # [mx, my, mz] unit magnetization components\n", "\n", "cmap = plt.get_cmap(\"plasma\")\n", "for i in range(na):\n", " plt.plot(bexts*1e3, np.dot(bs[:, i], ms[:, i]), c=cmap(i/na),\n", " label=f\"{bphis_deg[i]:.0f}°\")\n", "plt.xlabel(\"external field (mT)\")\n", "plt.ylabel(r\"$\\vec{m} \\cdot \\vec{b}$ ()\")\n", "plt.legend(loc=\"upper left\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7b7f24ae", "metadata": {}, "source": [ "Ta da! Nice and easy.\n", "\n", "Note that with the built-in method, we can sweep only external field parameters. To sweep something else, e.g. uniaxial anisotropy strength or direction, you need to code this yourself." ] } ], "metadata": { "kernelspec": { "display_name": ".venv (3.13.5)", "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }