{ "cells": [ { "cell_type": "markdown", "id": "27c4e760-831f-4852-b7cc-e4340006618f", "metadata": {}, "source": "# Composite chiral magnet benchmark\n\nThis example reproduces the benchmark problem introduced in\n\n> V. Laliena, S. A. Osorio, S. Bustingorry, and J. Campo. *Continuum of metastable helical states of monoaxial chiral magnets: Effect of boundary conditions.* Physical Review B, **109**:214424, 2024.\n\nA one-dimensional composite consisting of a chiral slab sandwiched between two ferromagnetic slabs is relaxed to its ground state. Because the Dzyaloshinskii–Moriya interaction (DMI) is non-zero only inside the chiral region, the ground state is a Bloch helix in the centre that is matched to exponentially decaying profiles in the outer ferromagnetic regions. Laliena *et al.* provide a closed-form analytical solution that we use to validate the numerical simulation.\n\n## Problem setup\n\nThe system is symmetric about $x=0$ and occupies $|x|\\le L=150\\,\\mathrm{nm}$. The chiral region covers $|x|\\le L_0=100\\,\\mathrm{nm}$ and uses exchange $A$, bulk DMI constant $D$ and easy-plane anisotropy $K_c = -(h_c-1)\\,D^2/A$ with reduced field $h_c=6$. The ferromagnetic slabs use exchange $\\rho\\,A$ (with $\\rho=3$), $D=0$ and easy-axis anisotropy $K_u = \\rho\\,D^2/(4A)$ with easy axis along $\\hat{\\mathbf y}$.\n\nThe ground state is the Bloch helix $\\mathbf m = (0,\\cos\\varphi,\\sin\\varphi)$ where the phase $\\varphi$ satisfies\n\n$$\\varphi(x) = p\\,q_0\\,x \\qquad \\text{for } |x|\\le L_0,$$\n\nwith $q_0 = D/(2A)$ and a pitch parameter $p$ that is fixed by matching the flux $2A\\varphi' - D$ across the chiral–ferro interface at $x=\\pm L_0$. Outside the chiral region the phase obeys the pendulum equation $\\varphi'' = q_u^2\\sin\\varphi\\cos\\varphi$ with $q_u = q_0$." }, { "cell_type": "markdown", "id": "c686a3f5-bcf6-497f-ba32-306b4222bf57", "metadata": {}, "source": [ "## Simulation\n", "### Import libraries\n", "We import NumPy, SciPy and NeuralMag and set the default precision to double to guarantee convergence." ] }, { "cell_type": "code", "execution_count": 1, "id": "b027cb1d-06a0-432f-9d22-0e7f99d06852", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:01.183071Z", "iopub.status.busy": "2026-04-07T16:17:01.182425Z", "iopub.status.idle": "2026-04-07T16:17:04.158728Z", "shell.execute_reply": "2026-04-07T16:17:04.156928Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:03 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Version 0.9.3\u001b[0m\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:04 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Backend set to 'jax'.\u001b[0m\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:04 NeuralMag:INFO \u001b[1;37;32m[NeuralMag] Set default dtype to 'float64'.\u001b[0m\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.integrate import solve_ivp\n", "from scipy.optimize import brentq\n", "\n", "import neuralmag as nm\n", "\n", "nm.config.dtype = \"float64\"" ] }, { "cell_type": "markdown", "id": "e659a648-f5a6-485a-aea1-5aa2ae63e7b4", "metadata": {}, "source": [ "### Material parameters and geometry\n", "\n", "All material constants are taken from the Laliena benchmark. The saturation magnetisation is $M_s = 10^6\\,\\mathrm{A/m}$, the exchange constant in the chiral region is $A = 10^{-11}\\,\\mathrm{J/m}$, and the bulk DMI constant is $D = 4\\,\\mathrm{mJ/m^2}$. The exchange ratio between ferro and chiral region is $\\rho=3$ and the reduced anisotropy field is $h_c=6$. The total length is $2L = 300\\,\\mathrm{nm}$ discretised with cell size $\\Delta x = 0.5\\,\\mathrm{nm}$ ($N=600$ cells)." ] }, { "cell_type": "code", "execution_count": 2, "id": "59b5bb45-7239-44dd-ad32-5b8bfe6ee2d6", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:04.168524Z", "iopub.status.busy": "2026-04-07T16:17:04.168026Z", "iopub.status.idle": "2026-04-07T16:17:04.179950Z", "shell.execute_reply": "2026-04-07T16:17:04.175541Z" } }, "outputs": [], "source": [ "# Physical parameters\n", "A = 1e-11 # Exchange constant [J/m]\n", "D = 4e-3 # Bulk DMI constant [J/m²]\n", "rho = 3.0 # Exchange ratio ferro/chiral\n", "hc = 6.0 # Reduced anisotropy field\n", "Ms = 1e6 # Saturation magnetization [A/m]\n", "q0 = D / (2 * A)\n", "qu = q0\n", "Kc = -(hc - 1) * D**2 / A # Easy-plane anisotropy (chiral)\n", "Ku = rho * D**2 / (4 * A) # Easy-axis anisotropy (ferro)\n", "\n", "# Geometry\n", "L0 = 100e-9 # Half-width of chiral region [m]\n", "L = 150e-9 # Half-width of total system [m]\n", "dx = 0.5e-9 # Cell size [m]\n", "N = round(2 * L / dx)" ] }, { "cell_type": "markdown", "id": "a0e07929-172a-46c0-abca-0eef178ecbde", "metadata": {}, "source": [ "### Analytical solution\n", "\n", "The matching condition at $x=\\pm L_0$ determines the pitch parameter $p$ as the root of\n", "\n", "$$f(p) = p - 1 + \\frac{\\rho\\,q_u}{q_0}\\sin(p\\,q_0\\,L_0) = 0$$\n", "\n", "that lies closest to unity. We bracket and refine it with Brent's method. The phase in the ferromagnetic slabs is then obtained by integrating the pendulum equation with initial conditions $\\varphi(L_0)=p\\,q_0\\,L_0$ and $\\varphi'(L_0)=(p-1)\\,q_0/\\rho$." ] }, { "cell_type": "code", "execution_count": 3, "id": "a4ff1b33-f978-445f-a5ec-bfba9cd32371", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:04.184094Z", "iopub.status.busy": "2026-04-07T16:17:04.183602Z", "iopub.status.idle": "2026-04-07T16:17:04.197810Z", "shell.execute_reply": "2026-04-07T16:17:04.196685Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pitch parameter p = 0.943421\n" ] } ], "source": [ "def f_trans(p):\n", " return p - 1 + (rho * qu / q0) * np.sin(p * q0 * L0)\n", "\n", "\n", "p_min = max(1 - np.sqrt(hc), 1 - rho * qu / q0)\n", "p_max = min(1 + np.sqrt(hc), 1 + rho * qu / q0)\n", "p_scan = np.linspace(p_min + 1e-10, p_max - 1e-10, 10000)\n", "f_scan = f_trans(p_scan)\n", "p_roots = []\n", "for i in range(len(f_scan) - 1):\n", " if f_scan[i] * f_scan[i + 1] < 0:\n", " p_roots.append(brentq(f_trans, p_scan[i], p_scan[i + 1]))\n", "p_val = np.array(p_roots)[np.argmin(np.abs(np.array(p_roots) - 1))]\n", "print(f\"pitch parameter p = {p_val:.6f}\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "e30bacd9-5fd6-4b72-a26a-6d7b1be58479", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:04.200042Z", "iopub.status.busy": "2026-04-07T16:17:04.199825Z", "iopub.status.idle": "2026-04-07T16:17:04.207442Z", "shell.execute_reply": "2026-04-07T16:17:04.206294Z" } }, "outputs": [], "source": [ "def analytical_profile(x, p):\n", " phi = np.zeros_like(x)\n", " # chiral region: linear phase\n", " mc = np.abs(x) <= L0\n", " phi[mc] = p * q0 * x[mc]\n", " # right ferro region: integrate pendulum equation\n", " mr = x > L0\n", " if np.any(mr):\n", " xr = np.clip(x[mr], L0, L)\n", " sol = solve_ivp(\n", " lambda t, y: [y[1], qu**2 * np.sin(y[0]) * np.cos(y[0])],\n", " [L0, L],\n", " [p * q0 * L0, (p - 1) * q0 / rho],\n", " t_eval=xr,\n", " rtol=1e-12,\n", " atol=1e-14,\n", " )\n", " phi[mr] = sol.y[0]\n", " # left ferro region: use symmetry\n", " ml = x < -L0\n", " if np.any(ml):\n", " xl = np.clip(-x[ml][::-1], L0, L)\n", " sol = solve_ivp(\n", " lambda t, y: [y[1], qu**2 * np.sin(y[0]) * np.cos(y[0])],\n", " [L0, L],\n", " [p * q0 * L0, (p - 1) * q0 / rho],\n", " t_eval=xl,\n", " rtol=1e-12,\n", " atol=1e-14,\n", " )\n", " phi[ml] = -sol.y[0][::-1]\n", " return phi" ] }, { "cell_type": "markdown", "id": "fee5ddf7-2526-4ce1-9fad-da0f6abb6804", "metadata": {}, "source": [ "### Create mesh and state\n", "\n", "We use a 1D nodal mesh with $N=600$ cells centred at the origin. The NeuralMag `State` holds all field quantities that live on this mesh." ] }, { "cell_type": "code", "execution_count": null, "id": "9c26468e-af17-46ae-8b18-c0416abd158b", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:04.211452Z", "iopub.status.busy": "2026-04-07T16:17:04.211172Z", "iopub.status.idle": "2026-04-07T16:17:04.667073Z", "shell.execute_reply": "2026-04-07T16:17:04.664562Z" } }, "outputs": [], "source": [ "mesh = nm.Mesh((N,), (dx, dx, dx), origin=(-L, 0, 0))\n", "state = nm.State(mesh)\n", "\n", "# cell-centre and node coordinates along x (x_c as backend tensor so the\n", "# conditions fed to state.add_domain are valid for both jax and torch)\n", "x_c = state.coordinates()[0]\n", "x_n = -L + np.arange(N + 1) * dx" ] }, { "cell_type": "markdown", "id": "3141080b-c10a-4244-a72f-d2ccab04c3c9", "metadata": {}, "source": [ "### Material domains\n", "\n", "The two regions (chiral and ferromagnetic) are introduced via domain labels, and the material parameters are assigned per domain using `fill_by_domain`. Domain `0` (the background) has zero material, domain `1` is the chiral slab and domain `2` is the ferromagnetic slab. The easy-axis direction of the anisotropy is $\\hat{\\mathbf x}$ (easy-plane $y$-$z$) in the chiral region and $\\hat{\\mathbf y}$ in the ferro region." ] }, { "cell_type": "code", "execution_count": 6, "id": "c74f8b05-ae28-48e3-a242-b67375f7ad3d", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:04.671624Z", "iopub.status.busy": "2026-04-07T16:17:04.671182Z", "iopub.status.idle": "2026-04-07T16:17:05.031559Z", "shell.execute_reply": "2026-04-07T16:17:05.030546Z" } }, "outputs": [], "source": [ "state.add_domain(1, abs(x_c) <= L0)\n", "state.add_domain(2, abs(x_c) > L0)\n", "\n", "state.material.Ms = nm.CellFunction(state).fill_by_domain([0.0, Ms, Ms])\n", "state.material.A = nm.CellFunction(state).fill_by_domain([0.0, A, rho * A])\n", "state.material.Db = nm.CellFunction(state).fill_by_domain([0.0, D, 0.0])\n", "state.material.Ku = nm.CellFunction(state).fill_by_domain([0.0, Kc, Ku])\n", "state.material.Ku_axis = nm.VectorCellFunction(state).fill_by_domain([[0, 0, 0], [1, 0, 0], [0, 1, 0]])\n", "state.material.alpha = 1.0" ] }, { "cell_type": "markdown", "id": "341313f5-d217-466a-a650-64b47146ad7d", "metadata": {}, "source": [ "### Initial magnetisation\n", "\n", "We seed the simulation with the analytical helix profile. The phase is evaluated at cell centres, the resulting magnetisation is averaged onto the nodal mesh and renormalised. Starting from the analytical profile ensures that the LLG relaxation converges to the correct winding number." ] }, { "cell_type": "code", "execution_count": 7, "id": "177bc840-dfd6-4395-9d02-55741c52c278", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:05.034041Z", "iopub.status.busy": "2026-04-07T16:17:05.033765Z", "iopub.status.idle": "2026-04-07T16:17:05.182992Z", "shell.execute_reply": "2026-04-07T16:17:05.181890Z" } }, "outputs": [], "source": [ "phi_n = analytical_profile(x_n, p_val)\n", "m_init = np.zeros((N + 1, 3))\n", "m_init[:, 1] = np.cos(phi_n)\n", "m_init[:, 2] = np.sin(phi_n)\n", "\n", "state.m = nm.VectorFunction(state, tensor=state.tensor(m_init))" ] }, { "cell_type": "markdown", "id": "9e78aa84-5538-49b0-a31a-d4a86853f65e", "metadata": {}, "source": [ "### Effective field and relaxation\n", "\n", "The total effective field contains contributions from exchange, bulk DMI and uniaxial anisotropy. After registering each contribution with the state, we relax the system to an energetic minimum with the Landau–Lifshitz–Gilbert solver." ] }, { "cell_type": "code", "execution_count": 8, "id": "7391350f-9bea-4ac7-8bd1-24d3bf1251c4", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:05.185536Z", "iopub.status.busy": "2026-04-07T16:17:05.185277Z", "iopub.status.idle": "2026-04-07T16:17:08.403581Z", "shell.execute_reply": "2026-04-07T16:17:08.402367Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:05 NeuralMag:INFO \u001b[1;37;32m[ExchangeField] Register state methods (field: 'h_exchange', energy: 'E_exchange', energy density: 'e_exchange')\u001b[0m\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:05 NeuralMag:INFO \u001b[1;37;32m[BulkDMIField] Register state methods (field: 'h_dmi', energy: 'E_dmi', energy density: 'e_dmi')\u001b[0m\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:05 NeuralMag:INFO \u001b[1;37;32m[UniaxialAnisotropyField] Register state methods (field: 'h_aniso', energy: 'E_aniso', energy density: 'e_aniso')\u001b[0m\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:05 NeuralMag:INFO \u001b[1;37;32m[TotalField] Register state methods (field: 'h', energy: 'E', energy density: 'e')\u001b[0m\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:05 NeuralMag:INFO \u001b[1;37;32m[LLGSolverJAX] Initialize RHS function\u001b[0m\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:05 NeuralMag:INFO \u001b[1;37;34m[LLGSolverJAX] Relaxation started, initial energy E = -4.98922e-20 J\u001b[0m\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:06 NeuralMag:INFO \u001b[1;37;34m[LLGSolverJAX] Relaxation step (max dm/dt = 3.12772e+09) 1/s\u001b[0m\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2026-04-07 18:17:08 NeuralMag:INFO \u001b[1;37;34m[LLGSolverJAX] Relaxation finished, final energy E = -4.98922e-20 J\u001b[0m\n" ] } ], "source": [ "nm.ExchangeField().register(state, \"exchange\")\n", "nm.BulkDMIField().register(state, \"dmi\")\n", "nm.UniaxialAnisotropyField().register(state, \"aniso\")\n", "nm.TotalField(\"exchange\", \"dmi\", \"aniso\").register(state)\n", "\n", "llg = nm.LLGSolver(state, rtol=1e-8, atol=1e-8)\n", "llg.relax()" ] }, { "cell_type": "markdown", "id": "1dd800a8-b715-4797-a817-e2028a376141", "metadata": {}, "source": [ "## Comparison with the analytical solution\n", "\n", "We interpolate the relaxed nodal magnetisation onto the cell centres and plot the $m_y$ and $m_z$ components against the analytical helix." ] }, { "cell_type": "code", "execution_count": 9, "id": "45fe5993-f748-45a8-928e-bdadf70e97a0", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:08.406470Z", "iopub.status.busy": "2026-04-07T16:17:08.406146Z", "iopub.status.idle": "2026-04-07T16:17:09.733065Z", "shell.execute_reply": "2026-04-07T16:17:09.731923Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m_np = nm.config.backend.to_numpy(state.m.tensor)\n", "\n", "phi_ref = analytical_profile(x_n, p_val)\n", "my_ref = np.cos(phi_ref)\n", "mz_ref = np.sin(phi_ref)\n", "\n", "fig, axes = plt.subplots(2, 1, figsize=(7, 5), sharex=True)\n", "axes[0].plot(x_n * 1e9, my_ref, \"k-\", label=\"analytical\")\n", "axes[0].plot(x_n * 1e9, m_np[:, 1], \"r--\", label=\"NeuralMag\")\n", "axes[0].axvspan(-L * 1e9, -L0 * 1e9, color=\"orange\", alpha=0.1)\n", "axes[0].axvspan(L0 * 1e9, L * 1e9, color=\"orange\", alpha=0.1)\n", "axes[0].set_ylabel(r\"$m_y$\")\n", "axes[0].legend()\n", "\n", "axes[1].plot(x_n * 1e9, mz_ref, \"k-\", label=\"analytical\")\n", "axes[1].plot(x_n * 1e9, m_np[:, 2], \"r--\", label=\"NeuralMag\")\n", "axes[1].axvspan(-L * 1e9, -L0 * 1e9, color=\"orange\", alpha=0.1)\n", "axes[1].axvspan(L0 * 1e9, L * 1e9, color=\"orange\", alpha=0.1)\n", "axes[1].set_xlabel(r\"$x$ [nm]\")\n", "axes[1].set_ylabel(r\"$m_z$\")\n", "axes[1].legend()\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c7ae10cb-d5f4-42c6-b6a3-d519455f6266", "metadata": {}, "source": "The shaded regions indicate the ferromagnetic slabs. The simulated magnetisation matches the analytical helix to within the discretisation error of the nodal finite-difference method. For a quantitative assessment one can compute the phase $\\varphi$ from the components and plot its deviation from the analytical profile." }, { "cell_type": "code", "execution_count": 10, "id": "34ced31b-b43e-4e7d-ac82-5ac9171ce39d", "metadata": { "execution": { "iopub.execute_input": "2026-04-07T16:17:09.735442Z", "iopub.status.busy": "2026-04-07T16:17:09.735162Z", "iopub.status.idle": "2026-04-07T16:17:09.892461Z", "shell.execute_reply": "2026-04-07T16:17:09.891325Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phi_sim = np.unwrap(np.arctan2(m_np[:, 2], m_np[:, 1]))\n", "phi_ref_u = np.unwrap(phi_ref)\n", "phi_sim += phi_ref_u[(N + 1) // 2] - phi_sim[(N + 1) // 2]\n", "\n", "plt.figure(figsize=(7, 3))\n", "plt.plot(x_n * 1e9, phi_sim - phi_ref_u)\n", "plt.axvspan(-L * 1e9, -L0 * 1e9, color=\"orange\", alpha=0.1)\n", "plt.axvspan(L0 * 1e9, L * 1e9, color=\"orange\", alpha=0.1)\n", "plt.xlabel(r\"$x$ [nm]\")\n", "plt.ylabel(r\"$\\varphi_{\\mathrm{sim}} - \\varphi_{\\mathrm{ana}}$ [rad]\")\n", "plt.tight_layout()\n", "plt.show()" ] } ], "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": "3.12.12" } }, "nbformat": 4, "nbformat_minor": 5 }