Reconstruction of magnetic structures and material parameters with convolutional neural network and bias field-constrained micromagnetic relaxation.

Abstract

We present framework for extracting internal magnetic structures and intrinsic magnetic material parameters from stray field measurements. The approach introduces a tunable bias field into Landau-Lifshitz-Gilbert dynamics and identifies optimal parameters by minimizing the mismatch between simulated and target stray fields or magnetic force microscopy (MFM) frequency shift contrast. Using synthetic data, we demonstrate recovery of global parameters including the uniaxial anisotropy constant [Formula: see text], saturation magnetization [Formula: see text], exchange stiffness [Formula: see text], and Dzyaloshinskii-Moriya interaction constant [Formula: see text]. A sensitivity analysis reveals that [Formula: see text] has the strongest influence on the optimization loss, while [Formula: see text] and [Formula: see text] exhibit relatively shallow minima. We further assess robustness to noise in the input stray field and find that accurate parameter estimation remains feasible at moderate noise levels. We further analyze the inverse reconstruction of magnetization textures and show that, while the strong stray-field side of Néel skyrmions allows for reliable reconstructions, the weak stray-field side poses significant challenges. These difficulties can be mitigated by employing a convolutional neural network (U-Net) trained on synthetic micromagnetic data to learn the mapping from stray-field slices to magnetization textures. The network provides a robust initialization for the subsequent physics-based relaxation, thereby improving convergence and reconstruction accuracy in challenging scenarios such as the weak stray-field side of Néel skyrmions. The framework is implemented using automatic differentiation in PyTorch, enabling gradient-based optimization and suggesting future extensions toward spatially resolved parameter reconstruction. This hybrid learning-and-physics method offers a flexible and robust strategy for material characterization based on micromagnetic forward models and experimental magnetic imaging data.