A Fourier-Space Approach to Physics-Informed Magnetization Reconstruction from Nitrogen-Vacancy Measurements

Abstract: Reconstructing complex magnetization textures from nitrogen-vacancy (NV) magnetometry stray-field measurements presents a challenging inverse problem. In this work, we introduce a physics-informed method that addresses this by incorporating the full micromagnetic energy directly into the variational formulation. Built on a PyTorch backend, our forward model integrates an auto-differentiable finite-differences micromagnetic framework with FFT-based stray-field calculations and Fourier-space upward continuation. This enables efficient gradient-based optimization via the adjoint method and allows the sensor-sample distance to be treated as an optimization parameter. By doing so, we eliminate the experimental uncertainty arising from unknown NV implantation depths and surface oxidation layers. Validation on synthetic data demonstrates high-fidelity reconstruction of spin textures and precise sensor height estimation. Furthermore, when applied to NV measurements of the van der Waals ferromagnet $Fe_{3-x}GaTe_2$, the method reconstructs the previously unknown NV-sample distance and physically plausible magnetization textures, which accurately reproduce the experimental observations.