Universal reconstruction of complex magnetic profiles with minimal prior assumptions

Understanding intricate magnetic structures in materials is essential for advancing materials science, spintronics, and geology. Recent developments of quantum-enabled magnetometers, such as those based on nitrogen-vacancy centers in diamond, have enabled direct imaging of magnetic field distributions across a wide range of magnetic profiles. However, reconstructing the magnetization from an experimentally measured magnetic field map is a complex inverse problem, further complicated by measurement noise, finite spatial resolution, and variations in sample-to-sensor distance. In this work, we present an efficient graphics-processing-unit-accelerated method for reconstructing spatially varying magnetization density from measured magnetic fields with minimal prior assumptions. We validate our method by simulating diverse magnetic structures under realistic experimental conditions, including multidomain ferromagnetism and magnetic spin textures such as a skyrmion, an antiskyrmion, and a meron. Experimentally, we reconstruct the magnetization of a micrometer-scale Apollo lunar mare basalt (sample 10003,184) and a nanometer-scale twisted double-trilayer CrI₃ sample. The basalt exhibits soft ferromagnetic domains consistent with previous paleomagnetic studies, whereas the CrI₃ system reveals a well-defined hexagonal magnetic moiré superlattice. Our approach provides a versatile and universal tool for investigating complex magnetization profiles, paving the way for future quantum sensing experiments.