Neural-network-based reconstruction of spin and orbital angular momentum from X-ray magnetic circular dichroism spectra

Abstract

X-ray magnetic circular dichroism (XMCD) is a powerful probe of element-specific spin and orbital angular momentum. Conventional analyses based on sum rules, however, rely on integrated spectral intensities and can become insufficient when multiple parameters influence the spectral line shape. Here, we formulate XMCD analysis as an inverse problem and develop a neural-network (NN) based approach to reconstruct spin and orbital angular momentum directly from full spectral line shapes. Using many-body multiplet calculations of Fe, Co, and Ni $L_{2,3}$-edge X-ray absorption spectra (XAS) and XMCD spectra as a physically well-defined training dataset, we systematically vary key parameters including crystal-field splitting, spin--orbit coupling, and exchange field. The NN is trained to map spectral line shapes onto the expectation values of spin and orbital angular momentm $\langle S_z \rangle$ and $\langle L_z \rangle$, and validated using strictly test-only data. The results demonstrate accurate and unbiased reconstruction, establishing a proof of concept for data-driven inverse reconstruction from XAS and XMCD spectra. These findings show that exploiting the full XAS and XMCD line shapes provide access to information beyond conventional sum-rule analyses while remaining consistent with established theoretical frameworks.