X-ray magnetic circular dichroism and resonant inelastic X-ray scattering explained: role of many-body correlation and valence fluctuations

X-ray magnetic circular dichroism (XMCD) and resonant inelastic X-ray scattering with magnetic circular dichroism (RIXS-MCD) provide unparalleled insights into the electronic and magnetic dynamics of complex materials. However, interpreting their spectra in mixed-valence systems remains challenging due to intricate many-body interactions and enhanced charge fluctuations. In this study, by utilizing the Anderson impurity model with a full consideration of charge transfer (CT), many-body core-valence exchange correlation (CVEC) effects, and Jahn-Teller (JT) distortions, we systematically investigate the XMCD and RIXS-MCD spectra for a prototypical mixed-valence ferromagnet, La$_{0.7}$Sr$_{0.3}$MnO$_3$ film. We demonstrate that simple calculation with limited CT effects fails to capture characteristic substructures observed experimentally. In contrast, an adequate treatment of CT and CVEC effects yields a more consistent description of both XMCD and RIXS-MCD spectra, providing practical guidance for the interpretation of dichroic x-ray spectroscopies in mixed-valence transition-metal oxides. Furthermore, we discuss the role of the JT effect in Mn$^{3+}$ ions in the determination of their spectra.