X-ray angular momentum and polarization behavior in magnetic x-ray scattering

X-ray spectroscopic techniques have had a transformative effect on our understanding of magnetic materials. These techniques are based on the idea of conservation of total angular momentum such that the x-ray angular momentum encodes the magnetic spin angular momentum inside materials.  Recently, however, an experiment and a theoretical prediction showed that an x-ray beam may maintain the same linear x-ray polarization during scattering yet causing a rotational spin-flip excitation inside the crystal. Such an imbalanced scattering process implies an apparent non-conservation of angular momentum.  In this investigation, we have utilized the x-ray scattering software EDRIXS to compute the trend in the left and the right circularly x-ray polarized beam causing magnetic spin-flip transition versus the x-ray scattering angle. Based on the study we conclude that a dipole-dipole scattering theory approach seems to conserve momentum without providing any further detail on how and why it occurs.