Exploring itinerant states in divalent hexaborides using rare-earth $L$ edge resonant inelastic X-ray scattering

We present a study of resonant inelastic X-ray scattering (RIXS) spectra collected at the rare-earth $L$ edges of divalent hexaborides YbB${}_6$ and EuB${}_6$. In both systems, RIXS-active features are observed at two distinct resonances separated by $\sim 10$ eV in incident energy, with angle-dependence suggestive of distinct photon scattering processes. RIXS spectra collected at the divalent absorption peak strongly resemble the unoccupied 5$d$ density of states calculated using density functional theory, an occurrence we ascribe to transitions between weakly-dispersing 4$f$ and strongly dispersing 5$d$ states. In addition, anomalous resonant scattering is observed at higher incident energy, where no corresponding absorption feature is present. Our results suggest the far-reaching utility of $L$-edge RIXS in determining the itinerant-state properties of $f$-electron materials.