Theoretical analysis of resonant inelastic x-ray scattering spectra of Ca2RuO4

Abstract

We calculate the resonant inelastic x-ray scattering (RIXS) spectra of a $4d$-electron Mott insulator ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$ that exhibits spin-orbit entangled magnetic ordering. Considering the Ru ${L}_{3}$-edge RIXS, we identify four different types of excitations: magnetic dipolar transitions, quadrupolar transitions changing total angular momentum by $\mathrm{\ensuremath{\Delta}}J=2$, spin-state transitions with $\mathrm{\ensuremath{\Delta}}S=1$, and ${t}_{2g}\ensuremath{\rightarrow}{e}_{g}$ orbital transitions across the crystal-field and Hund's coupling derived levels. We provide analytical expressions for the magnetic transitions and the $\mathrm{\ensuremath{\Delta}}J\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}2$ transitions in the tetragonal compression limit, which are generally applicable to other compounds with ${t}_{2g}^{4}$ configurations in a square lattice. Intriguingly, we find that upon tetragonal compression the dipole-forbidden $\mathrm{\ensuremath{\Delta}}J=2$ transitions acquire large spectral weights with pronounced polarization dependencies, which are consistent with the experimental observations. Our numerical simulations show that this is due to a constructive interference between dipolar and quadrupolar scattering channels.