Spin-orbit-induced orbital excitations in ${\text{Sr}}_{2}{\text{RuO}}_{4}$ and ${\text{Ca}}_{2}{\text{RuO}}_{4}$: A resonant inelastic x-ray scattering study

High-resolution resonant inelastic x-ray scattering (RIXS) at the oxygen $K$ edge has been used to study the orbital excitations of ${\text{Ca}}_{2}{\text{RuO}}_{4}$ and ${\text{Sr}}_{2}{\text{RuO}}_{4}$. In combination with linear dichroism x-ray absorption spectroscopy, the ruthenium $4d$-orbital occupation and excitations were probed through their hybridization with the oxygen $p$ orbitals. These results are described within a minimal model, taking into account crystal field splitting and a spin-orbit coupling ${{\lambda}}_{so}=200$ meV. The effects of spin-orbit interaction on the electronic structure and implications for the Mott and superconducting ground states of (Ca,Sr)${}_{2}\mathrm{RuO}_{4}$ are discussed