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High-resolution resonant inelastic X-ray scattering (RIXS) at the oxygenK-edge has been used to study the orbital excitations of Ca2RuO4 and Sr2RuO4.In combination with linear dichroism X-ray absorption spectroscopy, theruthenium 4d-orbital occupation and excitations were probed through theirhybridization with the oxygen p-orbitals. These results are described within aminimal model, taking into account crystal field splitting and a spin-orbitcoupling \lambda_{so}=200~meV. The effects of spin-orbit interaction on theelectronic structure and implications for the Mott and superconducting groundstates of (Ca,Sr)2RuO4 are discussed.

Spin-Orbit-Induced Orbital Excitations in Sr2RuO4 and Ca2RuO4: A Resonant Inelastic X-ray Scattering Study