Resolving the Orbital Character of Low-energy Excitations in Mott Insulator with Intermediate Spin-orbit Coupling

Multi-band Mott insulators with moderate spin-orbit and Hund's coupling are key reference points for theoretical concept developments of correlated electron systems. The ruthenate Mott insulator Ca$_{2}$RuO$_{4}$ has therefore been intensively studied by spectroscopic probes. However, it has been challenging to resolve the fundamental excitations emerging from the hierarchy of electronic energy scales. Here we apply state-of-the-art resonant inelastic x-ray scattering to probe deeper into the electronic excitations found in Ca$_{2}$RuO$_{4}$. In this fashion, we probe a series of spin-orbital excitations at low energies and resolve the level splitting of the intra-$t_{2g}$ structure due to spin-orbit coupling and crystal field splitting. Most importantly, the low-energy excitations exhibit strong orbital character. Such direct determination of relevant electronic energy scales is important, as it sharpens the target for theory developments of Mott insulators' orbital degree of freedom.