LAUSR

We derive general expressions for resonant inelastic x-ray scattering (RIXS) operators for ${t}_{2g}$ orbital systems, which exhibit a rich array of unconventional magnetism arising from unquenched orbital moments. Within the fast collision approximation, which is valid especially for $4d$ and $5d$ transition metal compounds with short core-hole lifetimes, the RIXS operators are expressed in terms of total spin and orbital angular momenta of the constituent ions. We then map these operators onto pseudospins that represent spin-orbit entangled magnetic moments in systems with strong spin-orbit coupling. Applications of our theory to such systems as iridates and ruthenates are discussed, with a particular focus on compounds based on ${d}^{4}$ ions with Van Vleck-type nonmagnetic ground state.