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.

• Received 2 May 2017
• Revised 12 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.085108