# Resonant inelastic x-ray scattering operators for $t_{2g}$ orbital systems

## TL;DR

This paper derives general RIXS operators for $t_{2g}$ orbital systems, linking them to spin and orbital moments, and applies the theory to spin-orbit coupled materials like iridates and ruthenates.

## Contribution

It provides a theoretical framework for RIXS operators in $t_{2g}$ systems, including mapping onto pseudospins for spin-orbit entangled states, especially relevant for 4d and 5d compounds.

## Key findings

- Derived RIXS operators in terms of spin and orbital angular momenta.
- Mapped operators onto pseudospins for spin-orbit entangled states.
- Discussed applications to iridates and ruthenates with $d^4$ ions.

## Abstract

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 4$d$ and 5$d$ 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.