Correlated motion of particle-hole excitations across the renormalized spin-orbit gap in $\mathrm{S}{\mathrm{r}}_2\mathrm{I}\mathrm{r}{\mathrm{O}}_4$

The high-energy collective modes of particle-hole excitations across the spin-orbit gap in $\mathrm{S}{\mathrm{r}}_2\mathrm{I}\mathrm{r}{\mathrm{O}}_4$ are investigated using the transformed Coulomb interaction terms in the pseudo-spin-orbital basis constituted by the $J=1\mathrm{/}2$ and $3\mathrm{/}2$ states arising from spin-orbit coupling. With appropriate interaction strengths and renormalized spin-orbit gap, these collective modes yield two well-defined propagating spin-orbit exciton modes, with energy scale and dispersion in excellent agreement with resonant inelastic X-ray scattering (RIXS) measurements.