Vibronic effect on resonant inelastic x-ray scattering of cubic iridium hexahalides

Resonant inelastic x-ray scattering spectra of K$_2$IrCl$_6$ show a splitting of the $j=3/2$ states resembling non-cubic crystal-field splitting although the compound is cubic down to 0.3 K. Here we theoretically describe the RIXS spectra based on the interplay of the spin-orbit interaction and the dynamic Jahn-Teller effect. We found that the dynamic Jahn-Teller effect in the $j=3/2$ multiplet states gives rise to the splitting of the RIXS spectra and the broadening of the spectra in raising the temperature. With the same approach, we could quantitatively reproduce the difference in the gap between the peaks of K$_2$IrCl$_6$ and K$_2$IrBr$_6$. We also showed that the interaction parameters used for the simulations agree well with our {\it ab initio} coupling parameters. Our results suggest that, in the excited $j=3/2$ multiplet of K$_2$IrCl$_6$, the dynamic Jahn-Teller effect develops and keeps the compound cubic.