Nonlocal features of the spin-orbit exciton in Kitaev materials

A comparative resonant inelastic x-ray scattering (RIXS) study of three well-known Kitaev materials is presented: $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Li}}₂{\mathrm{IrO}}₃, {\mathrm{Na}}₂{\mathrm{IrO}}₃$, and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}₃$. Despite similar low-energy physics, these materials show distinct electronic properties, such as the large difference in the size of the charge gap. The RIXS spectra of the spin-orbit exciton for these materials show remarkably similar three-peak features, including sharp low energy peak (peak A) as well as transitions between ${j}_{\text{eff}}=1/2$ and ${j}_{\text{eff}}=3/2$ states. Comparison of experimental spectra with cluster calculations reveals that the observed three-peak structure reflects the significant role that nonlocal physics plays in the electronic structure of these materials. In particular, the low-energy peak A arises from a holon-doublon pair rather than a conventional particle-hole exciton as proposed earlier. Our study suggests that while spin-orbit assisted Mott insulator is still the best description for these materials, electron itinerancy cannot be ignored when formulating low-energy Hamiltonian of these materials.