Electronic structure of the frustrated diamond lattice magnet NiRh₂O₄

NiRh₂O₄ is the first known realization of a S=1 diamond lattice magnet and is predicted to host various exotic phenomena such as topological paramagnetism, spiral spin liquid, and excitonic magnetism, caused by frustrated nearest and next-nearest neighbor exchange, as well as orbital degeneracy. Thermodynamic measurements found no sign of magnetic order and inelastic neutron scattering found excitations suggestive of a valence bond solid. Theoretical works using both ab-initio and effective models have explained these results by proposing a spin-orbital singlet ground state for NiRh₂O₄. Our recent RIXS measurements are mostly consistent with these predictions, but contain a feature that cannot be explained by a single-ion model with Coulomb interaction, crystal field, and spin-orbit coupling. Based on ab-initio calculations, we find that this feature is consistent with an interatomic orbital excitation between Ni and Rh sites. In addition, the spectral lineshapes suggests significant electron-phonon coupling, common to orbitally degenerate A-site spinels. These results provide insight into frustrated magnetism beyond fully localized moments in systems with coupled spin, orbital, and lattice degrees of freedom.