Electronic structure of the frustrated diamond lattice magnet NiRh2O4

Abstract

The $A$-site spinel ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$ is the only known realization of a spin-1 diamond lattice magnet and is predicted to host unconventional magnetic phenomena driven by frustrated nearest and next-nearest neighbor exchange as well as orbital degeneracy. Previous works found no sign of magnetic order but found a gapped dispersive magnetic excitation indicating a possible valence bond magnetic ground state. However, the presence of many competing low energy degrees of freedom and limited empirical microscopic constraints complicates further analysis. Here we carry out resonant inelastic x-ray scattering (RIXS), x-ray absorption spectroscopy (XAS), and inelastic neutron scattering (INS) to characterize the local electronic structure and lattice dynamics of ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$. The RIXS data can be partly described by a single-ion model for tetrahedrally coordinated ${\mathrm{Ni}}^{2+}$ and indicates a tetragonal distortion $\mathrm{\ensuremath{\Delta}}{t}_{2}=70$ meV that splits the ${t}_{2}$ orbitals into a high energy orbital singlet and lower energy orbital doublet. We identify features of the RIXS spectra that are consistent with a Rh-Ni two-site excitation indicating strong metal-metal hybridization mediated by oxygen in ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$. We also identify signatures of electron-phonon coupling through the appearance of phonon sidebands that dress crystal field excitations. These results establish the key energy scales relevant to the magnetism in ${\mathrm{NiRh}}_{2}{\mathrm{O}}_{4}$ and further demonstrate that covalency and lattice dynamics play essential roles in controlling the magnetic ground states of $A$-site spinels.