Electronic structure of the frustrated diamond lattice magnet NiRh$_2$O$_4$

TL;DR

This study investigates the electronic structure of NiRh$_2$O$_4$, a unique spin-1 diamond lattice magnet, revealing key energy scales and the influence of covalency and lattice dynamics on its magnetic ground state.

Contribution

The paper provides detailed spectroscopic analysis of NiRh$_2$O$_4$, highlighting the roles of orbital splitting, metal-metal hybridization, and electron-phonon coupling in its magnetic properties.

Findings

Identification of tetragonal distortion splitting $t_2$ orbitals

Evidence of strong Rh-Ni hybridization mediated by oxygen

Detection of electron-phonon coupling through phonon sidebands

Abstract

The $A$-site spinel NiRh$_2$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) and x-ray absorption spectroscopy (XAS) to characterize the local electronic structure of NiRh$_2$O$_4$. The RIXS data can be partly described by a single-ion model for tetrahedrally coordinated Ni$^{2+}$ and indicates a tetragonal distortion $\Delta t_2\!=\!70$ 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 NiRh$_2$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 NiRh$_2$O$_4$ and further demonstrate that covalency and lattice dynamics play essential roles in controlling the magnetic ground states of $A$-site spinels.