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Electronic structure of the frustrated diamond lattice magnet NiRh 2 O 4

We report 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), x-ray absorption spectroscopy (XAS), and inelastic neutron scattering (INS) to characterize the local electronic structure and lattice dynamics 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 Δt 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.

36 MATERIALS SCIENCE↗

Materials Data on NiRh by Materials Project

NiRh crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are two inequivalent Rh sites. In the first Rh site, Rh is bonded to six equivalent Rh and six Ni atoms to form distorted RhNi6Rh6 cuboctahedra that share corners with twelve RhNi6Rh6 cuboctahedra, edges with twelve RhNi6Rh6 cuboctahedra, edges with twelve NiNi6Rh6 cuboctahedra, faces with six equivalent RhNi6Rh6 cuboctahedra, and faces with twelve NiNi6Rh6 cuboctahedra. All Rh–Rh bond lengths are 2.65 Å. All Rh–Ni bond lengths are 2.59 Å. In the second Rh site, Rh is bonded to ten equivalent Rh and six Ni atoms to form distorted RhNi6Rh10 cuboctahedra that share corners with ten NiNi6Rh6 cuboctahedra, corners with twelve RhNi6Rh6 cuboctahedra, edges with eight NiNi6Rh6 cuboctahedra, edges with sixteen RhNi6Rh6 cuboctahedra, faces with sixteen equivalent RhNi6Rh10 cuboctahedra, and faces with eighteen NiNi6Rh6 cuboctahedra. There are a spread of Rh–Rh bond distances ranging from 2.65–5.31 Å. All Rh–Ni bond lengths are 2.59 Å. There are three inequivalent Ni sites. In the first Ni site, Ni is bonded to six equivalent Rh and six equivalent Ni atoms to form distorted NiNi6Rh6 cuboctahedra that share corners with twelve NiNi6Rh6 cuboctahedra, edges with twelve equivalent RhNi6Rh6 cuboctahedra, edges with twelve NiNi6Rh6 cuboctahedra, faces with six equivalent NiNi6Rh6 cuboctahedra, and faces with twelve equivalent RhNi6Rh6 cuboctahedra. All Ni–Ni bond lengths are 2.65 Å. In the second Ni site, Ni is bonded to six Rh and six equivalent Ni atoms to form distorted NiNi6Rh6 cuboctahedra that share corners with five equivalent RhNi6Rh10 cuboctahedra, corners with twelve NiNi6Rh6 cuboctahedra, edges with ten RhNi6Rh6 cuboctahedra, edges with twelve NiNi6Rh6 cuboctahedra, faces with six equivalent NiNi6Rh6 cuboctahedra, and faces with fifteen RhNi6Rh6 cuboctahedra. All Ni–Rh bond lengths are 2.59 Å. All Ni–Ni bond lengths are 2.65 Å. In the third Ni site, Ni is bonded to six Rh and six equivalent Ni atoms to form distorted NiNi6Rh6 cuboctahedra that share corners with five equivalent RhNi6Rh10 cuboctahedra, corners with twelve NiNi6Rh6 cuboctahedra, edges with ten RhNi6Rh6 cuboctahedra, edges with twelve NiNi6Rh6 cuboctahedra, faces with six equivalent NiNi6Rh6 cuboctahedra, and faces with fifteen RhNi6Rh6 cuboctahedra. All Ni–Ni bond lengths are 2.65 Å.

36 MATERIALS SCIENCE↗