Motivated by the interest in topological quantum paramagnets in candidate spin-1 magnets, we investigate the diamond-lattice compound ${\mathrm{NiRh}}_2{\mathrm{O}}_4$ using ab initio theory and model Hamiltonian approaches. Our density functional study, taking into account the unquenched orbital degrees of freedom, shows stabilization of $S=1$, $L=1$ state. We highlight the importance of spin-orbit coupling, in addition to Coulomb correlations, in driving the insulating gap, and uncover frustrating large second-neighbor exchange mediated by Ni-Rh covalency. A single-site model Hamiltonian incorporating the large tetragonal distortion is shown to give rise to a spin-orbit entangled nonmagnetic ground state, largely accounting for the entropy, magnetic susceptibility, and inelastic neutron scattering results. Incorporating intersite exchange within a slave-boson theory, we show that exchange frustration can suppress exciton condensation. We capture the dispersive gapped magnetic modes, uncover “dark states” invisible to neutrons, and make predictions.

• Received 27 May 2019
• Revised 23 September 2019

DOI:https://doi.org/10.1103/PhysRevB.100.140408