Spin-orbital entanglement in d8 Mott insulators: Possible excitonic magnetism in diamond lattice antiferromagnets

Motivated by the recent activities on the diamond lattice antiferromagnet ${\mathrm{NiRh}}₂{\mathrm{O}}₄$ with ${\mathrm{Ni}}²⁺\phantom{\rule{4pt}{0ex}}3{d}⁸$ local moments, we theoretically explore on general grounds the unique spin and orbital physics for the diamond lattice antiferromagnet with $3{d}⁸$ local moments. The superexchange interaction between the local moments usually favors magnetic orders. Due to the particular electron configuration of the $3{d}⁸$ ion with a partially filled upper ${t}_2g$ level and a fully filled lower ${e}_g$ level, the atomic spin-orbit coupling becomes active at the linear order and would favor a spin-orbital-entangled singlet with quenched local moments in the single-ion limit. Thus, the spin-orbital entanglement competes with the superexchange and could drive the system to a quantum critical point that separates the spin-orbital singlet and the magnetic order. We further explore the effects of magnetic field and uniaxial pressure. The nontrivial response to the magnetic field is intimately tied to the underlying spin-orbital structure of the local moments. We discuss future experiments such as doping and pressure and point out the correspondence between different electron configurations.