Emergent quantum criticality from spin-orbital entanglement in d⁸ Mott insulators: the case of a diamond lattice antiferromagnet

Motivated by the recent activities on the Ni-based diamond lattice antiferromagnet NiRh₂O₄, we theoretically explore on a general ground the unique spin and orbital physics for the Ni²⁺ ions with a 3d⁸ electron configuration in the tetrahedral crystal field environment and on a diamond lattice Mott insulator. The superexchange interaction between the local moments usually favors magnetic orders. Due to the particular electron configuration of the Ni²⁺ 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 non-trivial response to the magnetic field is intimately tied to the underlying spin-orbital structure of the local moments. We discuss the future experiments such as doping and pressure, and point out the general correspondence between different electron configurations under tetrahedral and octahedral crystal field environments.