Large-Japproach to strongly coupled spin-orbital systems

Abstract

We present an approach to study the ground-state and elementary excitations in compounds where spins and orbitals are entangled by on-site relativistic spin-orbit interaction. The appropriate degrees of freedom are localized states with an effective angular momentum $J$. We generalize $J$ to arbitrary large values while maintaining the delicate spin-orbital entanglement. After projecting the intersite exchange interaction to the manifold of effective spins, a systematic $1/J$ expansion of the effective Hamiltonian is realized using the Holstein-Primakoff transformation. Applications to representative compounds ${\text{Sr}}_{2}{\text{IrO}}_{4}$ and particularly vanadium spinels $A{\text{V}}_{2}{\text{O}}_{4}$ are discussed.