Large-J approach to strongly coupled spin-orbital systems

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 Sr₂IrO₄ and particularly vanadium spinels AV₂O₄ are discussed.