Spin–orbital locking, emergent pseudo-spin and magnetic order in honeycomb lattice iridates

The nature of the effective spin Hamiltonian and magnetic order in the honeycomb iridates is explored by considering a trigonal crystal field effect and spin–orbit (SO) coupling. Starting from a Hubbard model, an effective spin Hamiltonian is derived in terms of an emergent pseudo-spin-1/2 moment in the limit of large trigonal distortions and SO coupling. The present pseudo-spins arise from a spin–orbital locking and are different from the jeff = 1/2 moments that are obtained when the SO coupling dominates and trigonal distortions are neglected. The resulting spin Hamiltonian is anisotropic and frustrated by further neighbour interactions. Mean-field theory suggests a ground state with four-sublattice zigzag magnetic order in a parameter regime that can be relevant to the honeycomb iridate compound Na2IrO3, where a similar magnetic ground state has recently been observed. Various properties of the phase, the spin-wave spectrum and experimental consequences are discussed. The present approach contrasts with the recent proposals to understand iridate compounds starting from the strong SO coupling limit and neglecting non-cubic lattice distortions.