Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit

Recently, realizations of Kitaev physics have been sought in the A(2)IrO(3) family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the j(eff) = 1/2 Mott insulator in these materials, exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here, we provide the generic nearest-neighbor spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond-dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit, we find new magnetic phases, 120 degrees and incommensurate spiral order, as well as extended regions of zigzag and stripy order. Possible applications to Na2IrO3 and Li2IrO3 are discussed.