Importance of anisotropic exchange interactions in honeycomb iridates: Minimal model for zigzag antiferromagnetic order in Na2 IrO3

In this work, we investigate the microscopic nature of the magnetism in honeycomb iridium-based systems by performing a systematic study of how the effective magnetic interactions in these compounds depend on various electronic microscopic parameters. We show that the minimal model describing the magnetism in A2IrO3 includes both isotropic and anisotropic Kitaev-type spin-exchange interactions between nearest and next-nearest neighbor Ir ions, and that the magnitude of the Kitaev interaction between next-nearest neighbor Ir magnetic moments is comparable with nearest neighbor interactions. We also find that, while the Heisenberg and the Kitaev interactions between nearest neighbors are correspondingly antiferro- and ferromagnetic, they both change sign for the next-nearest neighbors. Using classical Monte Carlo simulations we examine the magnetic phase diagram of the derived super-exchange model. We find that the zigzag-type antiferromagnetic order occupies a large part of the phase diagram of this model and, for the ferromagnetic next-nearest neighbor Heisenberg interaction relevant for Na2IrO3, it can be stabilized at small and even at zero third nearest neighbor coupling. Our results suggest that a natural physical origin of the zigzag phase experimentally observed in Na2IrO3 is due to the interplay of the Kitaev anisotropic interactions between nearest and next-nearest neighbors.