First-principles study of the magnetic interactions in honeycomb Na2IrO3

Honeycomb iridate Na2IrO3, a J(eff) = 1/2 magnet, is a potential platform for realizing quantum spin liquid. Many experiments have shown that its magnetic ground state is a zigzag antiferromagnetic order. However, there is still a lack of consensus on the theoretical model explaining such order, since its second-nearest-neighbor (NN) and long-range third-NN magnetic interactions are highly unclear. By properly considering the orbital moments achieved through constraining their directions in first-principles calculations, we obtain that the relative angle between orbital and spin moments is fairly small and in the order of several degrees, which thus validates the J(eff) = 1/2 state in Na2IrO3. Surprisingly, we find that the long-range third-NN Heisenberg interactions are sizable, whereas the second-NN magnetic interactions are negligible. Furthermore, we show that sizable long-range third-NN Heisenberg interactions closely correlate with the appreciable distribution of Wannier orbitals of J(eff) = 1/2 states over the three NN Ir atoms. Based on our study, we propose a minimal J(1)-K-1-Gamma(1)-J(3) model in which the magnetic excitations have an intensity peak at 5.6 meV, consistent with the inelastic neutron-scattering experiment [Phys. Rev. Lett. 108, 127204 (2012)]. The present work demonstrates again that constraining orbital moments in first-principles calculations is a powerful way to investigate the intriguing magnetism in J(eff) = 1/2 magnets, and it paves the way toward gaining a deep insight into the novel magnetism discovered in the honeycomb J(eff) = 1/2 magnets.