Honeycomb iridate Na2IrO3, a Jeff=1/2 magnet, is a potential platform for realizing the quantum spin liquid. Many experiments have shown that its magnetic ground state has a zigzag antiferromagnetic (AFM) 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 taking into account the orbital moments, achieved through constraining their directions in the 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 Jeff=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. Using maximally localized Wannier functions, we show that the sizable long-range third NN Heisenberg interaction results from the extended nature of the Jeff=1/2 state. Based on our study, we propose a minimal J1-K1-{Gamma}_1-J3 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 the first-principles calculations is powerful to investigate the intriguing magnetism in the Jeff=1/2 magnets, and paves the way toward gaining a deep insight into the novel magnetism discovered in the honeycomb Jeff=1/2 magnets.
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