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An effective low-energy Hamiltonian of itinerant electrons for iridium oxideNa2IrO3 is derived by an ab initio downfolding scheme. The model is thenreduced to an effective spin model on a honeycomb lattice by the strongcoupling expansion. Here we show that the ab initio model contains spin-spinanisotropic exchange terms in addition to the extensively studied Kitaev andHeisenberg exchange interactions, and allows to describe the experimentallyobserved zigzag magnetic order, interpreted as the state stabilized by theantiferromagnetic coupling of the ferromagnetic chains. We clarify possibleroutes to realize quantum spin liquids from existing Na2IrO3.

First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations