First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the   Presence of Strong Spin-Orbit Interaction and Electron Correlations
  An effective low-energy Hamiltonian of itinerant electrons for iridium oxide Na2IrO3 is derived by an ab initio downfolding scheme. The model is then reduced to an effective spin model on a honeycomb lattice by the strong coupling expansion. Here we show that the ab initio model contains spin-spin anisotropic exchange terms in addition to the extensively studied Kitaev and Heisenberg exchange interactions, and allows to describe the experimentally observed zigzag magnetic order, interpreted as the state stabilized by the antiferromagnetic coupling of the ferromagnetic chains. We clarify possible routes to realize quantum spin liquids from existing Na2IrO3. 
Youhei Yamaji, Yusuke Nomura, Moyuru Kurita, Ryotaro Arita and   Masatoshi Imada
cond-mat.str-el