Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A2IrO3 (A=Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from θ≈-125  K for Na2IrO3 to θ≈-33  K for Li2IrO3, while the ordering temperature remains roughly the same T(N)≈15  K. Using functional renormalization group calculations we show that this evolution of θ and T(N) as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2IrO3 is deep in a magnetically ordered regime, while Li2IrO3 appears to be close to a spin-liquid regime.

We report a combined experimental and theoretical investigation of the magnetic structure of the honeycomb lattice magnet Na2IrO3, a strong candidate for a realization of a gapless spin-liquid. Using resonant x-ray magnetic scattering at the Ir L3-edge, we find 3D long range antiferromagnetic order below TN =13.3 K. From the azimuthal dependence of the magnetic Bragg peak, the ordered moment is determined to be predominantly along the a-axis. Combining the experimental data with first principles calculations, we propose that the most likely spin structure is a novel "zig-zag" structure.