Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A ₂IrO ₃

Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A ₂IrO ₃ (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-125K for Na ₂IrO ₃ to θ-33K for Li ₂IrO ₃, while the ordering temperature remains roughly the same T _N 15K. 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 Na ₂IrO ₃ is deep in a magnetically ordered regime, while Li ₂IrO ₃ appears to be close to a spin-liquid regime.