Finite-temperature phase diagram of the Heisenberg-Kitaev model

Abstract

We discuss the finite-temperature phase diagram of the Heisenberg-Kitaev model on the hexagonal lattice, which has been suggested to describe the spin-orbital exchange in the Mott-insulating iridate Na${}_{2}$IrO${}_{3}$. The model exhibits magnetically ordered ground states well beyond the isotropic Heisenberg limit as well as a gapless spin-liquid phase around the anisotropic Kitaev limit. Using a pseudofermion functional renormalization group (RG) approach we extract both the Curie-Weiss scale and the critical ordering scale from the RG flow of the magnetic susceptibility. The Curie-Weiss scale switches sign---indicating a transition of the dominant exchange from antiferromagnetic to ferromagnetic---deep in the magnetically ordered regime for which we find no significant frustration. We discuss our results in light of recent susceptibility measurements for Na${}_{2}$IrO${}_{3}$.