| We present a Monte Carlo study of the finite-temperature, magnetic phase diagram of the Classical Kitaev-heisenberg model on the hexagonal lattice. This model is a prominent example of anisotropic spin-orbital models, which can possibly describe the low-energy physics of Li2IrO3 and Na2IrO3. The competition between the simple, antiferromagnetic Heisenberg interaction and anisotropic Kitaev interaction can be described by one parameter, 0 ≤ α ≤ 1, which defines the relative strength of these two interactions. Using classical Monte Carlo simulations, we obtained a finite temperature phase diagram for the entire range of alpha. We established that the model undergoes two phase transitions as a function of temperature. The symmetry of the model is discrete Z(2)*Z(3). The Z(3) cubic symmetry is broken at the higher temperature, and Z(2) symmetry is broken at a lower temperature. The ordered phase at small alpha exhibits the Neel AF ordering. This becomes the Stripy ordering at larger alpha. We also computed the inverse susceptibility of the model, from which we extracted Curie-Weiss temperatures. Finally, we discuss the applicability of this model to the low-temperature physics of Li2IrO3 and Na2IrO3. |
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