Magnetic order and spin excitations in the Kitaev--Heisenberg model on the honeycomb lattice

We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev - Heisenberg model proposed for A2IrO3 (A=Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation (RPA) for four different ordered phases, observed in the parameter space of the model: antiferomagnetic, stripe, ferromagnetic, and zigzag phases. The N\'{e}el temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na2IrO3.