Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3

We study the ordered moment direction in the extended Kitaev-Heisenberg model relevant to honeycomb lattice magnets with strong spin-orbit coupling. We utilize numerical diagonalization and analyze the exact cluster groundstates using a particular set of spin coherent states, obtaining thereby quantum corrections to the magnetic anisotropy beyond conventional perturbative methods. It is found that the quantum fluctuations strongly modify the moment direction obtained at a classical level, and are thus crucial for a precise quantification of the interactions. The results show that the moment direction is a sensitive probe of the model parameters in real materials. Focusing on the experimentally relevant zigzag phases of the model, we analyze the currently available neutron and resonant x-ray diffraction data on Na2IrO3 and RuCl3, and discuss the parameter regimes plausible in these Kitaev-Heisenberg model systems.