Effects of Kitaev interaction on magnetic order and anisotropy

We systematically investigate the effects of Kitaev interaction on magnetic orders and anisotropy in both triangular and honeycomb lattices on the classical level. Our study highlights the critical role of the Kitaev interaction in modulating phase boundaries and predicting new phases, e.g., zigzag phase in triangular lattice and AABB phase in honeycomb lattice, which are absent with pure Heisenberg interactions. Moreover, we reveal the special state-dependent anisotropy of Kitaev interaction, and develop a general method that can determine the presence of Kitaev interaction in different magnets. It is found that the Kitaev interaction does not induce anisotropy in some magnetic orders such as ferromagnetic order, while it can cause different anisotropy in other magnetic orders. Furthermore, we emphasize that the off-diagonal $\mathrm{\ensuremath{\Gamma}}$ interaction also contributes to anisotropy, competing with the Kitaev interaction to reorient spin arrangements. Our work establishes a framework for comprehensive understanding the impact of Kitaev interaction on ordered magnetism.