Spin direction dependent quantum anomalous Hall effect in two-dimensional ferromagnetic materials

We propose a scheme for realizing the spin direction-dependent quantum anomalous Hall effect (QAHE) driven by spin–orbit couplings (SOC) in two-dimensional (2D) materials. Based on the sp³ tight-binding (TB) model, we find that these systems can exhibit a QAHE with out-of-plane and in-plane magnetization for the weak and strong SOC, respectively, in which the mechanism of quantum transition is mainly driven by the band inversion of p_x,y/p_z orbitals. As a concrete example, based on first-principles calculations, we realize a real material of monolayer 1T-SnN₂/PbN₂ exhibiting the QAHE with in-plane/out-of-plane magnetization characterized by the nonzero Chern number C and topological edge states. These findings provide useful guidance for the pursuit of a spin direction-dependent QAHE and hence stimulate immediate experimental interest.