Tuning the topological phase and anomalous Hall conductivity with magnetization direction in H-FeCl₂ monolayer

Most theoretical predictions and experimental reports of the two-dimensional (2D) quantum anomalous Hall effect (QAHE) are based on out-of-plane. In this work, we investigated the effect of deflected magnetization direction on both the topological properties and QAHE of the H-FeCl2 monolayer. We predicted that the H-FeCl2 monolayer possesses the intrinsic out-of-plane ferromagnetism and quantum anomalous valley Hall effect. By deflecting the magnetization direction to induce band inversion, the H-FeCl2 monolayer undergoes a phase transition between the topological insulator (C = +/- 1) and the normal insulator (C = 0) and the phase transition point characterized by a 2D half-valley-metal state. Particularly, via applying the in-plane biaxial strain, we found that topologically non-trivial states can be realized even as the magnetization direction approaches the in-plane, and the topologically protected anomalous Hall conductivity is robust against the deflection of the magnetization direction. These results enrich the physics of the QAHE and contribute to the design of topological devices with tunable edge-state electrons.