Electric field induced topological phase transition and large enhancements of spin-orbit coupling and Curie temperature in two-dimensional ferromagnetic semiconductors

                                                                                                                Jing-Yang You, Xue-Juan Dong, Bo Gu, and Gang Su

    Tuning the topological and magnetic properties of materials by applying an electric field is widely used in spintronics. In this work, we find a topological phase transition from topologically trivial to nontrivial states at an external electric field of about 0.1 V/Å in a ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ monolayer that is a topologically trivial ferromagnetic semiconductor. It is shown that when electric field increases from 0 to 0.15 V/Å, the magnetic anisotropy energy (MAE) increases from about 0.1 to 6.3 meV, and the Curie temperature $T_C$ increases from 13 to about 61 K. The increased MAE mainly comes from the enhanced spin-orbit coupling due to the applied electric field. The enhanced $T_C$ can be understood from the enhanced $p\text{−}d$ hybridization and decreased energy difference between $p$ orbitals of Te atoms and $d$ orbitals of Mn atoms. Moreover, we propose two Janus materials, ${\mathrm{MnBi}}_2{\mathrm{Se}}_2{\mathrm{Te}}_2$ and ${\mathrm{MnBi}}_2{S}_2{\mathrm{Te}}_2$ monolayers with different internal electric polarizations, which can realize the quantum anomalous Hall effect (QAHE) with Chern numbers $C=1$ and $C=2$, respectively. Our study not only exposes the electric field induced exotic properties of the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ monolayer but also proposes materials to realize QAHE in ferromagnetic Janus semiconductors with electric polarization.