Electric-field induced magnetic-anisotropy transformation to achieve spontaneous valley polarization

Valleytronics has been widely investigated for providing new degrees of freedom to future information coding and processing. Here, it is proposed that valley polarization can be achieved by electric field induced magnetic anisotropy (MA) transformation. Through first-principles calculations, our idea is illustrated by a concrete example of a VSi2P4 monolayer. The increasing electric field can induce an in-plane to out-of-plane transition of MA by changing magnetic anisotropy energy (MAE) from a negative to a positive value, which is mainly due to the increasing magnetocrystalline anisotropy (MCA) energy. The out-of-plane magnetization is in favour of spontaneous valley polarization in VSi2P4. Within the considered electric field range, VSi2P4 is always in the ferromagnetic (FM) ground state. In a certain range of the electric field, the coexistence of semiconductivity and out-of-plane magnetization makes VSi2P4 a true ferrovalley (FV) material. The anomalous valley Hall effect (AVHE) can be observed under an in-plane and out-of-plane electrical field in VSi2P4. Our studies pave the way in the design of ferrovalley materials using an electric field.