Nonvolatile electrical control of valley splitting by ferroelectric polarization switching in a two-dimensional AgBiP 2 S 6 /CrBr 3 multiferroic heterostructure.

The generation and controllability of valley splitting are the major challenge in effectively utilizing valley degrees of freedom in valleytronics. Using first-principles calculations, we propose a novel multiferroic system, a AgBiP 2 S 6 /CrBr 3 van der Waals heterostructure, with ferromagnetism, ferroelectricity and ferrovalley behaviors. The ferroelectric monolayer AgBiP 2 S 6 originally has two degenerate valleys with a large spin splitting (∼423.1 meV) at the conduction band minimum of K / K ' points, due to inversion symmetry breaking combined with strong spin orbit coupling. Magnetic proximity coupling with the ferromagnetic layer CrBr 3 breaks the time-reversal symmetry, damaging the degeneracy of K / K ' valleys and causing valley splitting (∼30.5 meV). The transition energy barrier between two ferroelectric states with opposite polarization direction of the heterostructure is sufficient to prevent the spontaneous transition at room temperature, and the large intermediate barrier suggests that the ferroelectric state should be observed experimentally under ambient conditions. Nonvolatile electrical control of the valley degrees of freedom is achieved by switching the polarization direction of the ferroelectric layer in the heterostructure. The modulation of valley splitting can also be achieved by applying an external electric field and biaxial strain, as well as changing the magnetization direction. The research of nonvolatile electrical control of valley splitting in the two-dimensional AgBiP 2 S 6 /CrBr 3 multiferroic heterostructure is crucial for designing all-in-one valleytronic devices, and has important theoretical significance and practical value.