Controlling the anomalous valley Hall (AVH) effect by external means is crucial for valleytronic devices in practical applications; however, most of the previously proposed control approaches are either irreversible or volatile. Here, we present a general scheme for achieving nonvolatile electrical control of the AVH effect based on multiferroic van der Waals heterostructure. Using density functional theory calculations and $\mathit{k}·\mathit{p}$ model analysis, we further demonstrate the feasibility of this design principle by stacking ferromagnetic monolayer $\mathrm{V}{\mathrm{Se}}_2$ on ferroelectric monolayer ${\mathrm{Al}}_2{\mathrm{S}}_3$. The reversible switching of AVH can be finely manipulated by reversing the ferroelectric polarization of ${\mathrm{Al}}_2{\mathrm{S}}_3$ via electric field. The regulated AVH state of $\mathrm{V}{\mathrm{Se}}_2$ can be stably preserved due to the ferroelectric nonvolatility of ${\mathrm{Al}}_2{\mathrm{S}}_3$. In addition, the sign of valley polarization can be simultaneously inverted by reversing ferroelectric polarization. Our results not only provide the basis for an intrinsic ferroelectricity controlled ferrovalley, but also uncover an outstanding candidate for realizing bidirectional and nonvolatile switching valleytronic devices.

• Received 18 May 2023
• Revised 4 September 2023
• Accepted 3 October 2023

DOI:https://doi.org/10.1103/PhysRevB.108.155431