The search for effective techniques to manipulate valley logic states is crucial for the current development of valleytronics. In this study, we investigate the external electric and magnetic field controllable anomalous valley Hall effect (AVHE) in multiferroic $\mathrm{VInS}{\mathrm{e}}_3$ monolayer and bilayer using first-principles calculations. $\mathrm{VInS}{\mathrm{e}}_3$ monolayer is asymmetric ferroelectrics in which the polarization can be reversed between the ground phase with V coordinated by Se octahedron (V-O phase) and the metastable phase with tetrahedrally coordinated V (V-T phase). V-O phase possesses ferromagnetism with in-plane easy-axis, while V-T phase adopts out-of-plane easy-axis and intrinsic valley polarization. As a result, the AVHE is observed in V-T phase while absent in V-O phase, corresponding to logic states “ON” and “OFF” of AVHE. The V-T phase bilayer possesses interlayer polarization and interlayer ferromagnetism. The interlayer ferroelectric switching could control AVHE occurrence in top layer or bottom layer (layer-polarized AVHE). Magnetic field could switch the AVHE between spin-up channel and spin-down channel for both monolayer and bilayer. This approach to manipulate the AVHE by electric and magnetic field broadens the potential of multiferroics towards valleytronics and spintronics.

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• Anomalous Hall effect
• Electronic structure
• Ferromagnetism
• First-principles calculations
• Valleytronics
• 2-dimensional systems