Reversible nonvolatile control of the anomalous valley Hall effect in two-dimensional multiferroic materials based on GdGe₂

Effectively controlling the anomalous valley Hall (AVH) effect is vital for the application of valleytronics. Herein, we propose a scheme for achieving reversible nonvolatile electrical control of the AVH effect via ferroelectric (FE) polarization based on two-dimensional multiferroic materials. Monolayer GdGe₂, a ferromagnetic (FM) semiconductor with intrinsic valley polarization and monolayer In₂Se₃ possessing FE polarization were chosen to construct the GdGe₂/In₂Se₃ heterostructure. As expected, the GdGe₂/In₂Se₃ heterostructure integrates the FM semiconducting feature and ferrovalley as well as exhibits the AVH effect. Importantly, a semiconductor-to-metal transition occurs upon reversing the FE polarization of In₂Se₃, demonstrating the reversible control of the AVH effect via applying an out-of-plane electric field. A bilayer GdGe₂ homostructure was also studied. We found two stable polar stacking configurations holding multiferroic integrating ferrovalley and FE. Two polar stacking configurations with opposite FE polarization directions have the opposite AVH effect, and the signs of Hall voltage can be precisely controlled by reversing the direction of FE polarization through an electric field. Our calculations thus provide a promising strategy for achieving reversible nonvolatile control of the AVH effect and help designing novel controllable devices.