Gate-controllable quadri-layertronics in a 2D multiferroic antiferromagnet

Layertronics systems that manifest the layer Hall effect are typically considered to intrinsically exhibit binary physics. Using symmetry arguments and a low-energy k·p model, we show that the layer physics in layertronics can be engineered into a quaternary mode, giving rise to the concept of quadri-layertronics. The mechanism correlates to the interplay between out-of-plane ferroelectricity and valley physics in an antiferromagnetic multiferroic quadrilayer, which enables layer-locked Berry curvature and the Hall effect, i.e., deflecting the carriers with four different layer physics to move in specific directions. More importantly, quadri-layertronics can be generated and manipulated by controlling interlayer dipole arrangements via gate voltage, allowing for the selective induction and detection of the layer Hall effect in specific layers. Using first-principles calculations, we further demonstrate the gate control of quadri-layertronics in the multiferroic antiferromagnet of quadrilayer OsCl₂. These explored phenomena and insights greatly enrich our understanding of layertronics.