Engineering Layertronics in Two-Dimensional Ferromagnetic Multiferroic Lattice.

Layertronics, rooted in the layer Hall effect (LHE), is an emerging fundamental phenomenon in condensed matter physics and spintronics. So far, several theoretical and experimental proposals have been made to realize LHE, but all are based on antiferromagnetic systems. Here, using symmetry and tight-binding model analysis, we propose a general mechanism for engineering layertronics in a two-dimensional ferromagnetic multiferroic lattice. The physics is related to the band geometric properties and multiferroicity, which results in the coupling between Berry curvature and layer degree of freedom, thereby generating the LHE. Using first-principles calculations, we further demonstrate this mechanism in bilayer (BL) TcIrGeS. Due to the intrinsic inversion and time-reversal symmetry breakings, BL TcIrGeS exhibits multiferroicity with large Berry curvatures at both the center and corners of the Brillouin zone. These Berry curvatures couple with the layer physics, forming the LHE in BL TcIrGeS. Our work opens a new direction for research on layertronics.