Orbital Longitudinal Magnetoelectricity in Quasi-2D Parity-Violating Antiferromagnets: Interplay of Berry Phase and Stacking Order

Abstract: The magnetoelectric (ME) effect traditionally arises from complex spin-orbital interactions in multiferroic materials. In this work, we propose a distinct, intrinsic mechanism for the magnetoelectric effect in quasi-2D magnetic systems that lack spatial inversion symmetry. We demonstrate that in such parity-violating magnets, the stacking order, which id coupled with Berry curvature and orbital magnetic moment, generates a stacking Berry curvature dipole (SBCD) and a stacking orbital magnetic moment dipole (SOMD). The SBCD and SOMD act as fundamental ingredients of the ME response. As concrete examples, we apply our framework to antiferromagnets such as monolayer Ca(CoN)$_2$ and multilayer MnBi$_2$Te$_4$ with stacking magnetic orders. Our results reveal the microscopic orbital origin of the ME effect in antiferromagnetic systems with vanishing net Berry curvature and orbital magnetization, governed by the interplay between layer stacking, Berry curvature, and magnetic order. The SBCD is also identified as the origin of electric-field-induced Hall effects.