Stacking-engineering magnetoelectric coupling effects in van der Waals type-I multiferroics

Multiferroic materials have attracted significant attention for their potential applications in multifunctional spintronic devices. However, conventional multiferroics exhibit limited magnetoelectric coupling, as the magnetic and ferroelectric orders typically arise from distinct and incompatible mechanisms. In this study, we introduce a specific theoretical approach to magnetoelectric coupling that capitalizes on the intrinsic tunability of two-dimensional (2D) materials. Taking the prototypical 2D magnet CrI3 as an example, we demonstrate the following issues: (i) the easy magnetization axis of anti-aligned bilayer CrI3 exhibits an inherent inclination, attributed to crystalline symmetry breaking as determined by interlayer shifts; and (ii) spontaneous sliding ferroelectricity emerges, wherein the reversal of polarization signifies a phase transition between energetically preferable states. These findings reveal a strong interplay among magnetization, polarization, and layer degree of freedom, establishing a stacking-engineering mechanism for multiferroic modulations, further offering innovative insights into realizing magnetoelectric coupling effects and multi-state control paradigm in type-I multiferroic systems.