Moiré-Induced Magnetoelectricity in Twisted Bilayer NiI_{2}

Twisted magnetic van der Waals materials offer a promising route for multiferroic engineering, yet modeling large-scale moiré superlattices remains challenging. Leveraging a newly developed SpinGNN++ framework that effectively handles spin-lattice coupled systems, we develop a comprehensive interatomic machine learning potential and apply it to twisted bilayer NiI_{2}. Structural relaxation introduces moiré-periodic "bumps" that modulate the interlayer spacing by about 0.55 Å and in-plane ionic shifts up to 0.48 Å. Concurrently, our machine learning potential, which faithfully captures all key spin interactions, produces reliable magnetic configurations; combined with the more accurate generalized Katsura-Nagaosa-Balatsky mechanism, it delivers precise spin-driven polarization. For twist angles 1.89°≤θ≤2.45°, both mechanisms become prominent, yielding rich polarization textures that combine ionic out-of-plane dipoles with purely electronic in-plane domains. In the rigid (unrelaxed) bilayer, skyrmions are absent; lattice relaxation is thus essential for generating polar-magnetic topologies. In contrast, near θ≈60°, stacking-dependent ferroelectric displacements dominate, giving rise to polar meron-antimeron networks. These results reveal cooperative ionic and spin-driven ferroelectricity in twisted bilayer NiI_{2}, positioning twisted van der Waals magnets as adaptable platforms for tunable multiferroic devices.