Long-range magnetoelectricity in type-II multiferroic NiI₂

Type-II multiferroics, where spin order induces ferroelectricity, exhibit strong magnetoelectric coupling. However, for the typical 2D type-II multiferroic NiI₂, the underlying magnetoelectric mechanism remains unclear. Here, applying generalized spin-current model, together with first-principles calculations and a tight-binding approach, we build a comprehensive magnetoelectric model for spin-induced polarization. Such model reveals that third-nearest-neighbor spin pairs provide an unexpectedly strong contribution to the electric polarization, which rivals that of the first-nearest neighbors. Adopting such model, both experimental-detectable bound charge induced by spin-induced polarization at the spiral domain boundary, as well as polar vortex lattice induced by magnetic skyrmion lattice under moderate magnetic field, are predicted. Furthermore, by analyzing the orbital-resolved contributions to polarization, our tight-binding model reveals that the long-range magnetoelectric coupling is enabled by the strong e_g-p hopping of NiI₂. These findings can guide the identification and design of strongly magnetoelectric multiferroics.