Microscopic origin of magnetoferroelectricity in monolayer NiBr${}_2$ and NiI${}_2$

Abstract

We investigate the magnetoelectric properties of the monolayer NiX${}_2$ (X = Br, I) through first-principles calculations. Our calculations predict that the NiBr${}_2$ monolayer exhibits a cycloidal magnetic ground state. For the NiI${}_2$ monolayer, a proper-screw helical magnetic ground state with modulation vector \(\boldsymbol{Q} = (q, 0, 0)\) is adopted, approximated based on experimental observations. The electric polarization in NiBr${}_2$ shows a linear dependence on the spin-orbit coupling strength \(λ_{\text{SOC}}\), which can be adequately described by the generalized Katsura-Nagaosa-Balatsky (gKNB) model, considering contributions from up to the third nearest-neighbor spin pairs. In contrast, the electric polarization in NiI${}_2$ exhibits a distinct dependence on \(q\) and \(λ_{\text{SOC}}\), which cannot be fully explained by the gKNB mechanism alone. To address this, the \(p\)-\(d\) hybridization mechanism is extended to NiI${}_2$ to explain the observed behavior. The respective contributions from the \(p\)-\(d\) hybridization and the gKNB mechanism in NiI${}_2$ are then quantitatively evaluated. Overall, our work elucidates the microscopic mechanisms underlying multiferroicity in NiBr${}_2$ and NiI${}_2$ monolayers, with the conclusions readily applicable to their bulk forms.