Competing multiferroic phases in monolayer and few-layer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Ni</mml:mi><mml:msub><mml:mi mathvariant="normal">I</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

Abstract

A recent experiment reported type-II multiferroicity in monolayer (ML) $\mathrm{Ni}{\mathrm{I}}_{2}$ based on a presumed spiral magnetic configuration (spiral-B), which is, as we found here, under debate in the ML limit. Freestanding ML $\mathrm{Ni}{\mathrm{I}}_{2}$ breaks its ${C}_{3}$ symmetry, as it prefers a striped antiferromagnetic order (AABB-AFM) along with an intralayer antiferroelectric (AFE) order. However, substrate confinement may preserve the ${C}_{3}$ symmetry and/or apply tensile strain to the ML. This leads to another spiral magnetic order ($\mathrm{spiral}\ensuremath{-}\mathrm{I}{\mathrm{V}}^{X}$), while bilayer shows a different order ($\mathrm{spiral}\ensuremath{-}{\mathrm{V}}^{X}$) and spiral-B dominates in thicker layers. Thus, three multiferroic phases, namely, spiral-B+FE, $\mathrm{spiral}\ensuremath{-}\mathrm{I}{\mathrm{V}}^{X}+\mathrm{FE}, \mathrm{spiral}\ensuremath{-}{\mathrm{V}}^{X}+\mathrm{FE}$, and an antimultiferroic AABB-AFM+AFE one, show layer thickness dependence and geometry-dependent dominance, ascribed to competition among thickness-dependent Kitaev, biquadratic, and Heisenberg spin-exchange interactions and single-ion magnetic anisotropy. Our theoretical results clarify the debate on the multiferroicity of ML $\mathrm{Ni}{\mathrm{I}}_{2}$ and shed light on the role of layer stacking induced changes in noncollinear spin-exchange interactions and magnetic anisotropy in thickness-dependent magnetism.

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