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A recent experiment reported type-II multiferroicity in monolayer (ML)NiI$_{2}$ based on a presumed spiral magnetic configuration (Spiral-B), whichis, as we found here, under debate in the ML limit. Freestanding ML NiI$_{2}$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 tensilestrain to the ML. This leads to another spiral magnetic order (Spiral-$IV^X$),while 2L shows a different order (Spiral-$V^Y$) and Spiral-B dominates inthicker layers. Thus, three multiferroic phases, namely, Spiral-B+FE,Spiral-$IV^X$ +FE, Spiral-$V^Y$+FE, and an anti-multiferroic AABB-AFM+AFE one,show layer-thickness-dependent and geometry-dependent dominance, ascribed tocompetitions among thickness-dependent Kitaev, biquadratic, and Heisenbergspin-exchange interactions and single-ion magnetic anisotropy. Our theoreticalresults clarify the debate on the multiferroicity of ML NiI$_{2}$ and shedlight on the role of layer-stacking-induced changes in noncollinearspin-exchange interactions and magnetic anisotropy in thickness-dependentmagnetism.

Competing Multiferroic Phases in NiI$_{2}$ Mono- and Few-layers