Competing multiferroic phases in monolayer and few-layer NiI$_{2}$

TL;DR

This study explores the complex multiferroic phases in monolayer and few-layer NiI$_{2}$, revealing how layer thickness and substrate effects influence magnetic and electric orders, clarifying previous debates on its multiferroicity.

Contribution

It provides a detailed theoretical analysis of layer- and geometry-dependent multiferroic phases in NiI$_{2}$, highlighting the role of competing spin interactions and anisotropy.

Findings

Multiple multiferroic phases depend on layer thickness and substrate effects.

Substrate confinement can preserve or alter magnetic symmetry and order.

Thickness influences the dominance of different spiral magnetic orders.

Abstract

A recent experiment reported type-II multiferroicity in monolayer (ML) NiI$_{2}$ based on a presumed spiral magnetic configuration (Spiral-B), which is, 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 tensile strain 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 in thicker 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 to competitions 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 NiI$_{2}$ and shed light on the role of layer-stacking-induced changes in noncollinear spin-exchange interactions and magnetic anisotropy in thickness-dependent magnetism.