Microscopic origin of multiferroic order in monolayer NiI$_2$

TL;DR

This paper uncovers the microscopic mechanisms behind multiferroic order in monolayer NiI$_2$, highlighting the roles of long-range magnetic interactions, non-collinear magnetism, and spin-orbit coupling in inducing helimagnetic and ferroelectric states.

Contribution

It provides the first detailed microscopic explanation of multiferroicity in monolayer NiI$_2$, emphasizing the interplay of magnetic exchange, non-collinear magnetism, and ligand spin-orbit coupling.

Findings

Helimagnetic order arises from long-range magnetic exchange interactions.

Ferroelectric order is driven by the interplay of non-collinear magnetism and spin-orbit coupling.

Iodine spin-orbit coupling controls the ferroelectric distortion.

Abstract

The discovery of multiferroic behavior in monolayer NiI$_2$ provides a new symmetry-broken state in van der Waals monolayers, featuring the simultaneous emergence of helimagnetic order and ferroelectric order at a critical temperature of $T=21$ K. However, the microscopic origin of multiferroic order in NiI$_2$ monolayer has not been established, and in particular, the role of non-colinear magnetism and spin-orbit coupling in this compound remains an open problem. Here we reveal the origin of the two-dimensional multiferroicity in NiI$_2$ using first-principles electronic structure methods. We show that the helimagnetic state appears as a consequence of the long-range magnetic exchange interactions, featuring sizable magnetic moments in the iodine atoms. We demonstrate that the electronic density reconstruction accounting for the ferroelectric order emerges from the interplay of non-collinear magnetism and spin-orbit coupling. We demonstrate that the ferroelectric order is controlled by the iodine spin-orbit coupling, and leads to an associated electronically-driven distortion in the lattice. Our results establish the microscopic origin of the multiferroic behavior in monolayer NiI$_2$, putting forward the coexistence of helical magnetic order and ligand spin-orbit coupling as driving forces for multiferroic behavior in two-dimensional materials.