# Frustrated Dipole Order Induces Noncollinear Proper Ferrielectricity in Two Dimensions

## TL;DR

This paper predicts a new type of noncollinear ferrielectricity in two-dimensional dioxydihalides, driven by frustrated dipole interactions, leading to unique topological and physical properties.

## Contribution

It introduces a theoretical prediction of noncollinear ferrielectricity in 2D materials induced by competing soft modes, a phenomenon rarely observed in electric dipole systems.

## Key findings

- Presence of $ ext{Z}_2 imes ext{Z}_2$ topological domains
- Atomic-scale dipole vortices
- Negative piezoelectricity observed

## Abstract

Within Landau theory, magnetism and polarity are homotopic, displaying a one-to-one correspondence between most physical characteristics. However, despite widely reported noncollinear magnetism, spontaneous noncollinear electric dipole order as ground state is rare. Here a dioxydihalides family is predicted to display noncollinear ferrielectricity, induced by competing ferroelectric and antiferroelectric soft modes. This intrinsic noncollinearity of dipoles generates unique physical properties, such as $\mathbb{Z}_2\times\mathbb{Z}_2$ topological domains, atomic-scale dipole vortices, and negative piezoelectricity.