# Two-dimensional ferromagnetic-ferroelectric multiferroics in violation of the d0 rule

## TL;DR

This paper introduces a new class of monolayer VOX2 multiferroics that combine ferroelectricity and magnetism from the same V cation, violating the d0 rule and enabling large polarization with strong magneto-electric coupling.

## Contribution

It reports monolayer VOX2 as a novel multiferroic material where ferroelectricity and magnetism originate from the same atom, violating the traditional d0 rule.

## Key findings

- VOX2 monolayers exhibit both ferroelectricity and magnetism from V cations.
- The d-orbital orientation allows ferroelectricity without hindrance.
- Large polarization and strong magneto-electric coupling are achieved.

## Abstract

Contribution of d-electron to ferroelectricity of type-II multiferroics causes strong magneto-electric coupling and distinguishes them from the conventional type-I multiferroics. However, their therein polarization is too small because the ferroelectricity is merely a derivative from the magnetic order. Here we report a new class of multiferroic materials, monolayer VOX2 (X = Cl, Br, and I), which combine the advantages of type-I and type-II multiferroics. Both ferroelectricity and magnetism arise from the same V cation, where the filled d-orbital is perpendicular to an a priori ferroelectric polarization and thus poses no hindrance to ferroelectricity, indicating a violation of the usual d0 rule. This makes the combination of large polarizations and strong magneto-electric coupling possible. Our findings not only add new ferromagnetic-ferroelectric multiferroics, but also point to a unique mechanism to engineer multiferroics.