Comment on "Ferroelectrically Induced Weak Ferromagnetism by Design", C. Fennie, PRL 100, 167203 (2008)

TL;DR

This paper critiques a previous analysis on magnetoelectric coupling in ABO3 multiferroics, showing that multiple distortions can enable coupling even when only one distortion breaks inversion symmetry.

Contribution

It provides a simplified analysis demonstrating that multiple distortions can generate magnetoelectric coupling in ABO3 multiferroics, challenging prior conclusions.

Findings

Multiple distortions enable magnetoelectric coupling.

Cross-terms in distortions generate coupling.

Guidelines for optimizing coupling in ABO3 materials.

Abstract

The question of how ferroelectric polarization is coupled to magnetism in magnetoelectric multiferroics, in which both types of order are simultaneously present, is of considerable scientific and practical interest. A recent Letter \cite{fennie} presents an analysis of the important ``ABO$_3$'' class of perovskite multiferroics. This Letter argues that antiferromagnetic multiferroics with magnetic ions on the B site, such as the well-studied room-temperature multiferroic bismuth ferrite (A=Bi, B=Fe), cannot show linear magnetoelectric coupling of the form ${\bf P} \cdot ({\bf L} \times {\bf M})$. Here ${\bf P}$ is polarization and ${\bf L}$ and ${\bf M}$ are antiferromagnetic and ferromagnetic moments. The conclusion of Ref. \onlinecite{fennie} is that only materials with magnetic A-site have this coupling. This Comment presents a compact analysis of magnetoelectric coupling in the ABO$_3$ multiferroics. We show that the argument of Ref. \onlinecite{fennie} does forbid $E_{PLM}$ if the final low-symmetry phase contains only one distortion that, like ${\bf P}$, breaks all inversion symmetries. In reality, there are multiple distortions in this symmetry class, and cross-terms generate $E_{PLM}$. Our analysis gives simple conclusions about existence and optimization of magnetoelectric coupling in ABO$_3$ materials.