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

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 $\mathbf{P}\cdot (\mathbf{L}\times \mathbf{M})$. Here $\mathbf{P}$ is polarization and $\mathbf{L}$ and $\mathbf{M}$ 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 $\mathbf{P}$, 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.

Published version (4 pages, including supplementary information)

References in corpus (4)

• Weak ferromagnetism and magnetoelectric coupling in bismuth ferrite
• Origin of magnetoelectric behavior in BiFeO${}_3$
• Ferroelectrically induced weak-ferromagnetism in a single-phase multiferroic by design
• Electric-field switchable magnetization via the Dzyaloshinskii-Moriya interaction: FeTiO_3 versus BiFeO_3

Cited by in corpus (5)

• Electric-field control of spin waves at room temperature in multiferroic BiFeO3
• Theory of spin-orbit enhanced electric-field control of magnetism in multiferroic BiFeO3
• High frequency susceptibility of a weak ferromagnet with magnetostrictive magnetoelectric coupling: using heterostructures to tailor electromagnon frequencies
• Toroidal moments as indicator for magneto-electric coupling: the case of BiFeO_3 versus FeTiO_3
• A coupled magneto-structural continuum model for multiferroic ${\mathrm{BiFeO}}_3$