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In this article the mechanism of the linear magnetoelectric (ME) effect inthe rhombohedral multiferroic BiFeO$_3$ is considered. The study is based onthe symmetry approach of the GinzburgLandau type, in which polarization,antiferrodistortion, and antiferromagnetic momentum vectors are viewed asordering parameters. We demonstrate that the linear ME effect in BFO is causedby reorientation of the antiferrodistortion vector in either electric ormagnetic field. The numerical estimations, which show quantitative agreementwith the results of the recent measurements in film samples, have beenperformed. A possibility of significant enhancement of the magnetoelectriceffect by applying an external static electric field has been investigated. Theconsidered approach is promising for explaining the high values of the MEeffect in composite films and heterostructures with BFO.

Origin of the giant linear magnetoelectric effect in perovskite-like multiferroic BiFeO$_3$