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

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