There is a profound analogy between inhomogeneous magnetoelectric effect in multiferroics and flexoelectric effect in liquid crystals. This similarity gives rise to the flexomagnetoelectric polarization induced by spin modulation. The theoretical estimations of flexomagnetoelectric polarization agree with the value of jumps of polarization in magnetoelectric dependences (~20muC/m^2) observed at spin cycloid suppression at critical magnetic field 200kOe.
@article{arxiv.0811.3677,
title = {Flexomagnetoelectric effect in bismuth ferrite},
author = {A. K. Zvezdin and A. P. Pyatakov},
journal= {arXiv preprint arXiv:0811.3677},
year = {2012}
}