Magnetically driven ferroelectricity is also caused by inhomogeneous magnetoelectric interaction. This effect appears due to the coupling between inhomogeneous order parameters. It was also called as flexomagnetoelectric effect. Usually it is describing using the Lifshitz invariant (i.e. single-constant coupling term). It was shown that in general case of cubic hexoctahedral crystal the four phenomenological constants approach is correct. The flexomagnetoelectric effect appears in spiral multiferroics or micromagnetic structures like domain walls and magnetic vortexes. Ferroelectricity developed from micromagnetic structure can appear in any magnetic material even in centrosymmetric one. Building of symmetry classification of domain walls leads to determination of the type of electric polarization rotation in volume of any magnetic domain wall. Existing symmetry classification of magnetic domain walls was applied for predictions of electric polarization spatial distribution in their volumes. The predictions for almost all symmetry groups conform with phenomenological theory in which inhomogeneous magnetization couples with homogeneous polarization. The total synergy between symmetry and phenomenological theory appears if energy terms with electrical polarization spatial derivatives are taking into account.
Read more about this topic: Multiferroics
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