On the free energy of the flexomagnetoelectric interactions

It was shown that free energy density of the local flexomagnetoelectric effect is determined by the four phenomenological constants in case of the cubic (hexoctahedral) crystal. The well-known single-constant Lifshitz invariant term is correct only when fixed electric polarization induces the inhomogeneity of the magnetization. Proposed phenomenological theory was applied to the magnetic domain walls. The domain wall structure has been investigated in details. The four-constant phenomenological theory conforms to the symmetry based predictions (Bar'yakhtar et al., 1984, [12]). The proposed experimental verification of the four-constant flexomagnetoelectric phenomenology is a detection of the shift of the Néel domain walls under the strong homogeneous electric field.

► Symmetry based predictions not completely conform to the single-constant phenomenology of the flexomagnetoelectric effect.
► Symmetry based predictions completely conform to the four-constant phenomenology.
► It was shown that four-constant description is more general.
► Flexomagnetoelectric effect can induce polarization component along the domain wall normal.
► The experimental verification of the new theory is the shift of the Néel domain walls under the strong homogeneous electric field.