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 (V.G. Bar'yakhtar et al., 1984). The proposed experimental verification of the four-constant flexomagnetoelectric phenomenology is a detection of the shift of the N\'eel domain walls under the strong homogeneous electric field. 
B. M. Tanygin
cond-mat.mtrl-sci