On the Free Energy of the Flexomagnetoelectric Interactions

TL;DR

This paper develops a four-constant phenomenological theory for the free energy of the flexomagnetoelectric effect in cubic crystals, analyzing domain wall structures and proposing experimental verification via Ne9el wall shifts under electric fields.

Contribution

It introduces a comprehensive four-constant model for flexomagnetoelectric free energy, extending previous single-constant approaches and aligning with symmetry-based predictions.

Findings

The four-constant theory accurately describes domain wall structures.

The model predicts Ne9el domain wall shifts under electric fields.

The theory conforms to established symmetry predictions.

Abstract

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.