On the free energy of the flexomagnetoelectric interactions

Abstract

a b s t r a c tIt 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 singleconstant 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 Né el domain walls under the strong homogeneous electric field.

Symmetry theory of the flexomagnetoelectric effect in the Bloch lines

“…Simple analysis of odd and even functions [24] shows that expressions (9a-c) give the results which correspond to the symmetry based predictions ( while Bloch DW was considered as structures with lack of the FME features [24,34,37]. So, the proposed here experimental investigation is free from the DW related FME coupling, i.e.…”

Symmetry theory of the flexomagnetoelectric interaction in the magnetic vortices and skyrmions

“…The polarization induced by the FME effect in the cubic m3 ത m crystal is described by the following four-constant expression [42]:…”

“…where "٣" defines ‫"ݔ"‬ or ‫. "ݕ"‬ The schematic illustration of the induced in-plane polarization was calculated at the γ ଷ γ ସ ൏ 0 and γ ଵ ଶ ‫ا‬ |γ ଷ γ ସ | [14,42] (Fig. 2).…”

Flexomagnetoelectric interaction in cubic, tetragonal and orthorhombic crystals

“…In the present work, we use the same group-theoretical analysis as in the Ref. [28]. The generalization of the polarization inducing scalar form [14] to the tensor form is required in case of the uniaxial and biaxial crystals:…”

“…was obtained for all possible cubic, tetragonal and orthorhombic ferriand ferromagnetic crystals (table 1). The method is the standard construction of the invariant using irreducible representations of the crystallographic point group of the crystal in the paramagnetic phase[8,13,28]. If taken into account that ‫ۻ‬ is an axial time-odd vector, the ‫۾‬ is a polar time-event vector, the action of operator ‫‬ is the analog of the multiplication on the ݇-th component of the polar time-even vector then it is possible to find invariants of the type(2), which are allowed by the magnetic symmetry group ‫ܩ‬ of the crystal in the paramagnetic phase (e.g., group ݉3 ത ݉1Ԣ in case of ݉3 ത ݉ cubic crystal, where 1Ԣ is a time reversal transformation).…”