Micromagnetic structures: flexomagnetoelectric coupling point symmetry and Neumann's principle

TL;DR

This paper explains how symmetry principles, especially Neumann's principle, underpin the prediction and calculation of flexomagnetoelectric effects in micromagnetic structures, bridging qualitative symmetry analysis with quantitative equilibrium state computations.

Contribution

It provides a formal mathematical justification for using symmetry-based descriptions to accurately compute equilibrium distributions of magnetization and polarization in micromagnetic structures.

Findings

Symmetry-based approach predicts electric polarization distribution.

Neumann's principle applied to real micromagnetic structures.

Formal link established between symmetry and quantitative calculations.

Abstract

Recent series of articles (B.M. Tanygin, 2011-2012) has been aimed to study flexomagnetoelectric properties of magnetically ordered crystals by means of a magnetic point symmetry description. Besides its fundamental interest (complete symmetry classification), applications to a classical micromagnetic variational problem of a thermodynamically equilibrium state calculation had been provided without a proof. It was shown that the magnetic point symmetry group determination of the given micromagnetic structure could be used to predict qualitatively the electric polarization distribution induced by a flexomagnetoelectric coupling. This article is an important addendum which provides a formal mathematical explanation why and how a symmetry-based description of flexomagnetoelectric phenomena conforms to a quantitative calculation of an equilibrium state of a magnetization and electrical polarization vectors spatial distribution. An application of the Neumann's principle and a group-theoretical methodology to real micromagnetic structures is clarified as well. The well-known role of a symmetry-based approach in new interactions and phenomena discoveries has been discussed.