  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.
