On the theory of periodic solutions of the stationary Landau-Lifshitz equation

Abstract

In the phenomenological approach, quasi-one-dimensional structures in a magnet of a definite symmetry are described by solutions of the stationary Landau-Lifshitz equation or, equivalently, by the solutions of a variational problem with Lagrangian L whose actual form is determined by the requirement of invariance with respect to the symmetry group of the paramagnetic phase of the given magnet. In the present note, the methods of the variational calculus in the large are used to estimate the number of possible magnetic phases with periodic superstructure corresponding to a given free energy functional of the magnet.