Solitons in the domain structure of a two-axis ferromagnet

Abstract

• New solutions of the initial-boundary problem for the Landau-Lifshitz model in the stripe domain structure of a two-axis ferromagnet are found and investigated on the basis of the Riemann problem on a torus. • The linear integral equations for analyzing the nonlinear dynamics of spin waves against the stripe structure background are obtained. • The contributions of solitons and spin waves into the spectral representation of the integrals of motion are found. We have found and investigated new solutions of the initial-boundary problem for the Landau–Lifshitz equation on the basis of the Riemann problem on a torus. They describe solitons and dispersive waves in the physically selected domain structure of a two-axis ferromagnet. We have shown, that even against a stronlgy nonlinear inhomogeneous ground state of the medium a spectral representation of the integrals of motion for arbitrary localized distribution of magnetization in the domain structure is written as a sum of independent solitons and spin waves contributions. Solitons in the domain structure are expressed in terms of the elliptic functions. Analysis of the essentially nonlinear dynamics of spin waves and their interaction with the solitons and domain structure reduces to solving linear integral equations on a torus.