Nonlinear self-localized surface spin waves in ferromagnets (abstract)

Abstract

It is well known that in linear theory, surface spin waves (SW) do not exist in a pure exchange-coupled ferromagnet for the case of free spins at the surface. However, in these approximations of the linear theory the plane volume spin waves (VW), propagating along the surface of a ferromagnet, satisfies not only the Landau–Lifshitz equation for the magnetization motion, but the boundary conditions for the free surface spins. Such VW can be unstable and can be transformed into SW under small changes of a magnetic medium, e.g., if the surface spins are partly pinned. In the present work a new type of self-localized SW in the ferromagnet has been considered. The existence of such waves is conditioned entirely by the nonlinear properties of a ferromagnet. The penetration length of such SW is proportional to 1/A, where A is a maximum of the magnetization amplitude on the surface of the crystal. The dispersion equations have been obtained for pure exchange and dipole-exchange nonlinear SW. In the latter case the influence of the second harmonic generation on the wave propagation at the fundamental frequency was studied. The conditions when the SW excites the VW, carrying the energy into the volume of the crystal, are derived. The nonlinear Schrödinger equation for the SW envelope amplitude was derived and its solitonic solutions are obtained. The estimations of threshold values for the wave numbers of the propagating waves are provided.