On the theory of nonlinear spin wave dynamics in ferromagnetic films (abstract)

Abstract

The aim of this work is to develop a theory of nonlinear spin waves (SW) in ferromagnetic films (FF) appropriate for description of rich nonlinear SW dynamics observed in Refs. 1 and 2. We use classical Hamiltonian formalism developed in Ref. 3 for unbounded ferromagnets in combination with the theory of dipole-exchange SW spectrum for FF.4 The main distinctions in theoretical description of nonlinear SW phenomena between the case of unbounded ferromagnet3 and the case of FF can be formulated as follows: (1) Local character of SW excitation in FF leads to the increase of threshold values for SW parametric decay processes because the parametrically excited travelling SW carry out energy from the region of pumping localization; (2) additional selection rules should be taken into account in the analysis of SW parametric processes in FF. These selection rules are determined by conservation law for the transverse component of the SW wave number. In particular, in three-wave decay of surface SW with the increase of its amplitude after degenerate decay into SW pairs having equal numbers (n, n) the nondegenerate decay into SW modes having numbers (n, n+1) takes place. This effect has been recently observed in Ref. 2; (3) three-wave and four-wave coefficients of the SW Hamiltonian function in FF turn out to be analytical functions of their arguments even in the longwave spectral region kL≪1 where the long-range dipole–dipole interaction is dominant. The analytical properties of these coefficients enable us to derive nonlinear Schrodinger equation which is used for theoretical description of SW envelope solitons formation, SW modulational instability, and formation of SW strange attractor observed in Ref. 1.