Instabilities of spin waves in parallel-pumped easy plane ferromagnets

Abstract

By applying the S-theory formalism of Zakharov et al. to a microscopic hamiltonian with uniaxial easy plane anisotropy, we arrive at a set of equations for the system that describe the spin waves and their mutual interactions. The parameters in the theory are related to the various interaction constants of the microscopic hamiltonian. Numerical studies of this system of equations indicate that the stationary states are ones where all spin-wave pair correlation functions have the same phase. The phenomenon of phase locking is universal, independent of the mode of approach to equilibrium. It is found that there is no dependence on the number of modes (up to 100) for the above behavior. This, together with the form of the equations, indicates that a similar result should hold for a macroscopic number of modes. Results for the stationary magnon population are presented. In the phase-locked regime, the approach to a stationary state is governed by a pair of coupled first-order differential equations. Linearizing these equations about the stationary points, we find that the approach to equilibrium involves purely exponential decay just above threshold, and, at higher power levels, we have damped oscillatory decay.