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Non-linear instabilites of spin waves in parallel-pumped easy plane ferromagnets
Starting from a microscopic Hamiltonian that describes an easy plane ferromagnet under the influence of external static and microwave fields parallel to one another, we arrive at a set of equations governing the behavior of the spin waves and their mutual interactions. The S-theory formalism of Zakharov et al. was applied to this end. Unlike previous studies where the parameters were chosen ad hoc, the parameters in our case are related to the various interaction constants of the microscopic Hamiltonian. Two important results follow from the analytical and numerical studies of this system of equations. The first is that the system tends to equilibrium states where only modes in a degenerate manifold are excited. The total population of this manifold is given by an analytic expression but the individual occupation numbers are dependent on initial conditions. Secondly, within this manifold, all spin wave pair correlation functions have the same phase. This 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 (to over 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. These two results offer a possible mechanism for the reduction in the effective number of modes that could be used to describe such systems. Results for the stationary magnon population are presented for our case. 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. There is some experimental evidence for this behavior. These results are shown to hold for orthorhombic antiferromagnets as well.