POSSIBLE MECHANISM FOR LIMITING THE NUMBER OF MODES IN SPIN-WAVE INSTABILITIES IN PARALLEL PUMPING

Recent numerical studies of chaotic dynamics in magnetic systems have featured a small number of interacting modes. By applying the S-theory formalism of Zakharov et al., we derive a set of dynamical equations that govern the behavior of the spin waves and their interactions for an easy-plane ferromagnet and an orthorhombic antiferromagnet under parallel-pumping conditions. All parameters in these equations are expressed in terms of the interaction constants of their respective microscopic Hamiltonian. Two distinguishing results follow from the analytical and numerical studies of these equations. First, the system tends to equilibrium states where only modes in a degenerate manifold are excited. The total population in this manifold is described by an analytic expression, but the individual occupation numbers are dependent on the initial conditions. Second, within this manifold, all spin-wave pair-correlation functions attain a common phase before the system reaches equilibrium. We refer to this phenomenon as "phase locking." In the presence of phase locking, we show that the approach to equilibrium for macroscopic number of modes is described by a pair of coupled first-order differential equations. These two results offer a possible mechanism for the reduction in the effective number of modes that could be used to describe such systems. © 1990 The American Physical Society.