Microscopic theory of spin-wave instabilities in parallel-pumped easy-plane ferromagnets

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Abstract
Spin-wave instabilities in parallel-pumped easy-plane ferromagnets are investigated using the S-theory formalism of Zakharov et al. The parameters in the theory are related to the interaction constants in a microscopic Hamiltonian with exchange anisotropy. A numerical study of two- and five-mode systems shows that the nonequilibrium stationary states are ones where all of the spin-wave pair correlation functions have the same phase. It is also found that the phases lock to a common value before the stationary state is reached. From the form of the equations it is argued that a similar result holds for a macroscopic number of modes. Results are presented for the stationary magnon population. The approach to a stationary state in the phase-locked regime is governed by two coupled first-order differential equations. When the equations are linearized about the fixed points, it is found that the approach to the stationary state involves purely exponential decay just above threshold and damped oscillatory decay at higher power levels. Possible experimental tests of the theory are discussed.