On the transient and stationary parametric excitation of spin waves

Buildup times and the stationary values of spin wave excitations near the Suhl instability threshold are calculated numerically. The study is done in the framework of the two-mode model. The time evolution of the excitation may approach the steady state via oscillations that may last for a very long time. The stationary excitation N₀, and the buildup time τ_b depend on the pumping power p, and the pumping field h via power laws: N₀ = B(p/p_c - 1)^δ and tau_b = A(h/h_c - 1)^-Δ. For the case of no de-tuning of the mode frequencies from ω-p$//2, δ = 0.5 and Δ = 0.98. In the case of modes that are de-tuned from ω-p$//2, δ = 0.42 and Δ = 1.1. The values for δ are consistent with experiments but the values for Δ are in bad agreement with experiment. It is shown that if a finite medium correction term is introduced into the equations of motion the threshold of the pumping field amplitude is below γ/V where γ is the spin wave relaxation rate and V is the coupling of the spin waves to the pumping field. This result is very strange and raises serious doubts about the justification of the finite medium correction term.