On the auto-oscillations of spin waves and the two modes model

Computer simulations of parametric excitations of spin waves are done in the frame work of the original two modes model (without adding the finite medium correction term). It is shown that h′_c , the threshold for auto-oscillations can be less than 0.2 db above h_c , the Suhl instability threshold. Moreover, the auto-oscillation is onset with a finite frequency that is smaller than 0.2γ where γ is the spin wave relaxation rate. This result reconciles two of the discrepancies between theory and experiment. The dependence of τ_d, the time delay in the excitation buildup on the pumping field h exhibits a "critical slowing down" power law: τ_d = A(h/h_c - 1)^-0.80 over a wide range of h values h_c < h < 2.2 h_c.