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

Computer simulations of parametric excitations of spin waves are done in th e frame work of the original two modes model (without adding the finite med ium correction term). It is shown that h(c), the threshold for auto-oscilla tions can be less than 0.2 db above h(c), the Suhl instability threshold. M oreover, the auto-oscillation is onset with a finite frequency that is smal ler than 0.2 gamma where gamma is the spin wave relaxation rate. This resul t reconciles two of the discrepancies between theory and experiment. The de pendence of tau(d), the time delay in the excitation buildup on the pumping field h exhibits a "critical slowing down" power law: tau(d) = A(h/h(c) - 1)(-0.80) over a wide range of h values h(c) < h < 2.2 h(c).