2002, Vol.5, No.3, pp.240-249

Computer simulations of spin waves parametric excitations are carried out in the framework of the two modes model. The dependence of the auto-oscillation frequency, f, on the pumping amplitude h is investigated. The results support the L'vov et.al.'s expression for this dependence in cases where the parametric excitation threshold, h_th is very close to the auto-oscillation threshold h_osc. In cases when h_osc is considerably larger than h_th a much better fit is obtained to a slightly modified expression: f = f₀ +B([ h /h_osc ] ² -1)^0.5 where f₀ is the onset frequency and B is a constant. Support is given to L'vov et.al's idea that auto oscillation evolves from an oscillation that is damped below h_osc and becomes self sustained at h_osc. We find that , the decay time of this oscillation is critically dependent on h and exhibits a critical slowing down power law: = A(1- h/h_osc)^-1.6 where A is a constant. The dependence of f on the inter mode interaction strengths when h is constant, satisfies the expression: f = D+C /(E+2T₁₁+ S ₁₁ + 2T₁₂+ S₁₂) where D, C, and E are constants and T₁₁, T₁₂, S₁₁, and S ₁₂ are the inter mode interaction strengths in the two modes model. This result supports the conjecture that the dependence of the auto-oscillation frequency on the physical parameters is very similar to that of N₀, the steady state value of the total number of parametric excitations.
Key words: Nonlinear spinwaves excitation; Parametric excitation; Two modes model; Auto-oscillations.

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