The dependence of the auto-oscillation frequency of parametric spin waves on the pumping power and inter mode interaction strengths

Computer simulations of spin waves parametric excitations are carried out in the framework of the two modes model. The dependence of the auto-oscillation (AO) frequency, f, on the pumping amplitude h is investigated. The results support the expression of Lvov et al. for this dependence in cases when 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 the idea of Lvov et al. that auto oscillation evolves from an oscillation that is damped below h_osc and becomes self sustained at h_osc. We find that τ_CO, the decay time of AO below h_osc exhibits a critical slowing down power law: τ_CO ∝ (1 - h/h_osc)^-2.2. The dependence of f on the inter mode interaction strengths when h is constant, satisfies the expression: f = D + C/(E + 2T₁₁ + S₁₁ + 2T₁₂ + S₁₂) where D, C, and E are constants and T₁₁ T₁₂, S₁₁, and S₁₂ are the inter mode interaction strengths. 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.