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 = f 0 + B ([ h / h osc ] 2 –1) 0.5 where f 0 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 + 2 T 11 + S 11 + 2 T 12 + S 12 ) where D , C , and E are constants and T 11 , T 12 , S 11 , and S 12 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 N 0 , the steady state value of the total number of parametric excitations.