On the transient and stationary parametric excitation of spin waves

Buildup times and the stationary values of spin wave excitations near the S uhl instability threshold are calculated numerically. The study is done in the framework of the two-mode model. The time evolution of the excitation m ay approach the steady state via oscillations that may last for a very long time. The stationary excitation N-0, and the buildup time tau(b) depend on the pumping power p, and the pumping field h via power laws: N-0 = B(p/p(c ) - 1)(delta) and tau(b) = A(h/h(c) - 1)(-Delta). For the case of no de-tun ing of the mode frequencies from omega(p)/2, delta = 0.5 and Delta = 0.98. In the case of modes that are de-tuned from omega(p)/2, delta = 0.42 and De lta = 1.1. The values for delta are consistent with experiments but the val ues for delta are in bad agreement with experiment. It is shown that if a f inite medium correction term is introduced into the equations of motion the threshold of the pumping field amplitude is below gamma/V where gamma is t he spin wave relaxation rate and V is the coupling of the spin waves to the pumping field. This result is very strange and raises serious doubts about the justification of the finite medium correction term. (C) 1999 Published by Elsevier Science B.V. All rights reserved.