Yv. Gulyaev et al., PARAMETRIC-EXCITATION OF SPIN-WAVES IN FERROMAGNETS BY LONGITUDINAL PUMPING LOCALIZED IN-SPACE, Journal of experimental and theoretical physics, 84(1), 1997, pp. 109-119
The equations of motion for the slowly varying complex amplitudes of s
pin waves parametrically excited by a localized pumping magnetic field
have been derived. A solution of these equations satisfying given bou
ndary and initial conditions has been obtained. The energy dissipated
by spin waves decreases with the pumping intensity beyond a certain pu
mping power, which can be termed the regeneration threshold. The losse
s vanish and change sign at the instability threshold. Both thresholds
depend heavily on the linear dimension L of the pumping zone, increas
ing with decreasing L. Owing to the regeneration process, the dissipat
ion length of spin waves increases without bound as the pumping power
approaches the instability threshold. Consequently, perturbations of a
uniform state due to the boundary penetrate throughout the pumping zo
ne, regardless of the dimension L. As a result, the full pattern of pa
rametric instability is strongly affected by the zone boundary: 1) the
spatial distribution of wave amplitudes becomes nonuniform everywhere
inside the zone; 2) the amplitude growth rate in the unstable regime
decreases at all points when perturbations due to the boundary reach t
hese points; 3) the instability threshold is independent of the spin-w
ave frequency offset from the parametric resonance frequency. The calc
ulated minimum instability threshold as a function of the bias magneti
c field (the ''butterfly'' curve) changes shape with L, in agreement w
ith the available experimental data. (C) 1997 American Institute of Ph
ysics.