  Spin-wave instability is studied analytically in the case of parallel pumping
for thin films under external field perpendicular to the film plane. It is
examined whether the instability threshold derived from only the
Landau-Lifshitz (LL) equation can explain experimental instability threshold
without using the microscopically-derived spin-wave line width, which is
conventionally used. It is revealed that the butterfly curve cannot be
explained from only the LL equation at least in an analytical way. By contrast,
for the case of perpendicular pumping, the Suhl instability was well explained
from the LL equation. The difference between the two cases comes from the
nonlinear terms describing the relaxation of spin waves. It is suggested how
the nonlinear terms in the LL equation should be related to the spin-wave line
width for parallel pumping.
