  We investigate the nonlinear dynamics underlying the evolution of a 2-D
nanoscale ferromagnetic film with uniaxial anisotropy in the presence of
perpendicular pumping. Considering the associated Landau-Lifshitz spin
evolution equation with Gilbert damping together with Maxwell equation for the
demagnetization field, we study the dynamics in terms of the stereographic
variable. We identify several new fixed points for suitable choice of external
field in a rotating frame of reference. In particular, we identify explicit
equatorial and related fixed points of the spin vector in the plane transverse
to the anisotropy axis when the pumping frequency coincides with the amplitude
of the static parallel field. We then study the linear stability of these novel
fixed points under homogeneous and spin wave perturbations and obtain a
generalized Suhl's instability criterion, giving the condition for exponential
growth of P-modes under spin wave perturbations. Two parameter phase diagrams
(in terms of amplitudes of static parallel and oscillatory perpendicular
magnetic fields) for stability are obtained, which differ qualitatively from
those for the conventional ferromagnetic resonance near thermal equilibrium and
are amenable to experimental tests.
