  We study the bifurcation and chaos scenario of the macro-magnetization vector
in a homogeneous nanoscale-ferromagnetic thin film of the type used in
spin-valve pillars. The underlying dynamics is described by a generalized
Landau-Lifshitz-Gilbert (LLG) equation. The LLG equation has an especially
appealing form under a complex stereographic projection, wherein the
qualitative equivalence of an applied field and a spin-current induced torque
is transparent. Recently chaotic behavior of such a spin vector has been
identified by Zhang and Li using a spin polarized current passing through the
pillar of constant polarization direction and periodically varying magnitude,
owing to the spin-transfer torque effect. In this paper we show that the same
dynamical behavior can be achieved using a periodically varying applied
magnetic field, in the presence of a constant DC magnetic field and constant
spin current, which is technically much more feasible, and demonstrate
numerically the chaotic dynamics in the system for an infinitely thin film.
Further, it is noted that in the presence of a nonzero crystal anisotropy field
chaotic dynamics occurs at much lower magnitudes of the spin-current and DC
applied field.
