Bifurcation and chaos in spin-valve pillars in a periodic applied magnetic field

We study the bifurcation and chaos scenario of the macromagnetization 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 Li et al. [ Phys. Rev. B 74, 054417 (2006)] 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.