  Nonlinear magnetization dynamics excited by spin-transfer effect with
feedback current is studied both numerically and analytically. The numerical
simulation of the Landau-Lifshitz-Gilbert equation indicates the positive
Lyapunov exponent for a certain range of the feedback rate, which identifies
the existence of chaos in a nanostructured ferromagnet. Transient behavior from
chaotic to steady oscillation is also observed in another range of the feedback
parameter. An analytical theory is also developed, which indicates the
appearance of multiple attractors in a phase space due to the feedback current.
An instantaneous imbalance between the spin-transfer torque and damping torque
causes a transition between the attractors, and results in the complex
dynamics.
