  We study the spin dynamics of a long nanomagnet driven by an electrical
current. In the case of only DC current, the spin dynamics has a sophisticated
bifurcation diagram of attractors. One type of attractors is a weak chaos. On
the other hand, in the case of only AC current, the spin dynamics has a rather
simple bifurcation diagram of attractors. That is, for small Gilbert damping,
when the AC current is below a critical value, the attractor is a limit cycle;
above the critical value, the attractor is chaotic (turbulent). For normal
Gilbert damping, the attractor is always a limit cycle in the physically
interesting range of the AC current. We also developed a Melnikov integral
theory for a theoretical prediction on the occurrence of chaos. Our Melnikov
prediction seems performing quite well in the DC case. In the AC case, our
Melnikov prediction seems predicting transient chaos. The sustained chaotic
attractor seems to have extra support from parametric resonance leading to a
turbulent state.
