  Synchronization and chaos caused by alternating current and microwave field
in a spin torque oscillator consisting of a perpendicularly magnetized free
layer and an in-plane magnetized reference layer is comprehensively studied
theoretically. A forced synchronization by the alternating current is observed
in numerical simulation over wide ranges of its amplitude and frequency. An
analytical theory clarifies that the nonlinear frequency shift, as well as the
spin-transfer torque asymmetry, plays a key role in determining locking range
and phase difference between the oscillator and current. Chaos caused by the
alternating current is identified for a region of large alternating current by
evaluating the Lyapunov exponent. Similar results are also obtained for
microwave field, although the parameter regions causing chaos are narrower than
those by the alternating current.
