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Synchronization and chaos caused by alternating current and microwave fieldin a spin torque oscillator consisting of a perpendicularly magnetized freelayer and an in-plane magnetized reference layer is comprehensively studiedtheoretically. A forced synchronization by the alternating current is observedin numerical simulation over wide ranges of its amplitude and frequency. Ananalytical theory clarifies that the nonlinear frequency shift, as well as thespin-transfer torque asymmetry, plays a key role in determining locking rangeand phase difference between the oscillator and current. Chaos caused by thealternating current is identified for a region of large alternating current byevaluating the Lyapunov exponent. Similar results are also obtained formicrowave field, although the parameter regions causing chaos are narrower thanthose by the alternating current.

Synchronization and chaos in a spin-torque oscillator with a perpendicularly magnetized free layer