Fractional Synchronization of Spin-Torque Nano-Oscillators

We experimentally demonstrate a series of fractional synchronization regimes (Devil's staircase) in a spin-torque nano-oscillator driven by a microwave field. These regimes are characterized by rational relations between the driving frequency and the frequency of the oscillation. An analysis based on the phase model of auto-oscillator indicates that fractional synchronization becomes possible when the driving signal breaks the symmetry of the oscillation, while the synchronization ranges are determined by the geometry of the oscillation orbit. Measurements of fractional synchronization can be utilized to obtain information about the oscillation characteristics in nanoscale systems not accessible to direct imaging techniques.