Phase-locking of multiple magnetic droplets by a microwave magnetic field

Manipulating dissipative magnetic droplet is of great interest for both the fundamental and technological reasons due to its potential applications in the high frequency spin-torque nano-oscillators. In this paper, a magnetic droplet pair localized in two identical or non-identical nano-contacts in a magnetic thin film with perpendicular anisotropy can phase-lock into a single resonance state by using an oscillating microwave magnetic field. This resonance state is a little away from the intrinsic precession frequency of the magnetic droplets. We found that the phase-locking frequency range increases with the increase of the microwave field strength. Furthermore, multiple droplets with a random initial phase can also be synchronized by a microwave field.