Strain-modulated magnetic droplet precession in spin-torque nano-oscillators

In this paper, we present a promising method for modulating the frequency of magnetic droplets using strain induced by an adjacent piezoelectric layer. This strain results in significant changes in droplet frequency (∼6 GHz) and variations in diameter or mode, while maintaining a fixed current density of 1.4×10^{12}A/m^{2} under both high and low fields. By applying strain pulses, we successfully modulate the magnetic droplet frequency, paving the way for potential implementation of digital binary frequency shift-keying modulation technique with magnetic droplets. Moreover, the effects of Oersted field and the Zhang-Li torque induced by lateral current have also been discussed, showing a minimal impact on the oscillation frequencies, especially at high fields.