  We predict frequency multiplication of surface acoustic waves in dielectric
substrates via the ferromagnetic resonance of adjacent magnetic transducers
when driven by microwaves. We find pure second harmonic generation (SHG)
without any linear and third harmonic components by a magnetic nanowire. The
SHG and linear phonon pumping are switched by varying the saturated
magnetization direction of the wire, or resolved directionally when pumped by
magnetic nano-disc. We address the high efficiency of SHG with comparable
magnitude to that of linear response, as well as unique non-reciprocal phonon
transport that is remarkably distinct in different phonon harmonics. Such
acoustic frequency comb driven by microwaves should bring unprecedented
tunability for the miniaturized phononic and spintronic devices.
