Piezoelectric microresonators for sensitive spin detection

Piezoelectric microresonators are indispensable in wireless communications, and underpin radio frequency filtering in mobile phones. These devices are usually analyzed in the quasi-(electro)static regime with the magnetic field effectively ignored. On the other hand, at GHz frequencies and especially in piezoelectric devices exploiting strong dimensional confinement of acoustic fields, the surface magnetic fields ($B_{1}$) can be significant. This $B_1$ field, which oscillates at GHz frequencies, but is confined to ${\mu}$m-scale wavelengths provides a natural route to efficiently interface with nanoscale spin systems. We show through scaling arguments that $B_1{\propto}f^2$ for tightly focused acoustic fields at a given operation frequency $f$. We demonstrate the existence of these surface magnetic fields in a proof-of-principle experiment by showing excess power absorption at the focus of a surface acoustic wave (SAW), when a polished Yttrium-Iron-Garnet (YIG) sphere is positioned in the evanescent field, and the magnon resonance is tuned across the SAW transmission. Finally, we outline the prospects for sensitive spin detection using small mode volume piezoelectric microresonators, including the feasibility of electrical detection of single spins at cryogenic temperatures.