We explore the prospects and benefits of combining the techniques of cavity optomechanics with efforts to image spins using magnetic resonance force microscopy (MRFM). In particular, we focus on a common mechanical resonator used in cavity optomechanics-high-stress stoichiometric silicon nitride (Si 3 N 4 ) membranes. We present experimental work with a 'trampoline' membrane resonator that has a quality factor above 10 6 and an order of magnitude lower mass than a comparable standard membrane resonators. Such high-stress resonators are on a trajectory to reach 0.1 aN Hz force sensitivities at MHz frequencies by using techniques such as soft clamping and phononic-crystal control of acoustic radiation in combination with cryogenic cooling. We present a demonstration of force-detected electron spin resonance of an ensemble at room temperature using the trampoline resonators functionalized with a magnetic grain. We discuss prospects for combining such a resonator with an integrated Fabry-Perot cavity readout at cryogenic temperatures, and provide ideas for future impacts of membrane cavity optomechanical devices on MRFM of nuclear spins.

We present techniques to model and design membrane phononic crystals with low-mass defects, optimized for force sensing. Further, we identify the importance of the phononic crystal mass contrast as it pertains to the size of acoustic bandgaps and to the dissipation properties of defect modes. In particular, we quantify the tradeoff between high mass contrast phononic crystals with their associated robust acoustic isolation, and a reduction of soft clamping of the defect mode. We fabricate a set of phononic crystals with a variety of defect geometries out of high stress stoichiometric silicon nitride membranes, and measured at both room temperature and 4 K in order to characterize the dissipative pathways across a variety of geometries. Analysis of these devices highlights a number of design principles integral to the implementation of low-mass, low-dissipation mechanical modes into optomechanical systems.