Ultrasensitive Measurements of Magnetism in Carbon-based Materials

In this dissertation I present MRFM measurements of spin dynamics across the interfacebetween pure a diamond region and a region of densely implanted spins, which we call a `spinwire’. These measurements demonstrate that spin diffusion mediated by spin flip-flopscan be the dominant effect that determines the lifetime of spins in nanoscale volumes. Inparticular, the ability to measure nanoscale volumes illuminates the need to specify exactlywhat one means by `spin lifetime,’ which most commonly refers to T1, the ensemble spinlattice relaxation time. As the measured ensemble shrinks down to small numbers of spins,or even a single spin, the notion of spin lifetime most intuitively means the amount of timeit takes for a spin to flip from up to down. We show that on an individual-spin basis, thespin lifetime can be much less than T1.Although MRFM has reached a number of milestones, one significant capability whichhas not yet been accomplished is direct measurement of the transverse component of themagnetization. Such a capability would open MRFM to a wealth of techniques commonlyused for conventional NMR, which detects the transverse moment inductively. This capabilitywould require matching the nuclear Larmor precession frequency to the mechanicalresonance frequency, which is in the MHz regime for typical applied fields. While cantileverstypically have kHz frequencies, there are membrane mechanical resonators that have MHzfrequencies. To this end, we began MRFM studies using membranes. In this dissertationI demonstrate the first MRFM measurements of the longitudinal magnetization using amembrane resonator. I show that membranes have a number of advantages compared tocantilevers for MRFM applications, and are a promising candidate for transverse mechanicaldetection of magnetic resonance.Finally, I use the sensitive technique of cantilever magnetometry to study two-dimensionalvan der Waals materials. En route to measuring graphene, I measure de Haas van Alphenoscillations from 300 layers of graphite. These measurements demonstrate that cantilevermagnetometry is a powerful technique for interrogating the magnetism of 2D materials.