Force-Detected NMR Study of Single-Crystal MgB$_2$ using Ultrasensitive Oscillators*

MgB$_2$ is a unique superconductor with a relatively high $T_c$ and two nearly independent electronic bands. An NMR study of $^{11}$B in MgB$_2$ using polycrystalline samples [1] did not observe any two-band effects, nor a Hebel-Slichter coherence peak, possibly due to large $H_{c2}$ anisotropy (and thus a distribution of $T_c$'s). Anisotropic NMR studies of MgB$_2$ have proven difficult due to the small size ($\sim 10\ \mu$m) of high-quality crystals. A large-single-crystal conventional NMR study [2] could not probe the superconducting state due to line broadening. We have set out to use the exquisite sensitivity of Nuclear Magnetic Resonance Force Microscopy (NMRFM) to probe the behavior of $^{11}$B in single crystal MgB$_2$. We have fabricated ultrasensitive mechanical oscillators using e-beam lithography to facilitate detection of the weak $^{11}$B resonance; these have resonance frequencies of 1--10 kHz, spring constants of $\sim 10^{-4}$ N/m, and quality factors $>$3000 at 77 K. We report our initial detection of the $^{11}$B nuclear resonance and our plans to study relaxation rates in single crystal MgB$_2$. [1] H. Kotegawa {\it et al.}, {\it Phys.~Rev.~Lett.} {\bf 87}, 127001 (2001). [2] S.~Str\"assle {\it et al.}, {\it Physica C} {\bf 466}, 168 (2007). *Supported by NSF DMR-0605828 and DGE-0549417.