Detection of Individual Vortices in Micron-Size Sr$_{2}$RuO$_{4}$ Rings by Phase-Locked Cantilever*

We describe a feedback-based dynamic cantilever magnetometry technique capable of achieving high magnetic moment sensitivity with low applied fields. Using this technique, we have observed periodic entry of vortices into mesoscopic Sr$_{2}$RuO$_{4}$ rings. The quantized jump in the magnetic moment of the particle produced by individual vortices was measured with a resolution of $7\times 10^{-19}J/T$ at an applied field of 1 G.