Precise determination of magnetic moment of a fluxoid quantum in a superconducting microring

Using dynamic cantilever magnetometry and experimentally determining the cantilever's vibrational mode shape, we precisely measured the magnetic moment of a lithographically defined micron-sized superconducting Nb ring, a key element for the previously proposed subpiconewton force standard. The magnetic moments due to individual magnetic fluxoids and a diamagnetic response were independently determined at T=4.3 K, with a subfemtoampere-square-meter resolution. The results show good agreement with the theoretical estimation yielded by the Brandt and Clem model within the spring constant determination accuracy.