  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.
