Experimental determination of fluxoid quantum's contribution to magnetic moment for force metrology

Utilizing a cantilever torque-magnetometry equipped with fiber-scanning capability, we have executed precision measurements of the magnetic moment of a micron-sized Nb ring in superconducting state at $T$ = 4 K, which is a key element for sub-piconewton force standard previously suggested by some of the authors. The magnetic moments due to diamagnetic response and individual magnetic fluxoid have been independently determined with a resolution of sub-femto-Am$^2$. Within the accuracy of the spring constant determined from a thermal noise method, the results are very consistent with the estimation by Brandt and Clem’s model that considers finite-penetration-depth effect.