Mechanical detection of single-quantum-level fluxoid relaxation in an Nb micro-ring

We developed a highly sensitive static force magnetometry, originally proposed for sub-pico-newton force standard, which enabled the observation of single fluxoids selectively and their dynamics in a superconducting micro-ring. For an Nb ring with inner diameter of 4.0 $\mu$m, the magnetic moment of a single fluxoid quantum was determined as 7.4 pico-emu, corresponding to the static force of 74 femto-newton, in good agreement with a theoretical estimate within 8\%. The magnetic relaxation of moderate number of fluxoids, ranging from 20 to 60, was also measured at temperatures of 4 $\sim$ 6 K and at zero magnetic field. The relaxation results with single-quantum-step feature were analyzed with a theoretical model for thermally activated transition.