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We report results of our low-temperature magneto electric transportmeasurements on micron-sized short cylinders of odd-parity, spin-tripletsuperconductor Sr$_2$RuO$_4$ with the cylinder axis along the $c$ axis. Thein-plane magnetic field and measurement current dependent magnetoresistanceoscillations were found to feature an amplitude much larger than that expectedfrom the conventional Little-Parks effect, suggesting that themagnetoresistance oscillations originate from vortex crossing. The free-energybarrier that controls the vortex crossing was modulated by the magnetic fluxenclosed in the cylinder, the in-plane field, measurement current, andstructural factors. Distinct features on magnetoresistance peaks were found,which we argue to be related to the emergence of half-flux quantum states, butonly in samples for which the vortex crossing is confined at specific parts ofthe sample.

Magnetoresistance oscillations and the half-flux-quantum state in spin-triplet superconductor Sr2RuO4