The odd-parity, spin-triplet superconductor Sr${}_2$RuO${}_4$ has been found to feature exotic vortex physics including half-flux quanta trapped in a doubly connected sample and the formation of vortex lattices at low fields. The consequences of these vortex states on the low-temperature magnetoresistive behavior of mesoscopic samples of Sr${}_2$RuO${}_4$ were investigated by using a ring device fabricated on mechanically exfoliated single crystals of Sr${}_2$RuO${}_4$ by photolithography and a focused ion beam. With the magnetic field applied perpendicular to the in-plane direction, thin-wall rings of Sr${}_2$RuO${}_4$ were found to exhibit pronounced quantum oscillations with a conventional period of the full-flux quantum even though the unexpectedly large amplitude and the number of oscillations suggest the observation of vortex-flow-dominated magnetoresistance oscillations rather than a conventional Little-Parks effect. For rings with a thick wall, two distinct periods of quantum oscillations were found in high- and low-field regimes, respectively, which we argue to be associated with the “lock-in” of a vortex lattice in these thick-wall rings. No evidence for half-flux-quantum resistance oscillations were identified in any sample measured so far without the presence of an in-plane field.

• Received 26 October 2012

DOI:https://doi.org/10.1103/PhysRevB.87.081104