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The observation of the highly unusual half-quantum vortex (HQV) in a singlecrystalline superconductor excludes unequivocally the spin-singlet symmetry ofthe superconducting order parameter. HQVs were observed previously inmesoscopic samples of Sr2RuO4 in cantilever torque magnetometry measurements,thus providing direct evidence for spin-triplet pairing in the material. Inaddition, it raised important questions on HQV, including its stability anddynamics. These issues have remained largely unexplored, in particular,experimentally. We report in this paper the detection of HQVs in mesoscopic,doubly connected cylinders of single-crystalline Sr2RuO4 of a mesoscopic sizeand the examination of the effect of the in-plane magnetic field needed for theobservation of the HQV by magnetoresistance (MR) oscillations measurements.Several distinct features found in our data, especially a dip and secondarypeaks in the MR oscillations seen only in the presence of a sufficiently largein-plane magnetic field as well as a large measurement current, are linked tothe formation of the HQV fluxoid state in and crossing of an Abrikosov HQVthrough the sample. The conclusion is drawn from the analysis of our data usinga model of thermally activated vortex crossing overcoming a free-energy barrierwhich is modulated by the applied magnetic flux enclosed in the cylinder aswell as the measurement current. Evidence for the trapping of an HQV fluxoidstate in the sample was also found. Our observation of the HQV in mesoscopicSr2RuO4 provided not only additional evidence for spin-tripletsuperconductivity in Sr2RuO4 but also insights into the physics of HQV,including its spontaneous spin polarization, stability, and dynamics. Our studyalso revealed a possible effect of the measurement current on the magnitude ofthe spontaneous spin polarization associated with the HQV.

Magnetoresistance oscillation study of the half-quantum vortex in doubly connected mesoscopic superconducting cylinders of Sr2RuO4