Magnetic response of Sr$_{2}$RuO$_{4}$ nanocrystals: search for chiral currents and fractional vortices*

The ruthenate superconductor Sr$_{2}$RuO$_{4}$ may have a chiral order parameter of the form p$_{x}\pm $ip$_{y,}$, making it a candidate for nucleation of excitations with non-Abelian statistics that could enable topologically-protected quantum computing. To test this scenario, we have measured the magnetic response of Sr$_{2}$RuO$_{4}$ nanocrystals to search for spontaneous chiral currents and half-integer vortices. Each nanocrystal (2$\mu $m x 2$\mu $m x 0.5$\mu $m) was extracted from a large single crystal with bulk transition temperature in the range 1.2K-1.4K. It was then glued into the pickup loop of a flux transformer or a gradiometer that is inductively-coupled to a dc-SQUID magnetometer. We monitor the diamagnetic screening of the crystal and the entry of discrete vortices in perpendicular and parallel applied magnetic fields and as a function of temperature to search for the existence of half-quantum vortices in this system. We are also developing other techniques such as nanoscale Scanning SQUID Microscopy for probing the vortex dynamics in Sr$_{2}$RuO$_{4}$.