Measurements of the critical current of small Sr$_2$RuO$_4$ crystals

We report critical current measurements of chiral $p$-wave superconductor Sr$_2$RuO$_4$. Because of the strong anisotropy possessed by Sr$_2$RuO$_4$, vortex lines along the in-plane direction are expected to be pinned more strongly than those along the $c$ axis, resulting in anisotropic critical currents. We prepared small single crystals of Sr$_2$RuO$_4$ with a typical size of 50$\mu$m$\times$ 10$\mu$m$\times$1$\mu$m by mechanical exfoliation and characterized them by Raman spectroscopy and high-resolution transmission electron microscopy, showing that they were either pure Sr$_2$RuO$_4$ or eutectic phase containing one or more Ru microdomains. Four-point or Hall probes were prepared on the small crystals by photo lithography. While samples of pure Sr$_2$RuO$_4$ exhibited a typical transition temperature ($T_c$) of 1.2K, slightly lower than the optimal bulk $T_c$, 1.5K, those with Ru microdomains showed multiple resistive transitions with the highest $T_c$ around 2K. The critical current and critical field phase diagrams were determined for these small crystals. Surprisingly, the in-plane critical current density, measured for the first time, was found to be significantly larger than that along $c$-axis of the bulk. The physical implications of these observations will be discussed. Supported by DOE.