Scanning SQUID Microscopy of Sr$_2$RuO$_4$ Under Uniaxial Pressure

The superconducting order parameter of Sr$_2$RuO$_4$ is thought to be $p_x \pm ip_y$ in the absence of a symmetry breaking field, owing to a degeneracy of the $p_x$ and $p_y$ components that results from tetragonal lattice symmetry. This order parameter would manifest as a cusp in the superconducting critical temperature, T$_c$, as a function of orthorhombic lattice distortion, applied through uniaxial pressure. T$_c$ has been found to respond sensitively to uniaxial pressure; however, the strain resolution of bulk measurements so far appears to be limited by inhomogeneity of the applied strain field and/or intrinsic sample inhomogeneity, such that the expected cusp might not have been observable. Here, we use scanning SQUID microscopy to resolve the low pressure response of T$_c$ on micron length scales, rendering the measurement insensitive to longer range spatial inhomogeneity. Furthermore, we report the dependence of T$_c$ on uniaxial strain to temperature and strain resolution sufficient to resolve the predicted cusp, thereby demonstrating the extent to which the symmetry protected degeneracy is lifted locally.