Heat Capacity Measurements of Sr$_{\mathrm{2}}$RuO$_{\mathrm{4}}$ Under Uni-axial Stress

One of the most-discussed possible pairing symmetries of the superconductor Sr$_{\mathrm{2}}$RuO$_{\mathrm{4}}$ is p$_{\mathrm{x}}+$/-ip$_{\mathrm{y}}$. By applying in-plane uniaxial stress, the degeneracy of the p$_{\mathrm{x}}$ and p$_{\mathrm{y}}$ components should be lifted, yielding two critical temperatures (T$_{\mathrm{c}})$. Hicks et al. observed an increase of T$_{\mathrm{c}}$ of Sr$_{\mathrm{2}}$RuO$_{\mathrm{4}}$ under both compressive and tensile stress [1], and did not find evidence for splitting of transition. However, that result was based on magnetic susceptibility measurements, which would be sensitive only to the upper transition. For a direct test of possible splitting, we measure the heat capacity of Sr$_{\mathrm{2}}$RuO$_{\mathrm{4}}$ under uniaxial stress. To do so, we have developed an approach to measure heat capacity under non-adiabatic conditions. We have observed the increase in T$_{\mathrm{c}}$ under compressive strain, providing the first thermodynamic evidence for the strain-induced increase in T$_{\mathrm{c}}$ of Sr$_{\mathrm{2}}$RuO$_{\mathrm{4}}$, and also resolve strong strain-induced changes in the normal-state heat capacity. [1] Clifford W. Hicks et al., Science \textbf{344}, 283 (2014).