We investigate the specific heat of ultra-pure single crystals of Sr2RuO4, a leading candidate of a spin-triplet superconductor. We for the first time obtained specific-heat evidence of the first-order superconducting transition below 0.8 K, namely divergent-like peaks and clear hysteresis in the specific heat at the upper critical field. The first-order transition occurs for all in-plane field directions. The specific-heat features for the first-order transition are found to be highly sensitive to sample quality; in particular, the hysteresis becomes totally absent in a sample with slightly lower quality. These thermodynamic observations provide crucial bases to understand the unconventional pair-breaking effect responsible for the first-order transition.
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