Jump in the $c_{66}$ shear modulus at the superconducting transition of Sr$_2$RuO$_4$: Evidence for a two-component order parameter.

The quasi-2D metal Sr$_2$RuO$_4$ is one of the best characterized unconventional superconductors, yet the nature of its superconducting order parameter is still highly debated. Here we use ultrasound velocity to probe the superconducting state of Sr$_2$RuO$_4$. We observe a sharp jump in the shear elastic constant $c_{66}$ as the temperature is raised across the superconducting transition at $T_c$. This directly implies that the superconducting order parameter is of a two-component nature. We discuss what states are compatible with this requirement and propose, given the other known properties of Sr$_2$RuO$_4$, that the most likely candidate is the $(1,0)$ state of the $E_g$ representation.