Thermodynamic Evidence for a Multi-component superconducting order parameter in Sr₂RuO₄

The unconventional superconductivity of Sr₂RuO₄ has remained a mystery for over 25 years, even though its normal metallic state is quite well-understood. Reaching a consensus on the bulk order parameter symmetry has been difficult primarily due to the contradictions that exist between several major experimental findings. We performed resonant ultrasound spectroscopy (RUS) measurements on Sr₂RuO₄, to measure its entire symmetry-resolved elastic tensor through T_C (∼1.43 K). Since different superconducting order parameters couple differently to shear and compressional sound modes, measurement of all elastic moduli places strong constraints on the order parameter symmetry, independent of microscopics. We observe a thermodynamic discontinuity in one of the shear moduli (c₆₆) at T_C, which requires a two-component superconducting order parameter (E representation of D_4h). We discuss leading E-symmetry order parameters, and suggest that it may be necessary to go beyond the conventional "singlet/triplet" paradigm to finally resolve the mystery that is Sr₂RuO₄. We also measure an anomalous attenuation peak in compressional sound below T_C, possibly arising due to sound absorption into order parameter collective modes.