Determination of the dynamic Young's modulus of quantum materials in piezoactuator-driven uniaxial pressure cells using a low-frequency a.c. method

We report on a new technique for measuring the dynamic Young's modulus, E, of quantum materials at low temperatures as a function of static tuning strain, ε, in piezoactuator-driven pressure cells. In addition to a static tuning of stress and strain, we apply a small-amplitude, finite-frequency a.c. (1 Hzω1000 Hz) uniaxial stress, σac, to the sample and measure the resulting a.c. strain, εac, using a capacitive sensor to obtain the associated modulus E. We demonstrate the performance of the new technique through proof-of-principle experiments on the unconventional superconductor Sr₂RuO₄, which is known for its rich temperature-strain phase diagram. In particular, we show that the magnitude of E, measured using this a.c. technique at low frequencies, exhibits a pronounced nonlinear elasticity, which is in very good agreement with previous Young's modulus measurements on Sr₂RuO₄ under [100] strain using a d.c. method (Noad et al., Science 382, 447-450 (2023)). By combining the new a.c. Young's modulus measurements with a.c. elastocaloric measurements in a single measurement, we demonstrate that these a.c. techniques are powerful in detecting small anomalies in the elastic properties of quantum materials. Finally, using the case of Sr₂RuO₄ as an example, we demonstrate how the imaginary component of the modulus can provide additional information about the nature of ordered phases.