Determination of the dynamic Young's modulus of quantum materials in piezoactuator-driven uniaxial pressure cells using a low-frequency AC 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 AC (1 Hz ≲ ω ≲ 1000 Hz) uniaxial stress, σac, to the sample and measure the resulting AC 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 AC technique at low frequencies, exhibits a pronounced nonlinear elasticity, which is in very good agreement with previous Young's modulus measurements on Sr2RuO4 under [1 0 0] strain using a DC method [Noad et al., Science 382, 447-450 (2023)]. By combining the new AC Young's modulus measurements with AC elastocaloric measurements in a single measurement, we demonstrate that these AC 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.

Elastocaloric determination of the phase diagram of Sr2RuO4.

One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research1. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning2,3, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr2RuO4 (refs. 4-9). Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr2RuO4.