Elastic quantum criticality in nematics and altermagnets via the elastocaloric effect

The coupling between electronic nematic degrees of freedom and acoustic phonons is known to significantly alter the universality class of a nematic quantum critical point (QCP). While non-Fermi-liquid behavior emerges in the absence of lattice coupling, the inclusion of interactions with acoustic phonons results in observables such as heat capacity and single-particle scattering rate exhibiting only subleading nonanalytic corrections to dominant Fermi-liquid terms. In this work, we demonstrate that the elastocaloric effect (ECE), the adiabatic temperature change under varying strain, and the thermal expansion deviate from this pattern. Despite lattice coupling weakening the singularity of the ECE, it preserves a dominant temperature dependence that deviates from the prediction one would obtain from Fermi-liquid theory, an effect which we will refer to as an elastocaloric anomaly. By drawing analogies between nematic systems and field-tuned altermagnets, we further show that similar responses are expected for the ECE near altermagnetic QCPs. We classify the types of piezomagnetic couplings and analyze the regimes arising from field-tuned magnetoelastic interactions. Our findings are shown to be consistent with the scaling theory for elastic quantum criticality and they further emphasize the suitability of the ECE as a sensitive probe near QCPs.