Elastic Quantum Criticality in Nematics and Altermagnets via the Elasto-Caloric 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 behaviour 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 non-analytic 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 non-Fermi-liquid temperature dependence. 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 analyse 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.