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The adiabatic elastocaloric effect measures the temperature change of givensystems with strain and probes the entropic landscape in the temperature-strainspace. In this study we demonstrate that the DC bias strain-dependence of ACelastocaloric effect can be used to decompose the latter into contributionsfrom symmetric (rotation-symmetry-preserving) and antisymmetric(rotation-symmetry-breaking) strains, using a tetragonal f-electron systemDyB2C2--whose antiferroquadrupolar order locally breaks four-fold rotationalsite symmetries while globally remaining tetragonal--as a showcase example. Wecapture the strain evolution of the quadrupolar and magnetic phase transitionsin the system using both singularities in the elastocaloric coefficient and itsjump at the transitions, and the latter we show follows a modified Ehrenfestrelation. We find that antisymmetric strain couples to the underlying orderparameter in a bi-quadratic manner in the antiferroquadrupolar (AFQ) phase butin a linear-quadratic manner in the canted antiferromagnetic (CAFM) phase; thecontrast is attributed to a preserved (broken) tetragonal symmetry in the AFQ(CAFM) phase, respectively. The broken tetragonal symmetry in the CAFM phase isfurther supported by elastocaloric strain-hysteresis and observation of twosets of domains with mutually perpendicular principal axes in opticalbirefringence. Additionally, when the quadrupolar moments are ordered in astaggered fashion, we uncover an elastocaloric response that reflects aquadratic increase of entropy with antisymmetric strain, analogous to the rolemagnetic field plays for Ising antiferromagnets by promoting pseudospin flips.Our results show that AC elastocaloric effect is a compact and incisivethermodynamic probe into the coupling between electronic degrees of freedom andstrain, which can potentially be applied to broader classes of quantummaterials.

Elastocaloric signatures of symmetric and antisymmetric strain-tuning of quadrupolar and magnetic phases in DyB2C2