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

Edited by John Tranquada, Brookhaven National Laboratory, Upton, NY; received February 17, 2023; accepted July 22, 2023

August 22, 2023

120 (35) e2302800120

Significance

Characterizing the symmetries of ordered phases is paramount in the study of strongly correlated electron systems, and anisotropic lattice distortion/strain offer a fruitful avenue for probing and tuning these phases. Our experimental framework resolves symmetric (rotation–symmetry–preserving) and antisymmetric (rotation–symmetry–breaking) strain effects in free energy using a thermodynamic quantity, the elastocaloric effect. By tracing out the entropy landscape of an f-electron intermetallic in the temperature–strain plane, we demonstrate that the strain-even (odd) component of the elastocaloric response corresponds to symmetric (antisymmetric) lattice deformation modes distinctively coupled to the underlying electronic degrees of freedom. Along with the derived Ehrenfest relation, the elastocaloric effect has potential applications in placing experimental constraints on the spatial symmetry of wider classes of emergent phases in quantum materials.

Abstract

The adiabatic elastocaloric effect measures the temperature change of a given system with strain and provides a thermodynamic probe of the entropic landscape in the temperature-strain space. Here, we demonstrate that the DC bias strain-dependence of AC elastocaloric effect allows decomposition of the latter into symmetric (rotation-symmetry-preserving) and antisymmetric (rotation-symmetry-breaking) strain channels, using a tetragonal $f$ -electron intermetallic DyB $_{2}$ C $_{2}$ —whose antiferroquadrupolar order breaks local fourfold rotational symmetries while globally remaining tetragonal—as a showcase example. We capture the strain evolution of its quadrupolar and magnetic phase transitions using both singularities in the elastocaloric coefficient and its jumps at the transitions, and the latter we show follows a modified Ehrenfest relation. We find that antisymmetric strain couples to the underlying order parameter in a biquadratic (linear-quadratic) manner in the antiferroquadrupolar (canted antiferromagnetic) phase, which are attributed to a preserved (broken) global tetragonal symmetry, respectively. The broken tetragonal symmetry in the magnetic phase is further evidenced by elastocaloric strain-hysteresis and optical birefringence. Additionally, within the staggered quadrupolar order, the observed elastocaloric response reflects a quadratic increase of entropy with antisymmetric strain, analogous to the role magnetic field plays for Ising antiferromagnetic orders by promoting pseudospin flips. Our results demonstrate AC elastocaloric effect as a compact and incisive thermodynamic probe into the coupling between electronic degrees of freedom and strain in free energy, which holds the potential for investigating and understanding the symmetry of a wide variety of ordered phases in broader classes of quantum materials.

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Acknowledgments

We thank R.M. Fernandes and A.P. Mackenzie for fruitful discussions. Experimental work performed at Stanford University was funded by the Gordon and Betty Moore Foundation EPiQS Initiative, grant GBMF9068. L.Y. also acknowledges support by the Marvin Chodorow Postdoctoral Fellowship at the Department of Applied Physics, Stanford University. M.D.B. acknowledges support by the Geballe Laboratory for Advanced Materials Fellowship. Optical measurements were performed at the Lawrence Berkeley Laboratory as part of the Quantum Materials program, Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the US Department of Energy under Contract No. DE-AC02-05CH11231. V.S. is supported by the Miller Institute for Basic Research in Science, UC Berkeley. J.O. and Y.S. received support from the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4537 to J.O. at UC Berkeley. J.F.R.-N. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grants GBMF4302 and GBMF8686.

Author contributions

L.Y. and I.R.F. designed research; L.Y., Y.S., V.S., M.S.I., T.W., and M.D.B. performed research; L.Y., J.F.R.-N. and M.E.S. contributed new reagents/analytic tools; L.Y., Y.S., V.S., and J.O. analyzed data; and L.Y. and I.R.F. wrote the paper.

Competing interests

The authors declare no competing interest.

Supporting Information

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Proceedings of the National Academy of Sciences

Vol. 120 | No. 35
August 29, 2023

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Received: February 17, 2023

Accepted: July 22, 2023

Published online: August 22, 2023

Published in issue: August 29, 2023

Keywords

antisymmetric strain
quadrupolar order
elastocaloric effect
strongly correlated electron systems

Acknowledgments

Author Contributions

Competing Interests

The authors declare no competing interest.

Notes

This article is a PNAS Direct Submission.

We note that a linear-dependence of $T_{c}$ with pressure may also arise from a mutual cancelation between quadratic terms of the two independent $A_{1 g}$ components $\frac{1}{2} (ϵ_{xx} + ϵ_{yy})$ and $ϵ_{zz}$ while this requires an unlikely degree of fine-tuning. As a second note, $T_{c}$ only puts constraints on the free energy close to phase transitions; we hypothesize that when $T_{c}$ is not strongly modified by $ϵ$ and $ϵ_{A_{1 g}}^{2}$ terms are excluded near the phase transition, the presence of such terms in the free energy away from $T_{c}$ is also unlikely.

†

The black solid curve is scaled along the temperature axis by a factor of 4, which we hypothesize originates from an imperfect adiabaticity of our experiments.

‡

To quantitatively compare $A ϵ_{xx}$ with $T_{N} (ϵ_{xx})$ in Fig. 4Ban additional factor 2.3 is required in front of $A$ . We note that this factor introduced to account for imperfect adiabaticity is comparable with that used above for $T_{Q}$ . The difference between the two factors may arise from a $T$ -dependence of the thermal conditions (thus the adiabaticity) of the experimental setup.

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Affiliations

Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305

Department of Applied Physics, Stanford University, Stanford, CA 94305

Department of Physics, University of California, Berkeley, CA 94720

Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

Department of Physics, University of California, Berkeley, CA 94720

Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

Department of Physics, Stanford University, Stanford, CA 94305

Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305

Department of Applied Physics, Stanford University, Stanford, CA 94305

Thanapat Worasaran

Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305

Department of Applied Physics, Stanford University, Stanford, CA 94305

Matthew E. Sorensen

Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305

Department of Physics, Stanford University, Stanford, CA 94305

Maja D. Bachmann

Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305

Department of Applied Physics, Stanford University, Stanford, CA 94305

Department of Physics, University of California, Berkeley, CA 94720

Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305

Department of Applied Physics, Stanford University, Stanford, CA 94305

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

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