Title: Multidimensional entropy landscape of quantum criticality

Hilbert v. Löhneysen

Institute for Quantum Materials and Technologies, and Physics Institute, Karlsruhe Institute of Technology, D-76049 Karlsruhe, Germany

Abstract:
The Third Law of Thermodynamics states that the entropy of any system in equilibrium has to vanish at absolute zero temperature. At nonzero temperatures, on the other hand, matter is expected to accumulate entropy near a quantum critical point (QCP), where it undergoes a continuous transition from one ground state to another as a function of a non-thermal tuning parameter [1,2]. Based on general thermodynamic principles, we determine the spatial-dimensional profile of the entropy S near a QCP and its steepest descent in the corresponding multidimensional stress space. We demonstrate this approach for the canonical quantum critical compound CeCu6-xAux near its onset of antiferromagnetic order [3]. We are able to link [4] the directional stress dependence of S to the previously determined geometry of quantum critical fluctuations [5]. Our demonstration of the multidimensional entropy landscape can be generalized to other tuning parameters and may provide the foundation to understand how quantum criticality nucleates novel phases.
In CePdAl, a Kondo-lattice state coexists with geometric frustration leading to an unusual antiferromagnetic phase in which one third of the Ce3+ magnetic moments are frustrated and do not participate in the long-range order observed below 2.7 K. To study the interplay between Kondo effect and frustration, we suppress the partial order by applying magnetic fields B and by replacing Pd with isoelectronic, but smaller Ni atoms [6,7]. The (x,B,T) phase diagram is established by using thermal expansion, magnetostriction, and magnetization measurements of CePd1-xNixAl single crystals with 0 ≤ x ≤ 0.14. We construct the entropy landscape and investigate its stress dependence along the quantum phase boundary. Surprisingly, the quantum critical behavior observed in the thermal expansion and the Grüneisen parameter changes with increasing Ni concentration and magnetic field. The effect of geometric frustration on these results is discussed and compared to the the suggested [8] global phase diagram of heavy-fermion compounds. 
[1] P. Coleman, and A. J. Schofield, Nature 433, 226 (2005).
[2] L. Zhu, M. Garst, A. Rosch, and Q. Si, Phys. Rev. Lett. 91, 066404 (2003)
[3] H. v. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, Rev. Mod. Phys. 79, 10185 (2007).
[4] K. Grube, S. Zaum, O. Stockert, Q. Si, H. v. Löhneysen, Nature Physics 13, 742 (2017).
[5] O. Stockert, H. v. Löhneysen, A. Rosch, N. Pyka, M. Loewenhaupt, Phys. Rev. Lett. 80, 5627 (1998).
[6] S. Lucas, K. Grube, C.-L. Huang, A. Sakai, S. Wunderlich, E. L. Green, J. Wosnitza, V. Fritsch, P. Gegenwart, O. Stockert, and H. v. Löhneysen, Phys. Rev. Lett. 118, 107204 (2017).
[7] A. Sakai et al., Phys. Rev. B 94, 22045(R) (2016). 
[8] Q. Si, Physica B 378–380, 23 (2006). 

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