Thermodynamic analysis of the quantum critical behavior of Ce-lattice compounds

Abstract

A systematic analysis of low-temperature magnetic phase diagrams of Ce compounds is performed in order to recognize the thermodynamic conditions to be fulfilled by those systems to reach a quantum critical regime or, alternatively, to identify other kinds of low-temperature behavior. Based on specific heat (C _m ) and entropy results, three different types of phase diagrams are recognized: (i) with the entropy involved in the ordered phase (S _MO) decreasing proportionally to the ordering temperature (T _MO); (ii) those showing a transference of degrees of freedom from the ordered phase to a non-magnetic component, with their C _m (T _MO) jumps (ΔC _m ) vanishing at finite temperature; and (iii) those ending at a critical point at finite temperature because their ΔC _m do not decrease sufficiently with T _MO, producing an entropy accumulation at low temperature.

Only those systems belonging to the first case, i.e. with S _MO → 0 as T _MO → 0, can be regarded as candidates for quantum critical behavior. Their magnetic phase boundaries deviate from the classical negative curvature below T ≈ 2.5 K, denouncing monotonic misleading extrapolations down to T = 0. Different characteristic concentrations are recognized and analyzed for Ce-ligand alloyed systems. In particular, a pre-critical region is identified where the nature of the magnetic transition undergoes significant modifications, with its ∂C _m /∂T discontinuity strongly affected by the magnetic field and showing an increasing remnant entropy at T → 0. Physical constraints arising from the third law at T → 0 are discussed and recognized from experimental results.

Keywords:

• quantum criticality
• entropy
• magnetic phase diagrams

Acknowledgments

The author thanks A. Eichler, M. Jaime, G. Knebel, M. Deppe, E. Bauer, E.-W. Scheidt, A. Pikul, R. Küchler and I. Zeiringer for allowing him to access to experimental data, S. Grigera, U. Karahasanovic, V. Correa and A. Aligia for motivating discussions and M. Gomez Berisso and P. Pedrazzini for experimental support. The studies on the CeIn_3−x Sn _x and CePd_1−x Rh _x systems were carried in collaboration with C. Geibel through cooperation supported by DAAD, Alexander von Humboldt Foundation. This work was partially supported by PICTP-2007-0812 and Universidad de Cuyo 06/C326 projects.

Notes

Notes

1. A change in the chemical potential μ implies a significant modification in the Fermi energy of the band because of the variation of the number of electrons n (e.g. Pd has one more electron than Rh, with similar atomic volume). On the other hand, a structural pressure p _str is originated by the difference of atomic volumes ΔV of the Ce-ligand atoms (cf. Pd and Ni, with similar electronic structure). In the former case the thermodynamic relations can be written through the Gibbs energy like μ = ∂G/∂n; and P _str = ∂G/∂ΔV for the latter.

2. Strictly, long-range or short-range magnetic order are not different in the following discussion because it is based on the entropy (i.e. degrees of freedom) involved in the decreasing magnetic interactions.

3. Ce₂Mg₃(NO₃)₁₂ · 24H₂O is a rhombohedral crystalline compound used as a standard magnetic thermometer for very low-temperature thermometer calibration because the extremely large Ce–Ce spacing inhibits magnetic interactions and θ _P  = 0.4 mK.

4. Ce-available volume is defined by the Wigner–Eckart cell whatever the nature of Ce nearest neighbours.

5. The LaIrSi-type structure provides a test for this possibility (I. Zeiringer, University of Vienna, private communication).