Entropy Bottlenecks at T $$\,\rightarrow \,$$ → 0 in Ce-Lattice and Related Compounds

Abstract

A number of specific heat \(C_\mathrm{m}\) anomalies are reported in Ce- and Yb-lattice compounds around 1 K which cannot be associated to usual phase transitions despite of their robust magnetic moments. Instead of a \(C_\mathrm{m}(T)\) jump, these anomalies show coincident morphology: (i) a significant tail in \(C_\mathrm{m}/T\), with similar power law decay above their maxima (\(T>T_\mathrm{m}\)), (ii) whereas a \(C_\mathrm{m}(T^2)\) dependence is observed below \(T_\mathrm{m}\). (iii) The comparison of their respective entropy gain \(S_\mathrm{m}(T)\) indicates that \(\approx 0.7R\)ln2 is condensed within the \(T>T_\mathrm{m}\) tail, in coincidence with an exemplary spin-ice compound. Such amount of entropy arises from a significant increase of the density of low energy excitations, reflected in a divergent \(C_\mathrm{m}(T>T_\mathrm{m})/T\) dependence. (iv) Many of their lattice structures present conditions for magnetic frustration. The origin of these anomalies can be attributed to an interplay between the divergent density of magnetic excitations at \(T\rightarrow 0\) and the limited amount of degrees of freedom: \(S_\mathrm{m}\) = \(R\)ln2 for a doublet-ground state. Due to this “entropy bottleneck,” the paramagnetic minimum of energy blurs out and the system slides into an alternative minimum through a continuous transition. A relevant observation in these very heavy fermion systems is the possible existence of an upper limit for \(C_\mathrm{m}/T_{\mathrm{Lim} T\rightarrow 0} ~\approx 7~\)J/mol K\(^2\) observed in four Yb- and Pr-based compounds.