Crystal electric fields in heavy-electron metals: The specific heats of ${\mathrm{U}}_2$${\mathrm{Zn}}_{17}$ and ${\mathrm{CeCu}}_6$ to 70 K

Two temperature scales–(1) $T_0$ (single impurity) and/or $T_F^{\mathrm{*}}$ (degenerate Fermi) and (2) crystal-electric-field splitting(s) Δ–provide the basis for dividing the excitation spectra of heavy-electron systems into three regimes. They are (i) for $T_0$<T<Δ, the specific heat and susceptibility are that due to independent f atoms in a crystal field; (ii) for T∼$T_0$, a bump appears in the specific heat due to the Kondo compensation; (iii) for T<$T_0$, interaction effects between the f atoms lead to a Fermi-liquid solid where band-structure effects show up in the low-temperature properties (T<$T_F^{\mathrm{*}}$/100). This paper is primarily concerned with region (i). In particular, we present new specific-heat data for ${\mathrm{U}}_2$ ${\mathrm{Zn}}_{17}$ up to 70 K and ${\mathrm{CeCu}}_6$ to 80 K. In comparing these data with those for other heavy-electron materials we conclude that the specific heat for T>$T_0$ is qualitatively consistent with the existence of crystal-electric-field levels, but that the overall experimental entropy is too high. We present a tentative model to account for this discrepancy through the use of Fermi statistics to describe transitions in a stylized band model with two peaks. Crystal-field levels in most cases have not been confirmed by neutron scattering.