Low-temperature specific heat of the high-$T_c$ superconductors ${\mathrm{La}}_{1.8}$${\mathrm{Sr}}_{0.2}$${\mathrm{CuO}}_{4\mathrm{-}\mathrm{\delta }}$ and R${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (R=Y, Eu, Ho, Tm, and Yb)

Low-temperature specific-heat measurements have been carried out between 0.5 and 30–50 K on the high-$T_c$ copper oxide superconductors ${\mathrm{La}}_{1.8}$ ${\mathrm{Sr}}_{0.2}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{\delta }}$ and R${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (R=Y, Eu, Ho, Tm, and Yb). The specific heat of the ${\mathrm{La}}_{1.8}$ ${\mathrm{Sr}}_{0.2}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{\delta }}$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ compounds below $T_c$ can be resolved into a contribution of the form $C_e$(T)=γ’T with a finite γ’ and a lattice contribution that consists of Debye and Einstein terms. Specific-heat data for the R${\mathrm{Ba}}_3$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ compounds with R=Ho, Tm, and Yb exhibit no features due to magnetic order above 0.5 K, but reveal electronic Schottky anomalies associated with crystalline electric field (CEF) splitting of the Hund’s-rules ground-state multiplet of the $R^{3+}$ ions. The Schottky anomalies can be described by calculations based on tentative energy-level schemes for the ${\mathrm{Ho}}^{3+}$, ${\mathrm{Tm}}^{3+}$, and ${\mathrm{Yb}}^{3+}$ ions in the CEF which are presented. Specific-heat data for the ${\mathrm{EuBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ compound, which can be separated into a γ’T term, a Debye contribution, and a low-temperature upturn, are consistent with a nonmagnetic J=0 ground state for ${\mathrm{Eu}}^{3+}$, as expected from Hund’s rules.