Low-temperature specific heat of single-crystal ${\mathrm{Bi}}_2$Ca${\mathrm{Sr}}_2$${\mathrm{Cu}}_2$${\mathrm{O}}_8$ and ${\mathrm{Tl}}_2$${\mathrm{Ca}}_2$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$

We report on specific-heat measurements from 2 to 15 K on single crystals of ${\mathrm{Bi}}_2$Ca${\mathrm{Sr}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_8$ and ${\mathrm{Tl}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$. We find low-temperature deviations from the Debye law that can be attributed to spin-glass behavior of a small concentration of isolated impurity copper moments. At higher temperatures, we observe contributions to the specific heat that can be attributed to a soft-phonon mode, possibly associated with the superstructure in the Bi-O and Tl-O layers. From our single-crystal data, we conclude that the thallium- and bismuth-based copper oxide superconductors show no measurable linear term in the specific heat [$\gamma \mathrm{}\left(0\right)\mathrm{}\le 1$ mJ/mole ${\mathrm{K}}^2$].