Specific Heat of Gadolinium and Ytterbium Metals between 0.4 and 4°K

The heat capacities of gadolinium and ytterbium metals have been measured between 0.4 and 4°K in a ${\mathrm{He}}^3$ cryostat. For gadolinium, in qualitative agreement with earlier results, anomalous humps were observed in $C_p$ at 1.1, 1.6, and 3.7°K. The ground state of the ${\mathrm{Gd}}^{3+}$ ion is ${}_{}{}^8{}_{}{}^{}S_{\frac{7}{2}}^{}{}_{}{}^{}$ and consequently, due to zero orbital angular momentum of the $4f$ electrons, the nuclear specific heat is small. The observed $C_p$ is much larger than one would expect for the metal alone; the excess entropy could be attributed to magnetic ordering of ${\mathrm{Gd}}^{3+}$ ions in the ${\mathrm{Gd}}_2$ ${\mathrm{O}}_3$ impurity (0.54% of oxygen in our sample). The specific heat of ytterbium, between 0.4 and 4°K, can be expressed accurately by $C_p\left(\frac{\mathrm{mJ}}{\mathrm{mole}°\mathrm{K}}\right)=1.180\mathrm{}{T}^3+2.90T+0.012\mathrm{}{T}^{-2\mathrm{}}$. The lattice specific heat corresponds to a Debye $\theta =118.1\mathrm{}$ °K, which is considerably lower than the value $\theta \sim 160$ °K observed for other higher rare earths. The electronic specific heat of ytterbium $C_E=2.90T$ is also much smaller than the usual value $C_E\sim 10T$. In the nonmagnetic ytterbium metal the $5d$ electron, normally in the conduction band, is added to the $4f$ shell which thereby becomes full. This explains the differences between the specific heat of ytterbium and of the other rare earths. The small term in $C_p$ proportional to $T^{-2\mathrm{}}$, is probably caused by long-range exchange-type coupling between the electronic moments of rare-earth impurities in our ytterbium sample.