Specific Heat of Gadolinium, Terbium, Dysprosium, Holmium, and Thulium Metals between 3 and 25°K

Abstract

The specific heat of gadolinium, terbium, dysprosium, holmium, and thulium metals has been measured between 3 and 25\ifmmode^\circ\else\textdegree\fi{}K using a germanium resistance thermometer. Anomalies, apparently associated with magnetic transformations in the metals themselves, were found for terbium at 16\ifmmode^\circ\else\textdegree\fi{}K and for holmium at 17.5\ifmmode^\circ\else\textdegree\fi{}K. Low-temperature peaks, probably resulting from impurities, were observed for gadolinium, terbium, and dysprosium. By assuming that the sum of the lattice and electronic specific heats of all these metals is given by the total ${C}_{p}$ of nonmagnetic lutetium and by calculating the nuclear contribution from previous work below 4\ifmmode^\circ\else\textdegree\fi{}K, the magnetic specific heat ${C}_{M}$ has been determined. For terbium and dysprosium an exponential temperature dependence, ${C}_{M}=36{T}^{\frac{3}{2}}\mathrm{exp}(\ensuremath{-}\frac{23.5}{T})$ and ${C}_{M}=107{T}^{\frac{3}{2}}\mathrm{exp}(\ensuremath{-}\frac{31}{T})$ ($T$ in \ifmmode^\circ\else\textdegree\fi{}K, ${C}_{M}$ in mj/mole \ifmmode^\circ\else\textdegree\fi{}K), respectively, was found. The results are in accord with current theories that take into account the strong basal anisotropy in the magnetic structure of these metals. For gadolinium ${C}_{M}=0.19{T}^{2.7}$ above 13\ifmmode^\circ\else\textdegree\fi{}K, but the functional form of ${C}_{M}$ is much less certain than for terbium and dysprosium. For holmium ${C}_{M}=1.5{T}^{3.2}$ represents the magnetic specific heat quite well below 8\ifmmode^\circ\else\textdegree\fi{}K. There is theoretical justification for a ${T}^{3}$ temperature dependence of ${C}_{M}$ for both gadolinium and holmium. The magnetic specific heat of thulium between 4 and 20\ifmmode^\circ\else\textdegree\fi{}K can be given by ${C}_{M}=8.3{T}^{2.3}$; no theoretical predictions are available for this metal. The observed behavior of ${C}_{M}$ for most of these rare earths can be correlated with existing data on magnetization and electrical resistivity.