Specific Heat of Thulium Metal Between 0.38 and 3.9°K

Abstract

The specific heat $C_p$ of thulium metal has been measured in a ${\mathrm{He}}^3$ cryostat. Between 0.38 and 3.9°K $C_p=2.839\mathrm{}{T}^3+17.94T+23.43\mathrm{}{T}^{-2\mathrm{}}-1.79\mathrm{}{T}^{-3\mathrm{}}-0.066\mathrm{}{T}^{-4\mathrm{}}$ (in mJ/mole °K). The last three terms represent the nuclear specific heat $C_N$. On the basis of earlier estimates, we put $C_L=0.243\mathrm{}{T}^3$ and $C_E=10.5T$ for the lattice and electronic specific heats, respectively. According to the simple spin-wave theory, the magnetic specific heat $C_M$ is proportional to $T^3$ for a ferrimagnetic metal; experimentally one finds $C_M=6.2\mathrm{}{T}^{\frac{5}{2}}$ for thulium, which has a rather complicated ferrimagnetic structure. Further, there seems to be no evidence in $C_M$ for an exponential factor, to be expected because of magnetic anisotropy. All conclusions on $C_M$ are tentative, however, until data at temperatures between 4 and 20°K become available. $C_N$ does not fit to the simple picture as given by Bleaney either. Since $I=\frac{1}{2}$ for the only stable thulium isotope ${\mathrm{Tm}}^{169}$, quadrupole interactions are zero and there are only two nuclear energy levels, their separation being determined by the magnetic hyperfine constant $a^{\prime }$. This would give a nuclear specific heat with even powers of $T$ only, with $a^{\prime }$ determining the values of the coefficients. The observed $C_N$ cannot be fitted into an equation of this type which indicates that other interactions, probably nuclear exchange interactions, are present. Formally, the experimental situation may be expressed by writing $a^{\prime }=a_0-\frac{b}{T}$, instead of treating $a^{\prime }$ as a constant. Our results are in good agreement with recent Mössbauer data by Kalvius et al. who found 22.9 for the coefficient of the $T^{-2\mathrm{}}$ term.