Specific Heat of Thulium Metal Between 0.38 and 3.9°K

The specific heat Cₚ of thulium metal has been measured in a He³ cryostat. Between 0.38 and 3.9^∘{}K Cₚ=2.839T³+17.94T+23.43T^-2-1.79T^-3-0.066T^-4 (in mJ/mole ^∘{}K). The last three terms represent the nuclear specific heat CN. On the basis of earlier estimates, we put CL=0.243T³ and CE=10.5T for the lattice and electronic specific heats, respectively. According to the simple spin-wave theory, the magnetic specific heat CM is proportional to T³ for a ferrimagnetic metal; experimentally one finds CM=6.2T5/2 for thulium, which has a rather complicated ferrimagnetic structure. Further, there seems to be no evidence in CM for an exponential factor, to be expected because of magnetic anisotropy. All conclusions on CM are tentative, however, until data at temperatures between 4 and 20^∘{}K become available. CN does not fit to the simple picture as given by Bleaney either. Since I=1/2 for the only stable thulium isotope Tm¹⁶⁹, quadrupole interactions are zero and there are only two nuclear energy levels, their separation being determined by the magnetic hyperfine constant a^'. This would give a nuclear specific heat with even powers of T only, with a^' determining the values of the coefficients. The observed CN 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^'=a₀-b/T, instead of treating a^' as a constant. Our results are in good agreement with recent M\"ossbauer data by Kalvius et al. who found 22.9 for the coefficient of the T^-2 term.