Heat conductivity measurements at low temperatures

The transport properties of the rare earth elements exhibit many interesting features, especially around the magnetic transition temperatures. The little data available on the thermal conductivity of the heavy rare earth metals cover mostly the high temperature range (5–300°K). The results reported at the lower end of this temperature range are unexpected, the thermal conductivity largely exceeding the value derived from the electrical conductivity via the Wiedemann–Franz law. For example, the Lorenz numbers given varied from 3 to 12 × 10−8 watts- ohms- K−2 (theoretical value 2.45 × 10−8 watts- ohms-K−2). These authors concluded that mechanisms of heat transport other than the usual dominant electronic term must also be present. Recently some anomalous results were reported for some of the heavy rare earths in the He4 temperature range and the results did not extrapolate to the origin at 0°K.
These discrepancies and the hope that at sufficiently low temperatures a predominantly electronic thermal conductivity obeying Wiedemann–Franz law would emerge were good reasons for a detailed investigation down to a lower limit of temperature. In this thesis we present a systematic thermal conductivity study of the heavy rare earth metals in the temperature range 0.4 to 4.2°K. covered by two different cryostats - a He3 and a He4 cryostat. The specimens studied were gadolinium (2 samples), dysprosium (2 samples), holmium (2 samples), erbium (2 samples), terbium (1 sample) and ytterbium (1 sample).
The results obtained by us show no anomaly and are very consistent. The thermal conductivity of all the specimens can be separated into a linear and a small quadratic term in temperature. Furthermore our results do not confirm the anomalously high Lorenz numbers previously referred to in the literature but when we relate the linear temperature dependence of the thermal conductivity to the residual electrical resistivity using Wiedemann–Franz law we obtain, for all the specimens, Lorenz numbers which are remarkably close to the theoretical value. We therefore conclude that the linear term represents an electronic contribution, with the electron mean free path limited by 'impurity' scattering.
To account for the small quadratic contribution, we have invoked other carriers – phonons and magnons. We have observed this term in specimens which have spin waves and also in those which have no spin waves below 4°K. Further measurements were done to see the effects of dislocations on this small quadratic contribution. The results of these experiments lead us to believe that the major contribution to this quadratic term in thermal conductivity is due to phonon conduction limited by electron scattering. We may have not reached the upper limit, for there may be a little additional scattering of the phonons due to dislocations, which has the same temperature dependence.
The thesis is divided into three chapters. In chapter one a brief account of the theory of thermal conduction in metals at low temperatures is presented. We have also given some magnetic properties of the rare earth ferromagnets in this chapter.
The second chapter describes the He3 cryostat, which we designed and built for measuring the thermal conductivity below 1°K. Also discussed are the techniques used.
Finally in the third chapter the results are discussed.