Heat flow between nuclei and conduction electrons in metals at very low temperatures

Abstract

Magnetic fieM and thermal gradients not only affect the heat flow between different parts of metallic samples but can also lead to anomalies in the observed energy transport between the electronic and nuclear energy reservoirs. Nuclear spin-lattice relaxation is considered in conditions of applied fieM and temperature such that the contribution of nuclear spins to the heat capacity dominates by far that of the electrons. The model presented is discussed with respect to recent steady state heat flow experiments on copper at submillikelvin temperatures in which a non-Korringa like, anomalously weak coupling between electrons and nuclei was observed. We show that in heat flow experiments at sufficiently low conduction electron temperatures, T~, when thermal gradients are present in the sample, the apparent Korringa constant takes the form tr = too (1 + ~(kT~) -I ) where ~ depends on the heat current and the nuclear heat capacity, too is the actual Korringa constant, and K is the thermal heat conductance of copper which in part depends on the applied field Bo as 1 2Bo assuming that the Wiedemann-Franz law holds. In fact, a BoTe dependence was reported for the anomalous nuclear spin electron coupling which we therefore conclude couM be explained by the finite thermal conductivity in an inhomogeneously heated sample. From a quantitative comparison of our model and the reported tr values, K wouM have to be one order of magnitude smaller than that expected for the used sample of high purity. Difficulties in comparing the over-simplified model with a real experiment are discussed and a comment concerning the effect of impurities in Pt-NMR thermometry at very low temperatures is given.