Review paper: Heat transfer between liquid helium and solids below 100 mK

The many experimental determinations of heat transfer between liquid helium and solids are reviewed and compared with the existing theories. Generally heat transfer is a complex process at low temperatures, involving parallel heat paths with several resistances in series in each path. The standard theories for the individual resistances are reviewed and as far as possible a definite value of the expected resistance obtained. The experiments have been considered in five groups: cerium magnesium nitrate in liquid³He, cerium magnesium nitrate in dilute³He in liquid⁴He, metals in liquid³He, metals in dilute³He in liquid⁴He, and miscellaneous experiments. Where appropriate, the experimental results have been reevaluated in terms of standard models for heat transfer and presented as resistance versus temperature on diagrams showing the theoretical predictions. Between 20 and 100 mK many measurements show good agreement with acoustic mismatch theory for thermal boundary resistance. Below 20 mK most experiments have been made with finely divided solids (sintered metals or powdered paramagnetic salts); invariably the resistance has been anomalously low, with the metal/³He systems showingR T ^–1 and the metal/dilute³He in⁴He systems showingR T ^–3. The cerium magnesium nitrate/helium experiments have shown a temperature—independent resistance and sometimes anR T ^~1 dependence. These resistances have been attributed to the spin-lattice resistance in cerium magnesium nitrate. Evidence for heat transfer by magnetic coupling has been reviewed and it is concluded that the positive evidence has other explanations, while the lack of dependence upon helium pressure,³He phase, and large magnetic fields is strong negative evidence. If the disagreement of experimental results with standard theory is not to be attributed to magnetic coupling, then several theoretical questions remain to be answered; these questions are posed. Basically, at low temperatures the excitations in solids and liquid helium have wavelengths and mean free paths much larger than the size of the finely divided particles or pores between the particles. Thus theories for bulk solids and bulk liquid helium are not appropriate for describing excitations and their interactions at these low temperatures.