Phase transition of two-dimensional He 3 from a dilute to a dense phase

TL;DR: Two puzzling aspects of the results are the lack of a significant heat-capacity jump at the transition and, based on a linear extrapolation of the data to zero temperature, a substantial amount of missingmore » entropy.

Abstract: We have measured the heat capacity of $^{3}\mathrm{He}$ in films of $^{4}\mathrm{He}$ as thin as 10 A\r{} formed on a Nuclepore filter substrate. At low temperatures, where the $^{3}\mathrm{He}$ is in the lowest state as far as motion perpendicular to the film surface, we find that the $^{3}\mathrm{He}$ undergoes a transition from a dilute phase to a dense phase. We have observed this transition for films of $^{4}\mathrm{He}$ of 12.3- and 10-A\r{} thickness and for coverages of $^{3}\mathrm{He}$ below about 0.2 atomic layers. For thicker $^{4}\mathrm{He}$ films, and higher $^{3}\mathrm{He}$ coverages, the $^{3}\mathrm{He}$ remains homogeneously spread out over the surface of the $^{4}\mathrm{He}$. The striking characteristic of the transition is the sudden onset of linear temperature dependence with a slope which is proportional to the amount of $^{3}\mathrm{He}$ in the calorimeter. This is consistent with the formation of islands of a dense two-dimensional phase which grows in extent proportionately to the amount of $^{3}\mathrm{He}$. Two puzzling aspects of our results are the lack of a significant heat-capacity jump at the transition and, based on a linear extrapolation of the data to zero temperature, a substantial amount of missing entropy.