${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ordering transition on single-leaf pyrolytic graphite: A microcalorimetry study

We have developed an ac microcalorimeter for the thermodynamic study of adsorbed gases on a single cleaved leaf of pyrolytic graphite. Our sensitivity of about 0.1 nJ/deg was sufficient to probe details of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ordering transition. After in situ baking of the sample we found heat-capacity peaks comparable to those measured on the best exfoliated graphite substrates. The phase diagram near ordering is narrower than previously measured and a critical analysis yields asymmetric peaks: The low-T side diverges logarithmically for the six coverages analyzed between 0.0633/A${̊}^2$ and 0.0649/A${̊}^2$ while the high-T side of the peak displays a power-law divergence. The critical-heat-capacity exponent α in this coverage range drops from 0.48 (stronger than that in the three-state Potts model) to -0.07 (slightly cusped). We interpret the narrow ordered-phase region as reflecting our excellent film geometry and the unexpected nonuniversality as caused by residual impurity, rather than size-limiting effects. Additional ac calorimetry studies should complement adsorbed-film single-crystal diffraction research.