He3specific heat and thermometry at millikelvin temperatures

Abstract

High-precision specific-heat measurements were made on pure liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in both the normal and superfluid phases for temperatures between 0.6 and 5 mK and for pressures between 0 and 34 bars. The data were obtained using a magnetic susceptibility thermometer which was calibrated against the National Bureau of Standards scale near 15 mK and at lower temperatures principally by the condition that the zero-pressure normal-phase specific heat be linear in temperature. The ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ phase diagram based on this scale is presented. In particular we find that $T_A$=2.49 mK which differs quite substantially from the currently accepted value of about 2.7 mK. Multiplying the Pt NMR temperatures determined by Haavasoja and co-workers by a factor of 0.89 or subtracting 0.13 mK from the magnetic temperatures of Paulson et al. brings both of these scales into excellent agreement with the new scale. The ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ quasiparticle effective mass, $m_3^{\mathrm{*}}$(P), extracted from the normal-phase data agrees well with our previously reported results based on higher-temperature specific-heat data. The values of $m_3^{\mathrm{*}}$(P) from Haavasoja and co-workers are ∼20% smaller. However, if their specific-heat data are reanalyzed using the new temperature scale, the two sets of $m_3^{\mathrm{*}}$(P) values are brought into good agreement. We thus claim that the large discrepancies between previous specific-heat measurements are due almost entirely to differences in temperature scales. The new normal-phase specific-heat data at low pressures show no evidence of the anomalous behavior observed by Haavasoja and co-workers. Consequently, the size of the specific-heat jump at $T_c$ could be determined with little ambiguity over the entire pressure range. ΔC/$C_{>}$ is only a few percent larger than the weak-coupling value at P=0 and increases linearly with sample density. At high density the temperature dependence of the specific heat below $T_c$ shows small deviations from theory.