Thermodynamics of the $\mathit{A}-\mathit{B}$ Phase Transition and the Geometry of the $\mathit{A}$-Phase Gap Nodes in Superfluid ${}_{}{}^3{}_{}{}^{}He$ at Low Temperatures

Since the $A$ phase of superfluid ${}^3\mathrm{He}$ has an energy gap with nodes while the $B$ phase has a uniform gap, the entropies of the two phases are very different at low temperatures. The latent heat of the $A-B$ transition is thus relatively large and provides a convenient probe for examining the structure of the $A$-phase gap nodes at low temperatures. We report here measurements of the latent heat down to $\sim 150\mu \mathrm{K}$ which show that at least to this temperature, the $A$-phase gap near the nodes is increasing linearly with deviation of the $k$ vector from the nodal line. From the measurements of the latent heat and of the transition field $B_{\mathrm{AB}}$ we can determine the magnetization difference between the two phases.