Theory of the field-dependent phase diagram of superfluidHe3below the polycritical point

Abstract

We examine a general class of Landau-Ginsburg (LG) theories of $l=1$ pairing characterizing superfluid $^{3}\mathrm{He}\ensuremath{-}A$ and $^{3}\mathrm{He}\ensuremath{-}B$ and show that the qualitative features of the observed magnetic-field-dependent phase diagram (below the polycritical point) can be understood within this framework. We find that a result of stability requirements is that in any arbitrarily small field the $\mathrm{normal}\ensuremath{\rightarrow}B$ transition is eliminated and that the $B$ state is metastable over a range of temperatures above the first-order $A\ensuremath{\rightarrow}B$ transition temperature ${T}^{\mathrm{AB}}$. New information about the fourth-order LG coefficients {${a}_{i}$} is gained from the present study. We find that the observed behavior of the field-dependent phase diagram implies that the five parameters {${a}_{i}$} must have the same sign as in weak-coupling theory with at most one exception. We demonstrate that a measurement of the linear field dependence of ${T}^{\mathrm{AB}}$ combined with three specific-heat discontinuity measurements will yield values for three of the five fourth-order LG coefficients and can serve, therefore, as an important (and previously unrecognized) test of microscopic theories of the pairing.