Theory of the field-dependent phase diagram of superfluid He3 below the polycritical point

We examine a general class of Landau-Ginsburg (LG) theories of l=1 pairing characterizing superfluid He3-A and He3-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 normalB transition is eliminated and that the B state is metastable over a range of temperatures above the first-order AB transition temperature TAB. New information about the fourth-order LG coefficients {ai} is gained from the present study. We find that the observed behavior of the field-dependent phase diagram implies that the five parameters {ai} 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 TAB 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.