Stability, orientational effects, and temperature dependence of nonunitary vortex structures in superfluid³He

Abstract

First we set up the nine Ginzburg-Landau (GL) equations for the ninecomplex radial functions of an axisymmetric vortex line in superfluid³He. These GL equations necessarily yield a nine-componentnonunitary state for the A-phase vortex that corresponds to the Mermin-Ho trial state. We then solve the GL equations and calculate the energies for the five B-phase vortices of different symmetries that have been discussed by Salomaa and Volovik. We find that the only stable vortex is theirv-vortex, which has a superfluid and ferromagnetic core. Theo-vortex, which has a normal core, turns out to bemetastable (it is a saddle point on the energy surface describing theuvw-vortices). Theu-,w-, anduvw-vortices are found to beunstable. In the second part of the paper we calculate, with the help of the generalized GL theory, the temperature corrections to the GL structures of theo- andv-vortices. It turns out that the corresponding temperature variations of the two orientational energies for the$\hat n$-vector that are linear and quadratic in the field disagree with the measured temperature variations of the parameters κ and λ (see Hakonenet al.). However, a novel new orientational energy due to the interaction of the field and superflow around the vortex line increases linearly asT is decreased, in agreement with the measured behavior of λ.