Effect of the dipole energy on a half-quantum vortex in the superfluid polar phase

Abstract

NMR experiments on superfluid $^{3}\mathrm{He}$ in a nematic aerogel have shown that the stability of the half-quantum vortex (HQV) realized in the polar phase depends on the relative direction between the magnetic field and the anisotropy axis brought by the aerogel. The vortex energy in the polar phase is examined in terms of the Ginzburg-Landau free energy incorporating the dipole energy, and the reason why the HQV in the polar phase in nematic aerogels became unstable in a transverse magnetic field upon a field cooling is explained.