NMR Frequency Shifts and Phase Identification in Superfluid $^3$He

TL;DR

This paper demonstrates that the NMR frequency shifts in superfluid $^3$He near the transition temperature directly measure the order parameter, which varies linearly with pressure, aiding phase identification.

Contribution

It shows that NMR frequency shifts provide a simple, linear measure of the order parameter in superfluid $^3$He, including in aerogels, facilitating phase identification.

Findings

NMR frequency shifts are proportional to the order parameter squared.

The pressure dependence of the order parameter is linear near $T_c$.

This behavior is consistent in bulk and aerogel-imbibed superfluid $^3$He.

Abstract

The pressure dependence of the order parameter in superfluid $^3$He is amazingly simple. In the Ginzburg-Landau regime, i.e. close to $T_c$, the square of the order parameter can be accurately measured by its proportionality to NMR frequency shifts and is strictly linear in pressure. This behavior is replicated for superfluid $^3$He imbibed in isotropic and anisotropic silica aerogels. The proportionality factor is constrained by the symmetry of the superfluid state and is an important signature of the corresponding superfluid phase. For the purpose of identifying various new superfluid states in the $p$-wave manifold, the order parameter amplitude of $^3$He-A is a useful reference, and this simple pressure dependence greatly facilitates identification.