Magnetic Field Dependence of $T_{AB}$ in Superfluid $^3He$

TL;DR

This paper reexamines how magnetic fields influence the superfluid transition temperature in helium-3, highlighting the importance of linear and quadratic field contributions and Fermi liquid effects on observability.

Contribution

It introduces a refined analysis of the magnetic field dependence of $T_{AB}$, accounting for linear-in-field effects beyond previous approximations.

Findings

Quadratic-in-field effects dominate at high magnetic fields.

Fermi liquid effects shift the linear-in-field region to lower fields.

The well-known quadratic dependence is confirmed in high field regimes.

Abstract

The magnetic field dependence of the $A\to B$ transition temperature $T_{AB}$ in the superfluid $^3He$ is reconsidered in order to take into account the linear-in-field contribution beyond the approximation used in Ref.[7]. In the high field region, where the quadratic-in-field contribution prevails, the well known answer is restored. On the other hand,it is pointed out that the Fermi liquid effects shift the observability of the linear-in-field region to rather low magnetic fields.