The Behavior of a Triplet Superconductor in a Spin Only Magnetic Field

TL;DR

This paper analyzes the behavior of a triplet superconductor, Sr$_2$RuO$_4$, under a spin-only magnetic field, revealing phase stability and thermodynamic differences between possible superfluid phases.

Contribution

It provides a theoretical analysis of the order parameter phases of Sr$_2$RuO$_4$ in a magnetic field, identifying the A$_2$ phase as energetically favored and characterizing their thermodynamic properties.

Findings

A$_2$ phase is lower in free energy than the A phase.

No A$_1$ phase is observed in the model.

Heat capacity behaviors differ between A and A$_2$ phases.

Abstract

We investigate the order parameter of Sr$_2$RuO$_4$ in an exchange-only magnetic field. A Ginzburg-Landau symmetry analysis implies three possibilities: a pure $^3$He A phase, a $^3$He A$_1$ or a $^3$He A$_2$ phase. We explore the exchange field dependence of the order parameter and energy gap in a one-band model of Sr$_2$RuO$_4$. The numerical solutions show no A$_1$ phase and that the A$_2$ phase is lower in free energy than the A phase. We explore heat capacity as a function of temperature and field strength and find quantitatively different behaviors for the A and A$_2$ phases.