Effects of Magnetic Order on the Upper Critical Field of UPt$_3$

TL;DR

This paper develops a Ginzburg-Landau theoretical model explaining the hexagonal oscillations of the upper critical field in UPt$_3$, linking magnetic order and superconductivity to observed anisotropic behaviors.

Contribution

It introduces a 2D order parameter model coupled with an in-plane AFM order to explain hexagonal anisotropy in UPt$_3$'s upper critical field near $T_c$, including sign changes and temperature dependence.

Findings

Explains the small magnitude of oscillations.

Describes persistence of oscillations near $T_c$.

Predicts a low-field crossover where oscillations vanish.

Abstract

I present a Ginzburg-Landau theory for hexagonal oscillations of the upper critical field of UPt$_3$ near $T_c$. The model is based on a $2D$ representation for the superconducting order parameter, $\vec{\eta}=(\eta_1,\eta_2)$, coupled to an in-plane AFM order parameter, $\vec{m}_s$. Hexagonal anisotropy of $H_{c2}$ arises from the weak in-plane anisotropy energy of the AFM state and the coupling of the superconducting order parameter to the staggered field. The model explains the important features of the observed hexagonal anisotropy [N. Keller, {\it et al.}, Phys. Rev. Lett. {\bf 73}, 2364 (1994).] including: (i) the small magnitude, (ii) persistence of the oscillations for $T\rightarrow T_c$, and (iii) the change in sign of the oscillations for $T> T^{*}$ and $T< T^{*}$ (the temperature at the tetracritical point). I also show that there is a low-field crossover (observable only very near $T_c$) below which the oscillations should vanish.