Phenomenological Theory of Superconductivity and Magnetism in Ho$_{1-x}$Dy$_x$Ni$_2$B$_2$C

TL;DR

This paper develops a phenomenological Ginzburg-Landau model to describe the coexistence and complex interplay of superconductivity and magnetism in Ho$_{1-x}$Dy$_x$Ni$_2$B$_2$C, explaining experimental doping-dependent behaviors.

Contribution

It introduces a multi-order parameter Ginzburg-Landau model capturing magnetic fluctuations and their impact on superconductivity in Ho-Dy nickel borocarbides.

Findings

Reproduces doping-dependent $T_c$ reentrance behavior.

Explains anomalous upper critical field behavior.

Aligns well with experimental data.

Abstract

The coexistence of the superconductivity and magnetism in the Ho$_{1-x}$Dy$_x$Ni$_2$B$_2$C is studied by using Ginzburg-Landau theory. This alloy shows the coexistence and complex interplay of superconducting and magnetic order. We propose a phenomenological model which includes two magnetic and two superconducting order parameters accounting for the multi-band structure of this material. We describe phenomenologically the magnetic fluctuations and order and demonstrate that they lead to anomalous behavior of the upper critical field. The doping dependence of $T_c$ in Ho$_{1-x}$Dy$_x$Ni$_2$B$_2$C showing a reentrance behavior are analyzed yielding a very good agreement with experimental data.