Order parameter symmetry in ferromagnetic superconductors

TL;DR

This paper investigates how the symmetry and nodal structure of the superconducting order parameter in cubic ferromagnets like ZrZn₂ are affected by electromagnetic interactions and spin-orbit coupling, predicting the gap node locations.

Contribution

It analyzes the evolution of the order parameter symmetry considering electromagnetic and spin-orbit interactions, revealing the two-component nature and symmetry breaking in ferromagnetic superconductors.

Findings

Order parameter has two components below critical temperature.

Symmetry is described by co-representations of magnetic point groups.

Predictions made about the location of gap nodes.

Abstract

We analyze the symmetry and the nodal structure of the superconducting order parameter in a cubic ferromagnet, such as ZrZn$_2$. We demonstrate how the order parameter symmetry evolves when the electromagnetic interaction of the conduction electrons with the internal magnetic induction and the spin-orbit coupling are taken into account. These interactions break the cubic symmetry and lift the degeneracy of the order parameter. It is shown that the order parameter which appears immediately below the critical temperature has two components, and its symmetry is described by {\em co-representations} of the magnetic point groups. This allows us to make predictions about the location of the gap nodes.