Nontrivial interplay between superconductivity and spin-orbit coupling in non-centrosymmetric ferromagnets

TL;DR

This paper develops a mean-field theory for ferromagnetic, non-centrosymmetric superconductors, revealing that spin-orbit coupling enhances both ferromagnetism and superconductivity, with implications for materials like UIr.

Contribution

It introduces a theoretical framework analyzing the interplay of ferromagnetism, superconductivity, and spin-orbit coupling in non-centrosymmetric materials, highlighting the enhancement effects.

Findings

Spin-orbit coupling enhances ferromagnetism.

Spin-orbit coupling enhances superconductivity.

Analysis of order parameter symmetries in UIr.

Abstract

Motivated by the recent discoveries of ferromagnetic and non-centrosymmetric superconductors, we present a mean-field theory for a superconductor that \textit{both} lacks inversion symmetry and displays ferromagnetism, a scenario which is believed to be realized in UIr. We study the interplay between the order parameters to clarify how superconductivity is affected by the presence of ferromagnetism and spin-orbit coupling. One of our key findings is that the spin-orbit coupling seems to enhance both ferromagnetism and superconductivity in all spin channels. We discuss our results in the context of the heavy fermion superconductor UIr and analyze possible symmetries of the order parameter by the group theory method.