Breakdown of the coexistence of spin-singlet superconductivity and itinerant ferromagnetism

TL;DR

This paper investigates the coexistence of spin-singlet superconductivity and ferromagnetism, finding that such coexistence is energetically unfavorable for spin-singlet pairing, and suggesting spin-triplet states are more likely in certain metals.

Contribution

The study provides a theoretical analysis of the coexistence of superconductivity and ferromagnetism, highlighting the energetic unlikelihood of spin-singlet coexistence and proposing spin-triplet states as more plausible.

Findings

Spin-singlet superconducting ferromagnetic state is energetically unfavorable.

Spin-triplet ferromagnetic superconducting state is more likely in some metals.

Thermodynamic potential favors non-magnetic superconducting state over ferromagnetic one.

Abstract

We discuss the possibility of coexistence of spin-singlet superconductivity and ferromagnetism in a model where the same electrons are assumed responsible for both of them. Our calculations include both zero and finite momentum pairing states with both s-wave and d-wave pairing symmetry. Under the mean-field approximation, the thermodynamic potential of the non-magnetic superconducting (SC) state is shown to be always lower than that of the superconducting ferromagnetic (SF) state. It follows that the spin-singlet SF state is energetically unfavorable, and a spin-triplet SF state is more likely to survive in metals such as UGe$_{2}$ and ZrZn$_{2}$.