Singlet-triplet conversion and the long-range proximity effect in superconductor-ferromagnet structures with generic spin dependent fields

TL;DR

This paper reveals new mechanisms for the long-range proximity effect in superconductor-ferromagnet structures, linking it to SU(2) fields and electric fields, beyond magnetic inhomogeneities.

Contribution

It establishes general conditions for long-range triplet components in S/F structures using SU(2) gauge theory and extends understanding beyond magnetic inhomogeneities.

Findings

Effective SU(2) electric field induces long-range triplet correlations.

Derived SU(2) covariant diffusive equations for condensate.

Universal condition for LRTC in generic ferromagnets.

Abstract

The long-range proximity effect in superconductor/ferromagnet (S/F) hybrid nano-structures is observed if singlet Cooper pairs from the superconductor are converted into triplet pairs which can diffuse into the fer- romagnet over large distances. It is commonly believed that this happens only in the presence of magnetic inhomogeneities. We show that there are other sources of the long-range triplet component (LRTC) of the con- densate and establish general conditions for their occurrence. As a prototypical example we consider first a system where the exchange field and spin-orbit coupling can be treated as time and space components of an effective SU(2) potential. We derive a SU(2) covariant diffusive equation for the condensate and demonstrate that an effective SU(2) electric field is responsible for the long-range proximity effect. Finally, we extend our analysis to a generic ferromagnet and establish a universal condition for the LRTC. Our results open a new avenue in the search for such correlations in S/F structures and make a hitherto unknown connection between the LRTC and Yang-Mills electrostatics.