title: Singlet-triplet conversion and the long-range proximity effect in superconductor-ferromagnet structures with generic spin dependent fields.
abstract: The long-range proximity effect in superconductor-ferromagnet (S/F) hybrid nanostructures is observed if singlet Cooper pairs from the superconductor are converted into triplet pairs which can diffuse into the ferromagnet 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 condensate 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.
authors.affiliation: Centro Mixto CSIC-UPV/EHU, Centro de Física de Materiales (CFM-MPC), Manuel de Lardizabal 4, E-20018 San Sebastián, Spain and Donostia International Physics Center (DIPC), Manuel de Lardizabal 5, E-20018 San Sebastián, Spain and Institut für Physik, Carl von Ossietzky Universität, D-26111 Oldenburg, Germany.
authors.forename: F S
authors.initials: FS
authors.lastname: Bergeret
authors.affiliation: Departamento Física de Materiales, Nano-Bio Spectroscopy Group, Universidad del País Vasco, Avenida Tolosa 72, E-20018 San Sebastián, Spain and IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain.
authors.forename: I V
authors.initials: IV
authors.lastname: Tokatly