Long-range spin-singlet proximity effect for a Josephson system with a single-crystal ferromagnet due to its band-structure features

A possible explanation for the long-range proximity effect observed in single-crystalline cobalt nanowires sandwiched between two tungsten superconducting electrodes [Nat. Phys. 6, 389 (2010)] is proposed. The theoretical model uses properties of a ferromagnet band structure. Specifically, to connect the exchange field with the momentum of quasiparticles the distinction between the effective masses in majority and minority spin subbands and the Fermi-surface anisotropy are considered. The derived Eilenberger-like equations allowed us to obtain a renormalized exchange interaction that is completely compensated for some crystallographic directions under certain conditions. The proposed theoretical model is compared with previous approaches.