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The possible explanation of the long-range proximity effect observed in thesingle-crystalline cobalt nanowire sandwiched between two tungstensuperconducting electrodes [Wang, M. \textit{et al}. \textit{ Nat. Phys}.\textbf{6}, 389 (2010)] is proposed. The theoretical approach is based on thefeatures of band structure of a ferromagnet. To connect the exchange field withthe momentum of quasiparticles the distinction between their effective massesin majority and minority spin bands and the Fermi surface anisotropy are takeninto account. The derived Eilenberger-like equations allow to obtain therenormalized effective exchange interaction that can be completely compensatedfor some crystallographic direction under certain conditions. The proposedtheoretical model is also compared with previous approaches.

The long-range spin-singlet proximity effect for the Josephson system with single-crystal ferromagnet due to its band structure features