- 'I. I. Soloviev'
- 'M. Yu. Kupriyanov'
- 'A. A. Golubov'
title: Theory of supercurrent transport in SIsFS Josephson junctions
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Introduction
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Josephson structures with a ferromagnetic layer became very active field of research because of the interplay between superconducting and magnetic order in a ferromagnet leading to variety of new effects including the realization of a $\pi $-state with phase difference $\pi $ in the ground state of a junction, as well as long-range Josephson coupling due generation of odd-frequency triplet order parameter [@RevG; @RevB; @RevV].

Further interest to Josephson junctions with magnetic barrier is due to emerging possibilities of their practical use as elements of a superconducting memory [@Oh]$^{-}$ [@APL], on-chip $\pi$- phase shifters for self-biasing various electronic quantum and classical circuits [@Rogalla]$^{-}$ [@Ustinov], as well as $\varphi$- batteries, the structures having in the ground state phase difference $\varphi _{g}=\varphi
$, $(0<|\varphi |<\pi )$ between superconducting electrodes [Buzdin,Koshelev,Pugach,Gold1,Gold2,Bakurskiy,Heim, Linder, Chan]{}. In standard experimental implementations SFS Josephson contacts are sandwich-type structures [@ryazanov2001]$^{-}$ [@Ryazanov2006a]. The characteristic voltage $V_{C}=J_{C}R_{N}$ ($J_{C}$ is critical current of the junction, $R_{N}$ is resistance in the normal state) of these SFS devices is typically quite low, which limits their practical applications. In SIFS structures 