Motivated by recent progress in development of cryogenic memory compatible with single flux quantum (SFQ) circuits we have performed a theoretical study of magnetic SIsFS Josephson junctions, where S is a bulk superconductor, s is a thin superconducting film, F is a metallic ferromagnet and I is an insulator. We calculate the Josephson current as a function of s and F layers thickness, temperature and exchange energy of F film. We outline several modes of operation of these junctions and demonstrate their unique ability to have large product of a critical current $I_{C}$ and a normal-state resistance $R_{N}$ in the $pi$ state, comparable to that in SIS tunnel junctions commonly used in SFQ circuits. We develop a model describing switching of the Josephson critical current in these devices by external magnetic field. The results are in good agreement with the experimental data for Nb-Al/AlO${_x}$-Nb-Pd$_{0.99}$Fe$_{0.01}$-Nb junctions.
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