  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.
