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Superconductor-ferromagnet-superconductor Josephson junctions are known toexist in the $0$ and $\pi$ states with the transitions between them controlledby the temperature and ferromagnetic interlayer thickness. We demonstrate thatthese transitions can be controlled also by the external magnetic fielddirected perpendicular to the layers. By varying the ratio of diffusioncoefficients in superconducting and ferromagnetic layers, thesefield-controlled transitions can be made detectable for arbitrary large valueof the exchange energy in the ferromagnet. We also show that the $0$-$\pi$transitions in the perpendicular field can be observed as the specific featuresof the flux-flow conductivity dependencies on the ferromagnetic thickness inaccordance with recent experimental results.

Magnetic field-controlled 0-$\pi$ transitions and their experimental signatures in superconductor-ferromagnet-superconductor junctions