Current-phase relations in SIsFS junctions in the vicinity of 0-π transition

We consider the current-phase relation (CPR) in Josephson junctions with complex insulator-superconductor-ferromagnetic interlayers in the vicinity of the 0-π transition. We find a strong impact of the second harmonic on the CPR of the junctions. It is shown that the critical current can be kept constant in the region of 0-π transition, while the CPR transforms through multivalued hysteretic states depending on the relative values of tunnel transparency and magnetic thickness. Moreover, the CPR in the transition region has multiple branches with distinct ground states.