Localized states in a superconducting SI(F)S junction in the presence of a weak magnetic field

A symmetric tunneling junction formed by two pure type I superconductors with a ferromagnetic insulator as a barrier is considered. We show that when an external magnetic field H 0 satisfying the conditions H 0 Φ 0 /δL, ξ 0 L δ J is applied in the plane of the barrier (Φ 0 is the flux quantum, δ the magnetic penetration depth in electrodes, ξ b the BCS coherence length, δ J the Josephson penetration depth, L the length of the barrier in the direction perpendicular to the applied field), the energy spectrum of the system contains two discrete levels corresponding to both orientations of spin (in the zero magnetic field there is only one polarized level). The energy levels are calculated based on the Bogolyubov equations