Quasiparticle energy spectrum in ferromagnetic Josephson weak links

The quasiparticles energy spectrum in clean ferromagnetic weak links between conventional superconductors is calculated. Large peaks in DOS, due to a special case of Andreev reflection at the ferromagnetic barrier, correspond to spin-splitt bound states. Their energies are obtained as a function of the barrier thickness, exchange field strength, and of the macroscopic phase difference $\phi$ at the link, related to the Josephson current. In the ground state, $\phi$ can be 0 or $\pi$, depending on the ferromagnetic barrier influence. Conditions for the appearence of the zero-energy bound states (ZES) and for the spin polarized ground state (SPGS) are obtained analytically. It is shown that ZES appear only outside the weak link ground state.