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Spin-polarized Josephson and quasiparticle currents in superconducting spin-filter tunnel junctions

We present a theoretical study of the effect of spin-filtering on the Josephson and dissipative quasiparticle currents in a superconducting tunnel junction. By combining the quasiclassical Green's functions and the tunneling Hamiltonian method we describe the transport properties of a generic junction consisting of two superconducting leads with an effective exchange field h separated by a spin-filter insulating barrier. We show that besides the tunneling of Cooper pairs with total spin-projection Sz = 0 there is another contribution to the Josephson current due to equal-spin Cooper pairs. The latter is finite and not affected by the spin-filter effect provided that the fields h and the magnetization of the barrier are non-collinear . We also determine the quasiparticle current for a symmetric junction and show that the differential conductance may exhibit peaks at different values of the voltage depending on the polarization of the spin-filter, and the relative angle between the exchange fields and the magnetization of the barrier. Our findings provide a plausible explanation for existing experiments on Josephson junctions with magnetic barriers, predict new effects and show how spin-polarized supercurrents in hybrid structures can be created.