Theory of Proximity Effect in Ferromagnet/Superconductor Heterostructures in the Presence of Spin Dependent Interfacial Phase Shift

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<jats:p> We study the proximity effect and charge transport in ferromagnet (F)/superconductor (S) and S/F/I/F/S junctions (where I is insulator) by taking into account simultaneously exchange field in F and spin-dependent interfacial phase shifts (SDIPS) at the F/S interface. We solve the Usadel equations using extended Kupriyanov–Lukichev boundary conditions which include SDIPS, where spin-independent part of tunneling conductance <jats:italic>G</jats:italic> <jats:sub>T</jats:sub> and spin-dependent one <jats:italic>G</jats:italic> <jats:sub>φ</jats:sub> coexist. The resulting local density of states (LDOS) in a ferromagnet depends both on the exchange energy <jats:italic>E</jats:italic> <jats:sub>ex</jats:sub> and <jats:italic>G</jats:italic> <jats:sub>φ</jats:sub>/<jats:italic>G</jats:italic> <jats:sub>T</jats:sub>. We show that the magnitude of zero-temperature gap and the height of zero-energy LDOS have a non-monotonic dependence on <jats:italic>G</jats:italic> <jats:sub>φ</jats:sub>/<jats:italic>G</jats:italic> <jats:sub>T</jats:sub>. We also calculate Josephson current in S/F/I/F/S junctions and show that crossover from 0-state to π. </jats:p>

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