Josephson effect in S/F/S junctions: Spin bandwidth asymmetry versus Stoner exchange

Abstract

We analyze the dc Josephson effect in a ballistic superconductor/ferromagnet/superconductor junction by means of the Bogoliubov--de Gennes equations in the quasiclassical Andreev approximation. We consider the possibility of ferromagnetism originating from a mass renormalization of carriers of opposite spin, i.e., a spin bandwidth asymmetry. We provide a general formula for Andreev levels that is valid for arbitrary interface transparency, exchange interaction, and bandwidth asymmetry, and we analyze the current-phase relation, free energy, and critical current in the short junction regime. We compare the phase diagrams and the critical current magnitudes of two identical junctions differing only in the mechanism by which the midlayer becomes magnetic. We show that a larger number of $0\ensuremath{-}\ensuremath{\pi}$ transitions caused by a change in junction width or polarization magnitude is expected when ferromagnetism is driven by spin bandwidth asymmetry compared to Stoner magnetism. Moreover, we show that these features can be present also for ferromagnets of the Stoner type having only a partial bandwidth asymmetry.