Superconductor spintronics: Modeling spin and charge accumulation in out-of-equilibrium NS junctions subjected to Zeeman magnetic fields

We study the spin and charge accumulation in junctions between a superconductor and a ferromagnet or a normal metal in the presence of a Zeeman magnetic field, when the junction is taken out of equilibrium by applying a voltage bias. We write down the most general form for the spin and charge current in such junctions, taking into account all spin-resolved possible tunneling processes. We make use of these forms to calculate the spin accumulation in NS junctions subjected to a DC bias, and to an AC bias, sinusoidal or rectangular. We observe that in the limit of negligeable changes on the superconducting gap, the NS dynamical conductance is insensitive to spin imbalance. Therefore to probe the spin accumulation in the superconductor, one needs to separate the injection and detection point, i. e. the electrical spin detection must be non-local. We address also the effect of the spin accumulation induced in the normal leads by driving a spin current and its effects on the detection of the spin accumulation in the superconductor. Finally, we investigate the out-of-equilibrium spin susceptibility of the SC, and we show that it deviates drastically from its equilibrium value.