Charge and spin currents in ferromagnetic Josephson junctions

We determine, using a self-consistent method, the charge and spin currents in ballistic Josephson junctions consisting of several ferromagnetic (F) layers sandwiched between superconducting (S) electrodes (SFS-type junctions). When there are two F layers, we also consider the experimentally relevant configuration where a normal (N) nonmagnetic spacer layer separates them. We study the current-phase relationships as functions of geometrical parameters that are accessible experimentally including particularly the angles that characterize the relative orientation of the magnetization in the F layers. Our self-consistent method ensures that the proper charge conservation laws are satisfied, and that important proximity effects are fully and properly accounted for. We find that as we vary the phase difference Lambda(phi) between the two outer S electrodes, multiple harmonics in the current-phase relations emerge, the extent of which depends on the interface scattering strength and on the relative F layer widths and magnetization orientations. By manipulating the relative F layer magnetization orientations, we find that the charge supercurrent can reverse directions or vanish altogether. These findings are discussed in the context of the generation and long-range nature of triplet pair correlation within these structures. We also investigate the spin currents and associated spin-transfer torques throughout the entire junction regions. For noncollinear relative magnetizations, the nonconserved spin currents in a given F region give rise to net torques that can switch directions at particular magnetic configurations or Lambda(phi) values. The details of the spin current behavior are shown to depend strongly on the degree of magnetic inhomogeneity in the system, including the number of F layers and the relative widths of the F and N layers.