Charge and spin currents in ferromagnetic Josephson junctions

摘要: 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 experimentally relevant configuration where normal ($N$) nonmagnetic spacer layer separates them. study current-phase relationships as functions geometrical parameters that accessible including particularly angles characterize relative orientation magnetization layers. Our method ensures proper conservation laws satisfied, important proximity effects fully properly accounted for. find vary phase difference $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}$ outer $S$ electrodes, multiple harmonics relations emerge, extent which depends on interface scattering strength widths orientations. By manipulating orientations, supercurrent can reverse directions or vanish altogether. These findings discussed context generation long-range nature triplet pair correlation within these structures. investigate associated spin-transfer torques throughout entire junction regions. For noncollinear magnetizations, nonconserved given region give rise to net switch at particular magnetic configurations values. The details current behavior shown depend strongly degree inhomogeneity system, number $N$