Ballistic transport in ferromagnet-superconductor-ferromagnet trilayers   with arbitrary orientation of magnetizations
  Transport phenomena in clean ferromagnet-superconductor-ferromagnet (FSF) trilayers are studied theoretically for a general case of arbitrary orientation of in-plane magnetizations and interface transparencies. Generalized expressions for scattering probabilities are derived and the differential conductance is computed using solutions of the Bogoliubov-de Gennes equation. We focus on size and coherence effects that characterize ballistic transport, in particular on the subgap transmission and geometrical oscillations of the conductance. We find a monotonic dependence of conductance spectra and magnetoresistance on the angle of misorientation of magnetizations as their alignment is changed from parallel to antiparallel. Spin-triplet pair correlations in FSF heterostructures induced by non-collinearity of magnetizations are investigated by solving the Gor'kov equations in the clean limit. Unlike diffusive FSF junctions, where the triplet correlations have a long-range monotonic decay, we show that in clean ferromagnet-superconductor hybrids both singlet and triplet pair correlations induced in the F layers are oscillating and power-law decaying with the distance from the S-F interfaces. 
Milos Bozovic and Zoran Radovic