Quantum transport of injected electrons in an asymmetric FM/I1/SC/I2/FM junction: Directional dependence

We have studied the directional dependence of the spin dependent coherent quantum transport in an asymmetric nano layer FM/I1/SC/I2/FM junction. We have used the Bogoliubov-de Gennes equations to describe the quasiparticles in the different layers in the junction. The two ferromagnetic layers are taken to be the same material, while the SC is taken to be a s-wave superconductor, I1 and I2 are taken to be thin insulating layers made with different materials. Both the effects of parallel (P) and anti parallel (AP) alignments of the magnetizations in the different FM layers are studied. We find that the probabilities for the Andreev and normal reflections and for the transmission of the particles into the ferromagnetic layers are dependent on the spins. We also find that the transports of the particles injected from the left side into the FM/I1/SC/I2/FM and into the FM/I2/SC/I1/FM junctions are different. When the I1 and I2 are removed (resulting in the formation of a trilayer FM/SC/FM junction) and the thickness of the SC layer is made small, the probability for the Andreev reflection is seen to depend on the spins of the particles in contradiction to the results obtained by Bozovic and Radovic [M. Bozovic, Z. Radovic, Phys. Rev. B 66 (2002) 134524].