The theory of GMR and TMR in segmented magnetic nanowires
  We calculate the resistivity and Giant Magnetoresistance (GMR) of a segmented nanowire consisting of two ferromagnetic segments separated by a thin paramagnetic spacer. The quantization of the electron motion due to the small nanowire cross-section is taken into account; s-d electron scattering gives rise to different mean free paths for spin-up and spin-down s-electrons. The calculated resistivity and GMR oscillate as a function of nanowire cross-section due to the difference in Fermi momenta of d-electrons with opposite spins. The GMR can reach values much higher than those which are obtained for "wires" of infinite cross-section (i.e., a multilayer). Similarly we have calculated the Tunneling Magnetoresistance (TMR) by replacing the paramagnetic spacer with an insulator spacer. 
M. Ye. Zhuravlev, H. O. Lutz, A. V. Vedyayev