  We present the combination of Density Functional Theory (DFT) and Dynamical
Mean Field Theory (DMFT) for computing the electron transmission through
two-terminals nanoscale devices. The method is then applied to metallic
junctions presenting alternating Cu and Co layers, which exhibit spin-dependent
charge transport and giant magnetoresistance (GMR) effect. The calculations
show that the coherent transmission through the $3d$ states is greatly
suppressed by electron correlations. This is mainly due to the finite lifetime
induced by the electron-electron interaction and is directly related to the
imaginary part of the computed many-body DMFT self-energy. At the Fermi energy,
where in accordance with the Fermi-liquid behavior the imaginary part of the
self-energy vanishes, the suppression of the transmission is entirely due to
the shifts of the energy spectrum induced by electron correlations. Based our
results, we finally suggest that the GMR measured in Cu/Co heterostructures for
electrons with energies about 1 eV above the Fermi energy is a clear
manifestation of dynamical correlation effects.
