Effects of band structure and spin-independent disorder on conductivity and giant magnetoresistance in Co/Cu and Fe/Cr multilayers

We develop a tight-binding model for calculating conductivity in multiband spin-dependent systems within the Kubo-Greenwood formalism. The model includes spin-independent disorder in the on-site atomic energies, representing intrinsic defects in real systems, and realistic spin-polarized electronic band structure. The model is applied to calculating conductivity in elemental $3d$ metals and giant magnetoresistance (GMR) in magnetic Co/Cu and Fe/Cr multilayers. We find that for disorder, producing a realistic resistivity of the multilayers, the values of GMR are in quantitative agreement with those observed experimentally. We demonstrate how the conductivity and GMR depend on the features of the electronic band structure and degree of disorder in the system. In particular, we show that (i) the $d$ electrons make an important contribution to the current in magnetic $3d$ metals and multilayers, (ii) the $sp-d$ hybridization is crucial for GMR, (iii) increasing disorder causes a decrease of the spin asymmetry of conductivity in magnetic metals and a drop of GMR in multilayers, (iv) GMR for the current-perpendicular-to-plane geometry is typically a factor of 2 higher than that for the current-in-plane geometry, and (v) the semiclassical treatment of conductivity applied to magnetic multilayers results in overestimated values of GMR due to the neglect of interband transitions.