First-principles calculations of electrical conductivity and giant magnetoresistance of Co‖Cu‖Co spin valves

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Abstract
We show that the Kubo formula can be used to calculate the nonlocal electrical conductivity of layered systems from first principles. We use the layer Korringa-Kohn-Rostoker method to calculate the electronic structure and Green function of a slab of copper embedded in cobalt. The electronic structure is calculated self-consistently within the local density approximation to density functional theory. We use the Green function to evaluate the Kubo formula and calculate the conductivity for both majority and minority spins and for alignment and antialignment of the Co moments on either side of the Cu spacer layers. This allows us to determine the giant magnetoresistance from first principles. We investigate three possibilities for the scattering in Co‖Cu‖Co: (i) equal electron lifetimes for Cu, majority-spin Co, and minority-spin Co, (ii) equal electron lifetimes for majority and minority Co, weaker scattering in Cu, and spin-dependent interfacial scattering, (iii) electron lifetimes for majority- and minority-spin cobalt proportional to their Fermi energy densities of states, spin-dependent interfacial scattering, and spin-independent boundary scattering.