First Principles Calculation of Electrical Conductivity and Giant Magnetoresistance of ColCu Multilayers
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X. -G. Zhang 8 , D. M. C. Nicholson ** and J. M. MacLaren
*Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6114 "Computational Physics and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6114 tDepartment of Physics Tulane University New Orleans, LA 70118 ABSTRACT We show that the Kubo formula can be used to calculate the non-local electrical conductivity of layered systems from first principles. We use the Layer Korringa Kohn Rostoker method to calculate the electronic structure and the Green function of ColCulCo trilayers within the local density approximation to density functional theory. This Green function is used to calculate the conductivity through the Kubo formula for both majority and minority spins and for alignment and anti-alignment of the Co moments on either side of the Cu spacer layer. This allows us to determine the giant magnetoresistance from first principles. We investigate three possibilities for the scattering in ColCulCo: (1) equal electron lifetimes for Cu, majority spin Co, and minority spin Co, (2) equal electron lifetimes for majority and minority Co, weaker scattering in Cu and spin dependent interfacial scattering, (3) electron lifetimes for majority and minority spin cobalt proportional to their Fermi energy densities of states and spin dependent interfacial scattering. Introduction Recently there has been great interest in the transport properties of layered magnetic materials because of the discovery of a new form of magnetoresistance[1, 2] called the giant magnetoresistance (GMR). GMR is a change (generally a pronounced decrease) in the electrical resistance of an inhomogeneous system that is observed when an applied magnetic field causes an alignment of the magnetic moments in different parts of the material. GMR has been observed in several geometries, but the most promising and interesting GMR systems are composed of thin layers of ferromagnetic material separated by non-magnetic or very weakly magnetic spacer layers. The transport properties of layered materials have been the subject of several theoretical investigations based on the model of free electrons with random point scatterers (FERPS). Using this model, Fuchs[3] and later Sondheimer[4] obtained a solution to the semi-classical Boltzmann equation with boundary conditions appropriate to free electrons in a thin film. Barnai and coworkers[5] extended this approach to the case in which the film has several layers with differing scattering rates. Levy and coworkers[6, 7, 8, 9, 10] applied the more rigorous Kubo-Greenwood[l 1, 12] formula to the FERPS model and developed two different approximations for transport in magnetic multilayers. Zhang and Butler[131 have recently evaluated the Kubo-Greenwood formula exactly for the FERPS model applied to multilayers. Their results allow a comparison of the relative success of the various approximations in representing the conductivity of the free electron model. They found that the semi-classical 291
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