Classical theory of giant magnetoresistance in granular metals

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Abstract
I have extended the one-dimensional spin-diffusion theory of Valet and Fert [Phys. Rev. B 48, 7099 (1993)] [which treats perpendicular giant magnetoresistance (GMR) in magnetic multilayers] to three dimensions in order to deal with the problem of GMR in granular magnetic metals. These materials are composed of tiny precipitates of magnetic granules suspended within an immiscible nonmagnetic metallic matrix. It is assumed that the granules are spherical in shape, and have identical radii. The differential equations are solved separately for three different physical situations: (1) Bulk spin-dependent scattering in the nonmagnetic matrix; (2) Bulk spin-dependent scattering within the magnetic spheres; and (3) surface spin-dependent scattering at the ferromagnetic-normal interface. The magnetically induced electrical interaction between spheres, which gives rise to observed GMR, is treated in lowest order only. It is found to act via an induced electric-dipole field for cases (1) and (3), and an induced spin-diffusion field for case (2). Using these solutions, and macroscopic parameters from experiment, I have attempted to explain the observed singular dependence of the GMR on annealing temperature.