Generalized Ruderman-Kittel-Kasuya-Yosida theory of oscillatory exchange coupling in magnetic multilayers

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Abstract
In Ruderman-Kittel-Kasuya-Yosida (RKKY) perturbation theories of magnetic multilayers, realistic energy bands are used to obtain the nesting required for oscillatory behavior, but the Bloch functions are generally approximated by plane waves. To account for the observed long-period oscillations of the exchange coupling, we present a generalized RKKY theory, which includes both the Bloch character of the wave functions and the boundary scattering at the film edges. In contrast to existing theories, these two effects lead to long-period oscillations, that are robust with regard to roughness of the spin distribution and to oscillation amplitudes that sharply increase with the localized nature of the Bloch functions, in agreement with experiment.