Exchange coupling in magnetic multilayers: A quantum-size effect

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Abstract
The long-wavelength oscillations observed in magnetic multilayers are explained by an indirect Ruderman-Kittel-Kasuya-Yosida–like (RKKY) exchange interaction. A perturbative theory of the RKKY-like exchange coupling between two ferromagnetic layers separated by a nonmagnetic slab is derived. The approach includes a realistic description of the multilayer one-electron states, whose wave functions satisfy matching conditions at the ferromagnetic-nonmagnetic interfaces. The quantum-size effects exhibited by the electron transmission coefficient give rise to a distinct multilayer wavelength λ, which provides the measured long periods.