Theory of the exchange coupling in magnetic metallic multilayers

Existing theories of the oscillatory exchange coupling in magnetic metallic multilayers are reconciled within a common approach. It is shown that Ruderman-Kittel-Kasuya-Yosida–type theories and full-confinement quantum-well results are obtained as limiting cases. Numerically useful and model-independent closed-form expressions for the exchange coupling across a nonmagnetic spacer are obtained in terms of the one-electron propagators. The theory can be extended to deal with nonmagnetic alloy spacers and it is argued that the existence of disorder in the spacer may lead to significant reduction of the interlayer coupling.