Quantum-well contributions to the RKKY coupling in magnetic multilayers

We study the effects of quantum-well states on the calculated RKKY coupling. We find that the bound states of a finite-size potential well of depth V give an added oscillation period of size πh/ √2mV. For the simplest case of a spherical free-electron Fermi surface, thus two periods appear: the original, 'fast', π/ kF oscillation, and the quantum-well one πh/√2mV. The quantum-well contributions have larger amplitude, and are in fact the predominant oscillation. For physically reasonable V (tenths of an eV) this period is around 8-10 Angstrom. We discuss evidence for these effects in experimental systems.