Quantum Well Theory of the Exchange Coupling in Co/Cu/Co(001)

The exchange coupling between two semi-infinite Co layers separated by a Cu(001) spacer is calculated by two different methods using $s,p$, and $d$ tight-binding bands fitted to ab initio band structures of Cu and ferromagnetic Co. The contributions to the coupling from the belly (long period) and necks (short period) of the Cu Fermi surface (FS) are determined separately. It is shown that the short-period oscillation due to the minority electrons from the vicinity of the Cu FS necks is dominant, the contribution of the long-period oscillations being negligible. This is due to the existence of quantum well bound states for the minority electrons at the Cu FS necks in the ferromagnetic configuration.