Period of oscillatory exchange interactions in Co/Cu and Fe/Cu multilayer systems

A simple expression is presented for the period {Λ} of oscillatory interlayer exchange interactions in Co/X and Fe/X magnetic multilayer systems (X= a nearly-free-electron metal). {Λ} is shown to be much longer than the period {λ} of the Ruderman-Kittel-Kasuya-Yosida-like spin-density oscillations in the X layers, which are induced by the coupling with the ferromagnetic layers, if {λ} is close to an integral fraction of the interlayer spacing in the X layers. The dependence of {Λ} on the growth direction of the multilayers is explained. From the available experimental data on fcc Co/Cu(111), fcc Co/Cu(100), and fcc Fe/Cu(100), and from results of recently published band-structure calculations for bcc Fe/Cu(100) effective values of {λ} have been derived. In some cases small but significant deviations were found from the value of {λ} which is predicted from the Ruderman-Kittel-Kasuya-Yosida theory.