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

Abstract

A simple expression is presented for the period \ensuremath{\Lambda} of oscillatory interlayer exchange interactions in Co/X and Fe/X magnetic multilayer systems (X= a nearly-free-electron metal). \ensuremath{\Lambda} is shown to be much longer than the period \ensuremath{\lambda} 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 \ensuremath{\lambda} is close to an integral fraction of the interlayer spacing in the X layers. The dependence of \ensuremath{\Lambda} 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 \ensuremath{\lambda} have been derived. In some cases small but significant deviations were found from the value of \ensuremath{\lambda} which is predicted from the Ruderman-Kittel-Kasuya-Yosida theory.