RKKY interactions across yttrium layers in Gd-Y superlattices

A simple calculation of the RKKY coupling between two Gd arrays in a Gd-Y superlattice is presented. The calculation is valid for Gd arrays consisting of a single atomic layer. The Fourier transform J(q) of the exchange interaction between two Gd layers separated by Y is taken to be that of Gd layers embedded in an Y matrix. Plausible arguments are given in support of this procedure. The coupling is calculated by making use only of the measured J(q) in bulk Gd and of the calculated generalized susceptibilities of Gd and Y. The coupling is found to be of fairly long range and to be consistent in sign with recent neutron scattering measurements of long-range order in Gd-Y superlattices. Numerical calculations on a model, one-dimensional superlattice with two free-electron metals of different electron densities have not provided a useful guide for calculating RKKY interactions in superlattices and further theoretical work is necessary.