  We report the first ab-initio study of the interlayer exchange coupling in
Fe/c-FeSi/Fe sandwiches and Fe/c-FeSi multilayers. We perform several
structural studies, which show the stability of the CsCl arrangement seen
experimentally for the spacer. We find antiferromagnetic coupling between the
Fe slabs for spacer thicknesses smaller than about 15 $\AA$, for both
sandwiches and multilayers structures. We also study the effect of pinholes,
interface roughness or structural misconfigurations of the spacer on the sign
and magnitude of the exchange constant J. We finally show that the asymptotic
behavior of J is determined by a flat band of the c-FeSi spacer, located at the
M point in the Brillouin zone.
