  We investigate the origin of the long period oscillation of the interlayer
exchange coupling in Fe/Cr trilayer systems. Within the stationary phase
approximation the periods of the oscillations are associated with extremal
vectors of the Fermi sphere of Cr. Using a realistic tight-binding model with
spin-orbit interaction we calculate the coupling strength for each extremal
vector based on the spin-asymmetry of the reflection amplitude for a
propagating state impinging from the Cr to Fe layer. We find that for (001) and
(110) growth direction the biggest coupling strength comes from the extremal
vector centered at the ellipsoid N of the Fermi surface of Cr.
