We investigate the origin of the long-period oscillation of the interl
ayer exchange coupling in Fe/Cr trilayer systems. Within the stationar
y phase approximation the periods of the oscillations are associated w
ith extremal vectors of the Fermi sphere of Cr. Using a realistic tigh
t-binding model with spin-orbit interaction we calculate the coupling
strength for each extremal vector based on the spin asymmetry of the r
eflection amplitude for a propagating state impinging from the Cr to F
e layer. We find that for the (001) and (110) growth directions the bi
ggest coupling strength comes from the extremal vector centered at the
ellipsoid N of the Fermi surface of Cr.