The exchange coupling J between Fe layers separated by nonmagnetic Cr is ca
lculated for Fe/Cr/Fe (001) trilayer structures as a function of the spacer
thickness N for several temperatures T. It is shown that for perfectly sha
rp interfaces J(N,T) is entirely dominated by short period oscillations for
0 K less than or equal to T less than or equal to 500 K and N varying from
5 to 50 atomic planes. At zero temperature the amplitude of J decays as N-
3/2 for large values of N. This behavior is caused by the particular type o
f singularity in the nesting of the Cr Fermi which is responsible for one o
f the dominant short-period oscillations of J(N). A strong temperature depe
ndence of the coupling strength is obtained for some values of N, in excell
ent agreement with experiments. The effect of interface mixing on J(N) redu
ces the overall coupling strength, as well as the relative importance of th
e short period oscillatory components, and causes a phase shift in the osci
llations of J(N). [S0163-1829(99)03317-2].