Ab initio calculations are presented for the giant magnetoresistance (
GMR) of Fe/Cr multilayers. The electronic structure of Fe/Cr superlatt
ices is calculated within the spin density functional theory. The spin
-dependent bulk impurity scattering is treated in a fully quantum mech
anical way using a Green function formalism. The transport is describe
d quasiclassically. The calculations suggest that the GMR in thin mult
ilayers is mainly determined by the electronic structure of the layere
d system. Spin-dependent impurity scattering can reduce, increase, or
invert the effect.