We present a model which allows the calculation of the relaxation rate
of magnetic transition-metal surfaces from the variation of the total
energy upon atomic displacements. We apply this model to calculate th
e top-layer relaxation of ferromagnetic Fe(001) and antiferromagnetic
Cr(001) surfaces, In the tight-binding scheme the relaxation rate is r
elated to the interatomic Green functions and p-d, p-f, p-g like hoppi
ng integrals between neutral atoms, We obtain in both cases a contract
ion of the top layers and we deduce in a self-consistent way the corre
sponding magnetic moments, Finally, we discuss the modifications which
occur with respect to the paramagnetic case and compare with availabl
e experimental results [J. Sokolov et al. Phys. Rev. B 33 (1986) 1397]
.