Relaxation of magnetic transition-metal surfaces

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 the top-layer relaxation of ferromagnetic Fe(001) and antiferromagnetic Cr(001) surfaces, In the tight-binding scheme the relaxation rate is related to the interatomic Green functions and p-d, p-f, p-g like hopping integrals between neutral atoms, We obtain in both cases a contraction of the top layers and we deduce in a self-consistent way the corresponding magnetic moments, Finally, we discuss the modifications which occur with respect to the paramagnetic case and compare with available experimental results [J. Sokolov et al. Phys. Rev. B 33 (1986) 1397].