The surface magnetisation of a tight-binding model ferromagnet

The surface magnetisation is determined for a semi-infinite simple cubic crystal described by a one-band Hubbard model. The author assumes changes in the model parameters on the first four layers of the crystal and he determines the magnetic moments for those layers by solving the eight Hartree-Fock equations numerically for the number of particles of each spin direction. The local densities of states required in the Hartree-Fock equations are determined by an integration over the Green functions for the semi-infinite crystal. Starting directly from the definition of the Green function as the resolvent of the Hamilton operator and proceeding by direct inversion of the corresponding infinite matrix, he derives an algorithm which significantly shortens the computation of the Green functions since it does not require the solution of a system of Dyson equations as in the Kalkstein-Soven method. The results of the author's numerical calculations show how the magnetic moments of the first four layers are reduced by a decrease of the Coulomb matrix elements or a downward shift of the bands and how they are enhanced by decreasing hopping matrix elements. Within the author's model calculation, he shows under what conditions dead layers could appear and how rapidly the magnetisation reaches its bulk value. The influence of hydrogen adsorption on the surface magnetisation of a model ferromagnet is briefly discussed.