Surface magnetism studied within the mean-field approximation of the Hubbard model

Collective surface magnetism is studied within the mean-field approximation of the semi-infinite Hubbard model for the (100) surface of a simple cubic lattice. We investigate the changes of electronic and related magnetic properties at the surface with respect to the bulk that are introduced due to the reduction of the coordination number of atoms at the surface. Using a standard recursion method, the equation of motion for the one-electron Green function is solved numerically yielding the spin- and layer-dependent local density of states (LDOS). From this the layer-dependent charge density and magnetization are derived self-consistently. The LDOS of the first few layers below the surface clearly deviates from the bulk density of states which results in strong changes of the layer magnetizations while charge-transfer effects may be rather small. We systematically investigate the dependence of the layer magnetization on the Coulomb interaction, the band filling, and the temperature for the ferromagnetic as well as for different antiferromagnetic structures. While for the antiferromagnetic solutions the (sublattice) magnetization of the topmost layer is always enhanced, a higher magnetization of the topmost layer is only found for not too strong Coulomb interaction in the case of the ferromagnet. In the fully polarized ferromagnetic tate the magnetization is dominated by the charge transfer between the bulk and the surface. First-order transitions from the ferromagnetic to a layerwise antiferromagnetic phase are studied in detail. Metastable ferromagnetic solutions are found beyond the critical point (Coulomb interaction, temperature). The actual transition of the metastable ferromagnetic into the stable antiferromagnetic phase starts from the very surface, which acts as an immanent perturbation of the infinitely periodic lattice. The antiferromagnetic order quickly extends into the bulk layer by layer.