Magnetic order in the doped Hubbard model and the crossover from two- to three-dimensions: a Hartree-Fock study

We report unrestricted Hartree-Fock (UHF) results for the ground state of the single-band Hubbard model in three-dimensions (3D), with repulsive onsite interactions and nearest-neighbor hopping. Magnetic and charge properties are determined by full numerical solutions of the self-consistent UHF equation in large supercells, and quantified as a function of hole doping $h$. We focus on weak to intermediate interaction strengths, where UHF has been shown to capture the main characteristics of the magnetic correlations in two-dimensions (2D).~\footnote{J. Phys.: Condens. Matter, in press (arXiv:1107.0976v2).} We find linear spin-density wave (SDW) states with AFM order and a long wavelength modulation whose wavelength is inversely proportional to $h$. We also study the dimensional crossover from 2D to 3D as the inter-plane distance is increased.