Magnetic and electric properties of the Hubbard model for the fcc lattice

Using the Hartree-Fock approximation, the half-filled Hubbard model is investigated for the fcc lattice at absolute zero. The results are quite different from those obtained for the simple cubic lattice arising from the nonsymmetric band structure of the nonalternate lattice. It is found that antiferromagnetism appears only when the intra-atomic Coulomb interaction $U$ exceeds a critical value. This magnetic phase transition from a paramagnetic to an antiferromagnetically ordered phase proves to be of first order. With increasing $U$, a metal-insulator transition occurs, caused by band separation. The gap collapse at the first critical $U$ causes jumps in the curves of conductivity and spin susceptibility. both quantities are calculated as functions of $U$ with the aid of a generalized density of states. Investigating criteria for the onset of magnetism and constructing a magnetic phase diagram for variable band occupation, the antiferromagnetic state is found to be stable with respect to ferromagnetic ordering in the region of finite $U$ only for electron densities within $0.27<\mathrm{}{n}_e<1.21\mathrm{}$. In the strong coupling limit $U\to \infty$ this stability criterion must be modified and is shown to coincide with the predictions of Nagaoka's rigorous investigations of an almost half-filled band. In the case where the band is almost filled, a first-order paramagnetic to ferromagnetic transition is obtained at a finite value of $U$, whereas the critical curve defining the antiferromagnetic phase boundary diverges as $n_e$ approaches $n_e=2\mathrm{}$. For a band which is almost vacant, the competitive phase boundaries both yield unphysically large values of $U$. In the latter case there is no magnetic phase transition in a region of experimentally observable value of $U$ at all.