Magnetism and superconductivity in the extended periodic Anderson model

The Anderson model for a periodic array of magnetic ions has been extended by a BCS like interaction term for the conduction electrons. This extended model is studied by means of a generalized Hartree-Fock approximation. Five coupled self-consistency equations are considered for situations where ferromagnetic, superconducting, coexistent and normal phases can occur. Which of these phases actually are allowed for a given set of parameters strongly depends upon the band structure (especially upon the type of electrons near the Fermi energy). Whereas for the general case the selfconsistency equations have to be solved numerically from the beginning, the situation is much simplified for the symmetric Anderson model (E0 = -U/2). Here, analytical results are obtained which explain the stability of the coexistent phase. We also use the symmetric model for an expansion of the Ginzburg-Landau type in the spatially homogeneous magnetic and superconducting order parameters. The onset of superconductivity and ferromagnetic order is well described within this approximation. However, at low temperatures we find drastically different solutions due to the strong temperature dependence of the expansion coefficients of the free energy. Therefore, it is difficult to obtain the correct transition temperatures within this approximation. These difficulties stem from general problems connected with the derivation of a Ginzburg-Landau theory for several order parameters from a microscopic theory. (orig.)