The magnetic nature of Cs 2 AgF 4 , an isoelectronic and isostructural analogue of La 2 CuO 4 , is analyzed using density functional calculations. The ground state is found to be ferromagnetic and nearly half metallic. We find strong hybridization of Ag-d and F-p states. Substantial moments reside on the F atoms, which is unusual for the halides and reflects the chemistry of the Ag͑II͒ ions in this compound. This provides the mechanism for ferromagnetism, which we find to be itinerant in character, a result of a Stoner instability enhanced by Hund's coupling on the fluorine ions.

We address the origin of the incipient magnetism in TiBe2 through precise first principles calculations, which overestimate the ferromagnetic tendency and therefore require correction to account for spin fluctuations. TiBe2 has sharp fine structure in its electronic density of states, with a van Hove singularity only 3 meV above the Fermi level. Similarly to the isovalent weak ferromagnet ZrZn2, it is flat bands along the K-W-U lines of hexagonal face of the fcc Brillouin zone make the system prone to magnetism, and more so if electrons are added. We find that the Moriya B coefficient (multiplying ω q in the fluctuation susceptibility ∆χ(q, ω)) is divergent when the velocity vanishes at a point on the Fermi surface, which is very close (3 meV) to occurring in TiBe2. In exploring how the FM instability (the q=0 Stoner enhancement is S ≈ 60) might be suppressed by fluctuations in TiBe2, we calculate that the Moriya A coefficient (of q 2 ) is negative, so q=0 is not the primary instability. Explicit calculation of χo(q) shows that its maximum occurs at the X point (1, 0, 0) 2π a ; TiBe2 is thus an incipient antiferromagnet rather than ferromagnet as has been supposed. We further show that simple temperature smearing of the peak accounts for most of the temperature dependence of the susceptibility, which previously had been attributed to local moments (via a Curie-Weiss fit), and that energy dependence of the density of states also strongly affects the magnetic field variation of χ.

The Bogoliubov-de Gennes equations for singlet superconductivity in an exchange field are analyzed with real materials having complex Fermi surfaces in mind. The resulting gap equation is reformulated in terms of a velocity spectrum on the Fermi surface in which the surface geometry is built in. The resulting analysis can readily be used for arbitrary dispersion relations. Fulde-Ferrell-Larkin-Ovchinnikov ͑FFLO͒ phases are studied in the temperature-field plane, with results providing a physically clear interpretation of why certain directions of pair momentum q ជ are energetically favored. We present clarifying results for models ͑the two-dimensional square Fermi surface, one-, two-, and three-dimensional isotropic surfaces͒ and provide an application to the weak ferromagnetic ZrZn 2 showing it is not a favorable case for an FFLO phase.A further simplification is made by making a small-q ជ approximation: