Electronic, magnetic, and dynamical properties of superconducting ␤-pyrochlore KOs 2 O 6 and related RbOs 2 O 6 and CsOs 2 O 6 compounds are calculated and compared with experiment and contrasted with structurally related spinel pyrochlores. The calculated susceptibility Stoner enhancement (110%) and thermal mass enhancement = 2.5-3 reflect moderate but perhaps important Coulomb correlations. The K + ion optic mode is found to be unstable, allowing large excursions of 0.5-0.6 Å from its ideal site of the K ion along ͗111͘ directions. This dynamical mode is much less anharmonic in the isostructural Rb and Cs compounds (with larger cations), perhaps accounting for their progressively lower values of T c . Electron scattering from this very anharmonic mode may be the cause of the anomalous concave-downward resistivity that is seen only in KOs 2 O 6 .

Due to increased interest in the unusual magnetic and transport behavior of MnSi and its possible relation to its crystal structure (B20) which has unusual coordination and lacks inversion symmetry, we provide a detailed analysis of the electronic and magnetic structure of MnSi. The non-symmorphic P213 spacegroup leads to unusual fourfold degenerate states at the zone corner R point, as well as "sticking" of pairs of bands throughout the entire Brillouin zone surface. The resulting Fermi surface acquires unusual features as a result of the band sticking. For the ferromagnetic system (neglecting the long wavelength spin spiral) with the observed moment of 0.4 µB/Mn, one of the fourfold levels at R in the minority bands falls at the Fermi energy (EF ), and a threefold majority level at k=0 also falls at EF . The band sticking and presence of bands with vanishing velocity at EF imply an unusually large phase space for long wavelength, low energy interband transitions that will be important for understanding the unusual resistivity and far infrared optical behavior.

The half-Heusler compound CuMnSb, the first antiferromagnet (AFM) in the Mn-based class of Heuslers and half-Heuslers that contains several conventional and half metallic ferromagnets, shows a peculiar stability of its magnetic order in high magnetic fields. Density functional based studies reveal an unusual nature of its unstable (and therefore unseen) paramagnetic state, which for one electron less (CuMnSn, for example) would be a zero gap semiconductor (accidentally so) between two sets of very narrow, topologically separate bands of Mn 3d character. The extremely flat Mn 3d bands result from the environment: Mn has four tetrahedrally coordinated Cu atoms whose 3d states lie well below the Fermi level, and the other four tetrahedrally coordinated sites are empty, leaving chemically isolated Mn 3d states. The AFM phase can be pictured heuristically as a selfdoped Cu 1+ Mn 2+ Sb 3− compensated semimetal with heavy mass electrons and light mass holes, with magnetic coupling proceeding through Kondo and/or antiKondo coupling separately through the two carrier types. The ratio of the linear specific heat coefficient and the calculated Fermi level density of states indicates a large mass enhancement m * /m ∼ 5, or larger if a correlated band structure is taken as the reference.

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 electronic properties of YbRh 2 Si 2 are studied by means of band structure calculations based on the density functional theory within the LDA (local density approximation), LDA + U , and fully relativistic scheme. The 4f derived bands are studied within a relativistic framework which yields flat and spinorbit split bands, and a correlated band method (LDA + U ) that includes correlation corrections. In both cases the uppermost 4f band is located roughly 150 meV below the Fermi energy E F , and hybridizes weakly with the dispersive Rh 4d bands and a Rh 4d xy band that does not disperse perpendicular to the Rh layers. When we applied the fully relativistic scheme, the 4f derived bands split into j = 7/2 and 5/2 excitations due to spin-orbit coupling effects. The f 7/2 multiplet is located much closer to E F , hybridizing anisotropically with a Rh 4d derived conduction band. This mixing induces a non-integer occupation of the f levels n f and hence reveals that YbRh 2 Si 2 is a mixed-valence heavy fermion. The 4f electrons can be delocalized through the hybridization with conduction electrons. And the hybridization between f and conduction d electrons plays a important role in YbRh 2 Si 2 . The Fermi surface splits into three different nontouching sheets. There are two tiny cylinder Fermi surfaces around Z points which are from the Rh 4d bands and the larger Fermi surfaces are from the 4f derived bands.