A new X-ray diffraction study of the one-dimensional spin-Peierls compound α ′ -NaV2O5 reveals a centrosymmetric (Pmmn) crystal structure with one type of V site, contrary to the previously postulated non-centrosymmetric P21mn structure with two types of V sites (V +4 and V +5 ). Density functional calculations indicate that NaV2O5 is a quarter-filled ladder compound with the spins carried by V-O-V molecular orbitals on the rungs of the ladder. Estimates of the chargetransfer gap and the exchange coupling agree well with experiment and explain the insulating behavior of NaV2O5 and its magnetic properties. . A spin-Peierls system undergoes a lattice instability at T SP and for T < T SP the system dimerizes and a spin-gap opens. Here we propose that the spin-Peierls compound NaV 2 O 5 is at the same time a quarter-filled ladder system, in contrast to the previous notion which assumed NaV 2 O 5 to be made up of weakly coupled pairs of V +4 and V +5 chains [4,6]. Our proposition is based on a re-determination of the crystal structure of NaV 2 O 5 by X-ray diffraction and on density-functional calculations. Mapping of the density functional results on Hubbard and Heisenberg models yields values for the model parameters which explain readily the insulating behavior of NaV 2 O 5 and its the magnetic properties. Our results also show that NaV 2 O 5 and CaV 2 O 5 are isostructural and consequently establish CaV 2 O 5 as a half-filled ladder system.Crystal structure The crystal structure of α ′ -NaV 2 O 5 consists of double chains of edge-sharing distorted tetragonal VO 5 -pyramids running along the orthorhombic baxis, which are linked together via common corners of the pyramids to form sheets. These in turn are stacked

Anomalous properties of the magnetization, the crystal dilatation, and other physical quantities observed in the mixed state of compounds such as UPd2Al3 and CeRu2 suggest the occurrence of a new state near H-c2. In such compounds with large spin susceptibility and high H-c2, a new inhomogeneous superconducting state is theoretically predicted to occur in high magnetic fields. In this inhomogeneous state which is shown to be a generalized Fulde-Ferrell-Larkin-Ovchinnikov state, the order parameter is spatially modulated, and planar nodes of the order parameter are periodically aligned perpendicular to the vortices. Various theoretical predictions are compared with experimental results on UPd2Al3 and CeRu2 related to this new superconducting high-field state

Dilatometric and magnetic experiments on high-quality single crystals of the superconducting compounds UPd2Al3 and CeRu2, which have enhanced spin susceptibilities, demonstrate a first-order transition between weak and strong pinning at T < 0.9T(c) (H > 10 kOe). This is compatible with a staggered order parameter due to the formation of a ''Fulde-Ferrell-Larkin-Ovchinnikov'' state

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