Charge and orbital ordering in the low-temperature monoclinic structure of magnetite (Fe3O4) is investigated using the local spin density approximation with Coulomb interaction correction method. While the difference between t(2g) minority occupancies of Fe(2+)(B) and Fe(3+)(B) cations is large and gives direct evidence for charge ordering, the screening is so effective that the total 3d charge disproportion is rather small. The charge order has a pronounced [001] modulation, which is incompatible with the Anderson criterion. The orbital order agrees with the Kugel-Khomskii theory.

The optical and magneto-optical ͑MO͒ spectra of Tm monochalcogenides are investigated theoretically from first principles, using the fully relativistic Dirac linear combination of muffin-tin orbitals band structure method. The electronic structure is obtained with the local-spin-density approximation ͑LSDA͒, as well as with the so-called LSDAϩU approach. In contrast to LSDA, where the stable solution in TmTe is a metal, the LSDAϩU gave an insulating ground state. LSDAϩU theory predicts the thulium ion in TmTe to be in an integer divalent state. It also shows a gradual decreasing of the energy gap with reducing of the lattice constant. LSDAϩU theoretical calculations produce a similar energy band structure in TmS and TmSe, with twelve 4 f bands fully occupied and hybridized with chalcogenide p states. The 14th f hole level was found to be completely unoccupied and well above the Fermi level and a hole 13th f level is partly occupied and pinned at the Fermi level. The occupation number of the 13th f level is equal to 0.12 and 0.27 in TmS and TmSe, respectively ͑valence 2.88ϩ and 2.73ϩ͒. Such an energy band structure of thulium monochalcogenides describes well their measured bremsstrahlung isochromat spectroscopy ͑BIS͒, and x-ray and ultraviolet photoemission spectra as well as the optical and MO spectra. The origin of the Kerr rotation realized in the compounds is examined.

Charge ordering in the low-temperature monoclinic structure of iron oxoborate ͑Fe 2 OBO 3 ͒ is investigated using the local spin density approximation ͑LSDA͒ + U method. While the difference between t 2g minority occupancies of Fe 2+ and Fe 3+ cations is large and gives direct evidence for charge ordering, the static "screening" is so effective that the total 3d charge separation is rather small. The occupied Fe 2+ and Fe 3+ cations are ordered alternately within the chain which is infinite along the a direction. The charge order obtained by LSDA+ U is consistent with observed enlargement of the ␤ angle. An analysis of the exchange interaction parameters demonstrates the predominance of the interribbon exchange interactions which determine the whole L-type ferrimagnetic spin structure.