Orbital magnetism and valence instabilities in narrow bands

Spatial electron ordering and uniform mixed-valence behavior, experimentally observed in many transition and rare-earth metals and compounds with narrow d and f bands, can be interpreted in terms of a generalized Hubbard-like two-hand model. In the strong interaction limit (U/spl rarr//spl infin/) and exactly at half-filling, an effective Hamiltonian for such a model becomes strictly equivalent to an anisotropic XYZ model in an external field. The problem of forming either an "antiferromagnetic" orbital crystal with valence density waves (VDW) or a liquid-like mixed valence state (MVS) with strong excitonic correlations is then analogous to the problem of finding the magnetization of the corresponding Heisenberg antiferromagnet. The variation of the orbital occupation number versus the energy difference between the centers of two hands and the conditions for smooth and first-order transitions at half-filling from VDW into MVS have been found using a generalized mean field approximation at large U. The observed anomalies of the valence behavior and compressibility in mixed-valence compounds can be viewed in this context as a diamagnetic response an applied external field. We demonstrate strong evidence for the existence in the ground state of a sequence of spatially modulated phases with periodic arrangement of d or f electrons (commensurate VDW) in the presence of an external field.