Role of Orbitals in Manganese Oxides - Ordering and Fluctuation

We study the manganese oxides from the viewpoint of the strongly correlated doped Mott insulator. The magnetic ordering and the charge transport are governed by the orbital degrees of freedom, and their dimensionality is controlled by the anisotropic transfer integrals between the eg orbitals. As x increases the magnetic structure is predicted to change as A → F → A → C → G ( F : ferromagnet, A: layered antiferromagnet, C: rod-type antiferromagnet, G: usual antiferromagnet), in agreement with experiments. Especially the orbital is aligned as dx2−y2 in the metallic A state, which explains the quasi 2D transport and no canting of the spin observed experimentally. Next we discuss the ferromagnetic state without the orbital ordering due to the quantum fluctuation. Here the interplay between the electron repulsion