Magnetic, orbital, and charge ordering in the electron-doped manganites

The three-dimensional perovskite manganites R(1-x)A(x)MnO(3) in the range of hole doping x>0.5 are studied in detail using a double-exchange model with degenerate e(g) orbitals including intraorbital and interorbital correlations and near-neighbor Coulomb repulsion. We show that such a model captures the observed phase diagram and orbital ordering in the intermediate- to large-bandwidth regimes. It is argued that the Jahn-Teller effect, considered to be crucial for the region x<0.5, does not play a major role in this region, particularly for systems with moderate to large bandwidths. The anisotropic hopping across the degenerate e(g) orbitals is essential for the understanding of the ground-state phases of this region, an observation emphasized earlier by Brink and Khomskii. Based on calculations using a realistic limit of finite Hund's coupling, we show that the inclusion of interactions stabilizes the C phase, and the antiferromagnetic metallic A-phase moves closer to x=0.5 while the ferromagnetic phase shrinks, in agreement with recent observations. The charge ordering close to x=0.5 and the effect of reduction of bandwidth are also outlined. The effect of disorder and the possibility of inhomogeneous mixture of competing states are discussed.