Charge-orbital ordering and phase separation in the two-orbital model for manganites: Roles of Jahn-Teller phononic and Coulombic interactions

The main properties of realistic models for manganites are studied using an alytic mean-field approximations and computational numerical methods, focus ing on the two-orbital model with electrons interacting through Jahn-Teller (JT) phonons and/or Coulombic repulsions. Analyzing the model including bo th interactions by the combination of the mean-field approximation and the exact diagonalization method, it is argued that the spin-charge-orbital str ucture in the insulating phase of the purely JT-phononic model with a large Hund couphng J(H) is not qualitatively changed by the inclusion of the Cou lomb interactions. As an important application of the present mean-held app roximation, the CE-type antiferromagnetic state, the charge-stacked structu re along the z axis, and (3x(2) - r(2))/(3y(2) - r(2))-type orbital orderin g are successfully reproduced based on the JT-phononic model with large JH for the half-doped manganite, in agreement with recent Monte Carlo simulati on results. Topological arguments and the relevance of the Heisenberg excha nge among localized t(2g) spins explains why the inclusion of the nearest-n eighbor Coulomb interaction does not destroy the charge stacking structure. It is also verified that the phase-separation tendency is observed both in purely JT-phononic (large JH) and purely Coulombic models in the vicinity of the hole undoped region, as long as realistic hopping matrices are used. This highlights the qualitative similarities of both approaches and the re levance of mixed-phase tendencies in the context of manganites. In addition , the rich and complex phase diagram of the two-orbital Coulombic model in one dimension is presented. Our results provide robust evidence that Coulom bic and JT-phononic approaches to manganites are not qualitatively differen t ways to carry out theoretical calculations, but they share a variety of c ommon features.