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Charge- and magnetic-ordering in a two-orbital double-exchange model for manganites

Phase diagram of half-doped perovskite manganites is studied within the extended double-exchange model. To demonstrate the role of orbital degrees of freedom both one- and two-orbital models are examined. A rich phase diagram is obtained in the mean-field theory at zero temperature as a function of J (antiferromagnetic (AFM) superexchange interaction) and V (intersite Coulomb repulsion). For the one-orbital model a charge-ordered (CO) state appears at any value of V with different types of magnetic order which changes with increasing J from ferromagnetic (F) to AFM ones of the types A, C and G. The orbital degeneracy results in appearance of a new CE-type spin order that is favorable due to opening of the "dimerization" gap at the Fermi surface. In addition, the CO state appears only for V>V_c for F and CE states while C-type AFM state disappears and A-type AFM state is observed only at small values of V as a charge disordered one. The relevance of our results to the experimental data are dicussed.