Competition between ferromagnetic and charge-orbital ordered phases in Pr1-xCxMnO3 for x=1/4, 3/8, and 1/2

Spin, charge, and orbital structures in models for doped manganites are studied by a combination of analytic mean-field and numerical relaxation techniques. At realistic values for the electron-phonon and antiferromagnetic t(2g) Spin couplings, a competition between a ferromagnetic (FM) phase and a charge-orbital ordered (COO) insulating state is found for x=1/4, 3/8, and 1/2, as experimentally observed in Pr1-xCaxMnO3 for x=0.3-0.5. The theoretical predictions for the spin-charge-orbital ordering pattern are compared with experiments. The FM-COO energy difference is surprisingly small for the densities studied, and the results compatible with the presence` of a robust colossal-magnetoresistive effect in Pr1-xCaxMnO3 in a large density interval.