A comprehensive analysis of half-doped manganites is presented using Monte Carlo simulations applied to the double-exchange model with cooperative Jahn-Teller lattice distortions in two dimensions. A variety of novel results are reported. In particular: (i) The phase diagram is established in the λ-JAF plane, with λ the electron-phonon coupling and JAF the antiferromagnetic exchange between classical t2g spins. The results include standard phases, such as the CE-insulating and FM-metallic regimes, but they also include novel states, such as a ferromagnetic charge-ordered (CO) orbital-ordered phase originally predicted by Hotta et al.. This state is compatible with recent experimental results by Loudon et al. (ii) For realistic couplings, it was observed that the charge disproportionation δ of the CO phase is far from the widely accepted extreme limit δ=0.5 of a 3+/4+ charge separation. A far smaller δ appears more realistic, in agreement with recent experiments by Garcia et al. and Daoud-Aladine et al. (iii) Colossal magnetoresistance (CMR) effects are found in calculations of cluster resistances using the Landauer formalism. This occurs near the ubiquitous first-order phase transitions between the insulating and metallic states. The present result reinforces the previous conjecture that CMR phenomenology exists in two forms: the low-temperature CMR addressed here and the more standard CMR above the Curie temperature. (iv) The CE-state is found to be very sensitive to disorder since its long-range order rapidly disappears when quenched-disorder is introduced, contrary to the FM state which is more robust. This is also in qualitative agreement with recent experiments by Akahoshi et al. and Nakajima et al. (v) The phase diagram in the half-doped electron doping regime is briefly discussed as well. A charge-ordered state is found which is the analog of the x=0.5 CE phase. It contains a 3+/2+ charge arrangement at large λ. Numerical results suggest that an approximate symmetry exists between the hole-and electron-doped systems in the large Hund coupling limit.

The ferromagnetic Kondo lattice model with an antiferromagnetic interaction between localized spins is a minimal description of the competing kinetic t and magnetic K energy terms which generate the rich physics of manganite systems. Motivated by the discovery in one dimension of homogeneous ``island phases'', we consider the possibility of analogous phases in higher dimensions. We characterize the phases present at commensurate fillings, and consider in detail the effects of phase separation in all filling and parameter regimes. We deduce that island and flux phases are stable for intermediate values of K/t at the commensurate fillings n = 1/4, 1/3, 3/8, and 1/2. We discuss the connection of these results to the charge and magnetic ordering observed in a wide variety of manganite compounds.Comment: 13 pages, 17 figure