They found that the expected double-exchange-induced strong tendencies to ferromagnetic correlations at low temperatures were in competition with a regime of phase separation, which occurred between the hole-undoped antiferromagnetic and hole-rich ferromagnetic regions. Although, the one-orbital model for manganites contains interesting physics, notably, a FM-AF competition that has similarities with those found in experiments. However, to explain the notorious orbital order tendency in Mn-oxides, it is crucial to use a model with two orbitals, where there is an electron Jahn-Teller phonon coupling and also Coulomb interactions

[89, 90]. Under the assumption that both localized eg-spins and phonons are classical, the model without Coulombic terms can be studied fairly accurately using numerical and mean-field approximations. The Smoothened Agonist price calculated results for a one-dimensional system at low temperature by considering the two eg orbitals and the Jahn-Teller U0126 in vivo phonons enrich the phase diagram considerably, as shown in Figure  9 [90]. Obviously, the phase diagram is much rich,

which includes different selleck compound phases such as metallic and insulating regimes with orbital order. It is clear that phase separation appears at small eg-densities between an electron-undoped AF-state and a metallic uniform-orbital-ordered FM state. Ahn et al. also proposed a model Hamiltonian including Clostridium perfringens alpha toxin electron–phonon interactions and long-range elastic coupling between the local lattice distortions [91]. They presented a scenario for mesoscopic/microscopic inhomogeneities and suggested them to be the main source of the CMR effect. Since the physics of perovskite manganites is controlled by many degrees of freedom at the atomic level and the associated energy scales, Ramakrishnan et al. also developed

a microscopic model for manganites that includes all the important energy scales present in them [92]. In this model, the degeneracy of the two eg orbitals is split into two types of states, l and b at each manganese site by electron-lattice coupling. The l state is polaronic and has an exponentially reduced hopping amplitude, whereas the electrons within the b states hop with the bare amplitude. Such two-fluid model of manganites demonstrates colossal magnetoresistive response and reproduces the physical transport properties confirmed by the experimental measurements. Due to the local strong Mott-Hubbard repulsion, the simultaneous occupation at both the l and b states on a given site is not allowed; this model exhibits macroscopic phase separation, where the region with l polarons corresponds to the charge-ordered states, while that with b electrons corresponds to the FM metal.