Double exchange model and the unique properties of the manganites

In this review the double exchange (DE) model, which is the basis for the description of the physics of colossal magnetoresistance manganites, is discussed. For Hund exchange interaction large compared with the band width, the effective Hamiltonian of the DE-model is derived. Since this Hamiltonian is very complicated, however, the dynamical mean-field approximation, successful for other strongly correlated systems, is found to be more suitable for describing the model. Two simplified versions of the DE model, both capable of accounting for a wide range of physical properties, are proposed, one using classical localized spins and the other involving quantum spins but no transverse spin fluctuations. A temperature-electron density phase diagram for a system with phase separation is determined, whose basic features are shown to be in qualitative agreement with experimental data for the manganites, as also are the temperature and electron density dependences of resistivity, magnetization, and spectral characteristics. At the quantitative level, introducing the electron-lattice coupling yields good agreement. A number of yet unresolved problems, including the mechanism of temperature- or doping-induced metal-insulator transitions and the nature of charge ordering, are also discussed. By comparing predictions with the experimental data, the adequacy of the DE model is assessed. Numerous recent studies of the unique properties of this broad class of strongly correlated systems are summarized in this review.