Double exchange model and the unique properties of the manganites

In this review the double exchange (DE) model forming a basis for the description of the physics of colossal magnetoresistance manganites is discussed. For a limiting case of exchange interaction which is large compared with the band width, the effective Hamiltonian of the DE model is derived from that of the sd-exchange model. Since this Hamiltonian is very complicated, the dynamical mean field approximation, successful for other strongly correlated systems, is found to be more suitable for describing the model of interest. 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 concentration phase diagram for a system with consideration for the domain of phase separation is constructed, whose basic features are shown to be in qualitative agreement with experimental data for the manganites, as also are the temperature and electron concentration dependences of their electrical resistivity, magnetization, and spectral characteristics. At the quantitative level, introducing additional electron-lattice interaction yields a good agreement. A number of yet unresolved problems in the physics of manganites, including the mechanism of temperature- or doping-induced metal-insulator phase transition and the nature of charge ordering, are also discussed. By comparing predictions made by computing approach with the experimental data, the adequacy of the DE model is assessed and its drawbacks are analyzed. Numerous recent theoretical studies of the unique properties of this broad class of strongly correlated systems are summarized in this review. (reviews of topical problems)