Ferromagnetism and Transport in the Double-Exchange Model, with and without Phonons; Application to the Manganites

An introduction is given to the many-body coherent potential approximation (CPA) for the double-exchange (DE) model and the Holstein-DE model, the latter including coupling of the electrons to local phonons as well as to local spins. It is shown how the method can treat the local spins and phonons quantum-mechanically and how it is equivalent to dynamical mean field theory in the classical limit. In the Holstein-DE model a full discussion is given of the cross-over from weak electron-phonon coupling through intermediate coupling, where small-polaron bands begin to appear, to strong coupling where some results similar to those of standard small-polaron theory are recovered. The theory is applied to ferromagnetic manganites with a full discussion of magnetic, transport and spectroscopic data. It is found that many manganites are in the critical regime on the verge of small-polaron formation, which explains their sensitivity to parameters such as applied magnetic field and pressure.