Ferromagnetism and electron-phonon coupling in the manganites
  The physics of ferromagnetic doped manganites, such as \chem{La_{1-x}Ca_xMnO_3} with $x\approx0.2$--0.4, is reviewed. The concept of double exchange is discussed within the general framework of itinerant electron magnetism. The new feature in this context is the coupling of electrons to local phonon modes. Emphasis is placed on the quantum nature of the phonons and the link with polaron physics. However it is stressed that the manganites fall in an intermediate coupling regime where standard small-polaron theory does not apply. The recently-developed many-body coherent potential approximation is able to deal with this situation and Green's recent application to the Holstein double-exchange model is described. Issues addressed include the nature of the basic electronic structure, the metal-insulator transition, a unification of colossal magnetoresistance, pressure effects and the isotope effect, pseudogaps in spectroscopy and the effect of electron-phonon coupling on spin waves. 
D. M. Edwards