Theory of colossal magnetoresistance in doped manganites

The exchange interaction of polaronic carriers with localized spins leads t o a ferromagnetic/paramagnetic transition in doped charge-transfer insulato rs with strong electron-phonon coupling. The relative strength of the excha nge and electron-phonon interactions determines whether the transition is f irst or second order. A giant drop in the number of current carriers during the transition, which is a consequence of local bound-pair (bipolaron) for mation in the paramagnetic phase, is extremely sensitive to an external mag netic field. Below the critical temperature of the transition, T-c, the bin ding of the polarons into immobile pairs competes with the ferromagnetic ex change between polarons and the localized spins on Mn ions, which tends to align the polaron moments and, therefore, breaks up those pairs. The number of carriers abruptly increases below T-c, leading to a sudden drop in resi stivity. We show that the carrier-density collapse explains the colossal ma gnetoresistance of doped manganites close to the transition. Below T-c tran sport occurs by polaronic tunnelling, whereas at high temperatures the tran sport is by hopping processes. The transition is accompanied by a spike in the specific heat, as experimentally observed. The gap feature in tunnellin g spectroscopy is related to the bipolaron binding energy, which depends on the ion mass. This dependence explains the giant isotope effect of the mag netization and resistivity upon substitution of O-18 for O-16. It is shown also that the localization of polaronic carriers by disorder cannot explain the observed huge sensitivity of the transport properties to the magnetic field in doped manganites.