Theory of Colossal Magnetoresistance in Doped Manganites
  The exchange interaction of polaronic carriers with localized spins leads to a ferromagnetic/paramagnetic transition in doped charge-transfer insulators with strong electron-phonon coupling. The relative strength of the exchange and electron-phonon interactions determines whether the transition is first or second order. A giant drop in the number of current carriers during the transition, which is a consequence of local bound pair (bipolaron) formation in the paramagnetic phase, is extremely sensitive to an external magnetic field. Below the critical temperature of the transition, $T_c$, the binding of the polarons into immobile pairs competes with the ferromagnetic exchange 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 resistivity. We show that the carrier density collapse describes the colossal magnetoresistance of doped manganites close to the transition.   Below $T_c$, transport occurs by polaronic tunneling, whereas at high temperatures the transport is by hopping processes. The transition is accompanied by a spike in the specific heat, as experimentally observed. The gap feature in tunneling spectroscopy is related to the bipolaron binding energy, which depends on the ion mass. This dependence explains the giant isotope effect of the magnetization and resistivity upon substitution of $^{16}$O by $^{18}$O. It is shown also that the localization of polaronic carriers by disorder {\em cannot} explain the observed huge sensitivity of the transport properties to the magnetic field in doped manganites. 
A.S. Alexandrov and A.M. Bratkovsky