Bound ferromagnetic and paramagnetic polarons as an origin of the resistivity peak in ferromagnetic semiconductors and manganites

A theory of resistivity is developed for ferromagnetic semiconductors, possibly, including manganites. The theory is based on analysis of the interaction of the free and bound charge carriers with the magnetization of the crystal. The temperature dependence of free energy for nonionized donors and free electrons is calculated for the spin-wave and paramagnetic regions. In addition to the trapping by the ferromagnetic fluctuations (the ferromagnetic polarons), the electron trapping by the random magnetization fluctuations as T → is taken into account (the paramagnetic polarons). For the nondegenerate semiconductors, the theory makes it possible to explain a nonmonotonic temperature dependence of the activation energy, with the value for T = 0 being lower than that for T → ∞. For degenerate semiconductors, the theory explains a metal-insulator transition that occurs with increasing temperature in samples with relatively low charge carrier density. If the density is larger, a reentrant metal-insulator transition should take place, so that the crystal is highly conductive as T → ∞.