Electronic Theory of Colossal Magnetoresistance Materials

Abstract

We study a model based on the double exchange mechanism and diagonal disorder to calculate magnetization and conductivity for La_1−x Sr _x MnO₃ type crystals as a function of temperature. The model represents each Mn⁴⁺ ion by a spin

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, on which an electron can be added to produce Mn³⁺. We include a hopping energy t, and a strong intra-atomic exchange interaction J. To represent in a simple way the effects of disorder we assume a Lorentzian distribution of diagonal energies of width F at the Mn sites. We calculate the mobility edge and the Fermi level as functions of magnetization. We add the spin entropy to build up the free energy of the system. In the strong coupling limit, J ≫ t, Γ, the model results can be expressed in terms of t and F only. We use the results of the model to draw “phase diagrams” that separate ferromagnetic from paramagnetic states and also “insulating” states where the Fermi level falls in a region of localized states from “metallic” where the Fermi level falls in a region of extended states. We then add the contributions to the conductivity of extended states to those of localized states to calculate the resistivity for different concentrations and the magnetoresistance. We conclude that the model can be used successfully to represent the transport properties of the systems under consideration.