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Effect of double exchange and diagonal disorder on the magnetic and transport properties of La_{1-x}Sr_xMnO_3

We use a model previously formulated based on the double exchange mechanism and diagonal disorder to calculate magnetization and conductivity for La_{1-x}Sr_xMnO_3 type crystals as a function of temperature. The model represents each Mn^{4+} ion by a spin S=1/2, on which an electron can be added to produce Mn$^{3+}$. We include a hopping energy $t,$ two strong intratomic interactions: exchange $J$, and Coulomb $U,$ and, to represent in a simple way the effects of disorder, a Lorentzian distribution of diagonal energies of width $Γ$ at the Mn sites. In the strong coupling limit, $J,U>>t,Γ$, the model results can be expressed in terms of $t$ and $Γ.$ 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. Finally, assuming that particles in extended states make the largest contribution to conductivity, we calculate the resistivity for different concentrations and magnetic fields and compare with experiment. We conclude that for the model can be used successfully to represent the transport properties of the systems under consideration.