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Spin Excitations in Doped Manganites

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We generalize the double exchange to describe holes doped in degenerate e_{g} orbitals in La_{1-x}A_{x}MnO_{3} manganites, where A are divalent alkaline earth ions. Assuming an orbital liquid of disordered e_{g} orbitals we find isotropic ferromagnetic exchange interactions which increase with hole doping. The magnon dispersion agrees very well with the experimental data in ferromagnetic metallic manganites.
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