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The interplay of the electron-phonon interaction and of the double and superexchange magnetic effects is analyzed in the $La_{1-x}Ca_xMnO_3$ perovskiteswith $0<x<0.5$. By using an analytical variational scheme that allows to treatthe electron-phonon interaction in a fully quantum manner it is shown that inthe intermediate electron-phonon coupling regime a charge density instabilityoccurs near the metal-insulator transition, induced by either temperature orhole doping. The system segregates in antiferromagnetic or paramagnetic smallpolarons and ferromagnetic large polarons domains characterized by differentvalues of the lattice distortions that are satisfactory compared with thoseexperimentally observed.Comment: 10 pages, 2 figures, to appear on Phys. Rev.

Coexistence of large and small polarons in manganites