Interplay between spin and phonon fluctuations in the double-exchange model for the manganites

We present exact solutions, mainly analytical, for the two-site double-exchange-Holstein model, that allow us to draw a complete picture of the role of both phonon and spin quantum fluctuations in determining the short-range correlations in the manganites. We provide analytical solutions of the model for arbitrary electron-phonon coupling and phonon frequency, for S= ½ and for the classical spin limit S = ∞, and compare these results with numerical diagonalization of the realistic S = 3/2 case. The comparison reveals that the realistic case S = 3/2. is not well described by the classical spin limit, which is often used in literature. On the other hand, the phonon fluctuations, parametrized by the phonon frequency ω 0 , stabilize ferromagnetic phases with respect to the adiabatic limit. We also provide a complete analysis on the polaron crossover in this model.