Interplay between Spin and Phonon Fluctuations in the double-exchange model for the manganites

摘要

We present exact solutions, mainly analytical, for the two-sitedouble-exchange-Holstein model, that allow us to draw a complete picture of therole of both phonon and spin quantum fluctuations in determining theshort-range correlations in the manganites. We provide analytical solutions ofthe model for arbitrary electron-phonon coupling and phonon frequency, for$S=1/2$ and for the classical spin limit $S=\infty$, and compare these resultswith numerical diagonalization of the realistic $S=3/2$ case. The comparisonreveals that the realistic case $S=3/2$ is not well described by the classicalspin limit, which is often used in literature. On the other hand, the phononfluctuations, parametrized by the phonon frequency $\omega_0$, stabilizeferromagnetic phases with respect to the adiabatic limit. We also provide acomplete analysis on the polaron crossover in this model.