Optical conductivity of colossal magnetorestistance compounds: Role of orbital degeneracy in the ferromagnetic phase

Recent optical conductivity $\sigma(\omega)$ experiments have revealed an anomalous spectral distribution in the ferromagnetic phase of the perovskite system $La_{1-x}Sr_xMnO_3$. Using finite temperature diagonalization techniques we investigate $\sigma(\omega)$ for a model that contains only the $e_g$-orbital degrees of freedom. Due to strong correlations the orbital model appears as a generalized t-J model with anisotopic interactions and 3-site hopping. In the orbital t-J model $\sigma(\omega)$ is characterized by a broad incoherent spectrum with increasing intensity as temperature is lowered, and a Drude peak with small weight, consistent with experiment. Our calculations for two-dimensional systems, which may have some particular relevance for the double-layer manganites, show that the scattering from orbital fluctuations can explain the order of magnitude of the incoherent part of $\sigma(\omega)$ in the low temperature ferromagnetic phase. Moreover orbital correlation functions are studied and it is shown that $x^2$-$y^2$ orbital order is prefered in the doped planar model at low temperature.