Recent experimental study reveals the optical conductivity of La$_{1-x}$Ca$_x$MnO$_3$ over a wide range of energy and the occurrence of spectral weight transfer as the system transforms from paramagnetic insulating to ferromagnetic metallic phase [Ru
sydi {it et al.}, Phys. Rev. B {bf 78}, 125110 (2008)]. We propose a model and calculation within the Dynamical Mean Field Theory to explain this phenomenon. We find the role of oxygens in mediating the hopping of electrons between manganeses as the key that determines the structures of the optical conductivity. In addition, by parametrizing the hopping integrals through magnetization, our result suggests a possible scenario that explains the occurrence of spectral weight transfer, in which the ferromagnatic ordering increases the rate of electron transfer from O$_{2p}$ orbitals to upper Mn$_{e_g}$ orbitals while simultaneously decreasing the rate of electron transfer from O$_{2p}$ orbitals to lower Mn$_{e_g}$orbitals, as temperature is varied across the ferromagnetic transition. With this scenario, our optical conductivity calculation shows very good quantitative agreement with the experimental data.
