The observed frequency dependent optical response of hole doped La_0.8Ca_0.2MnO₃ manganites, has been theoretically analysed. Starting from an effective two-dimensional (2D) interaction potential for hole doped manganites, the spectral function is developed. Calculations of the optical conductivity σ(ω) have been made within the two-component scheme: one is the coherent Drude free carrier excitations. The other is incoherent motion of carriers from one site to other leading to a polaron formation, originated from interband transitions between the Hund rule split bands (Mn-Mn) and due to charge-transfer transitions between the O 2p and the Mn e_g bands. The approach successfully accounts for the anomalies reported in the optical measurements for the ferromagnetic metallic state. Estimating the effective mass from heat capacity measurement, the model has only one material parameter, the relaxation rate. The frequency dependent relaxation rates are expressed in terms of memory functions and the coherent Drude carriers from the effective interaction potential leads to a sharp peak at zero frequency and a long tail at higher frequencies, i.e. in the infrared region. While to that the hopping of carriers from Mn site to Mn and Mn site to O (incoherent motion of doped carriers) yields two-peak value around 0.4 and 4.0 eV in the optical conductivity centred at mid-infrared region. We find that both the Drude and hopping carriers in the manganites will contribute to the optical process of conduction in the Mn-O planes and shows similar results on optical conductivity in the mid-infrared as well as infrared frequency regions as those revealed from experiments.

Keywords: Optical conductivity, layer interactions, Drude carriers, and hopping carriers.

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