We report on a systematic study of the thickness dependence of the optical properties of thin films epitaxially grown on a substrate. The x-ray powder-diffraction data indicate that the -axis lattice constant is enhanced with decreasing the film thickness due to the compressive strain in the film plane produced by lattice mismatch. Magnetization curves show a decrease of the Curie temperature for decreasing thickness of films. Optical reflectance and transmittance measurements provide evidence that the position of Mn-O stretching mode shifts toward low frequency and the energy of the charge-transfer transition between O and Mn states increases with the decrease of film thickness. Most importantly, an analysis of the small-polaron absorption in the mid-infrared region shows that the polaron binding energy increases with decreasing the film thickness, suggesting that the strain dependence of mainly results from the strain-induced electron–phonon coupling.
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, , and are the oscillator strength, center frequency, and scattering rate of the Lorentzian oscillators.
The center frequency given in Table I corresponds closely to two times of the small polaron binding energy.
