Electron-phonon interactions in insulating nanoparticles:Eu2O3

Abstract

The temperature and particle size dependencies of the linewidth of spectral holes burned in the ${}^7{\overrightarrow{F_0}}^5{D}_0$ transition of ${\mathrm{Eu}}^{3+}$ ions in ${\mathrm{Eu}}_2{\mathrm{O}}_3$ are calculated and compared with experiment. The power-low temperature behavior $\sim T^7,$ well-known experimentally and theoretically for the bulk, is observed to be strongly weakened to $\sim T^3$ for the nanoparticles. A calculation is performed that assumes a two-phonon Raman-scattering mechanism involving the discrete phonon modes of a homogeneous nanoparticle with stress-free boundary conditions. The experimental results are successfully described assuming that the phonon modes broaden with frequency as $\sim {\omega }^2.$ A quantitative comparison of the calculations with experiment allows the determination of the linewidth of the phonon resonances of the nanoparticles. The calculations predict that the size dependence of the hole linewidth is $\sim D^{-2.5},$ in close agreement with experiment.