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With a terahertz time-domain spectrometer (0.3 - 3.0 THz) we have measuredthe optical conductivity of the type-I clathrate Ba$_8$Ga$_{16}$Sn$_{30}$ attemperatures from 300 K down to 7 K. Independent six spectra superimposed onthe Drude conductivity are identified to infrared active vibrational modes ofguest Ba ions and the cages. While the spectra of five higher-frequency modesdepend hardly on temperature, the lowest-lying spectrum with a peak at 0.72 THzdue to the Ba(2) ion's off-centering vibration in the oversized cage changeswith temperature characteristically. With lowering temperature, the spectralshape of this so-called rattling phonon continues to become so broad that theline-width amounts to be comparable to the peak frequency. Furthermore, belowabout 100 K, the single broad peak tends to split into two subpeaks. While thissplitting can be explained by assuming a multi-well anharmonic potential, thestrong enhancement of the line-width broadening toward low temperature, cannotbe understood, since the Boltzmann factor generally sharpens thelow-temperature spectra.

Low temperature line-width broadening in optical-conductivity spectra of the off-center rattling phonons in type-I clathrate Ba$_8$Ga$_{16}$Sn$_{30}$