Optical conductivity of rattling phonons in type-I clathrate Ba${}_8$Ga${}_{16}$Ge${}_{30}$

Abstract

A series of infrared-active optical phonons have been detected in type-I clathrate Ba${}_8$Ga${}_{16}$Ge${}_{30}$ by terahertz time-domain spectroscopy. The conductivity spectra with the lowest-lying peaks at 1.15 and 1.80 THz are identified with so-called rattling phonons, i.e., optical modes of the guest ion Ba${}^{2+}(2)$ with $T_{1u}$ symmetry in the oversized tetrakaidecahedral cage. The temperature dependence of the spectra from these modes are totally consistent with calculations based on a one-dimensional anharmonic potential model that, with decreasing temperature, the shape becomes asymmetrically sharp associated with a softening for the weight to shift to lower frequency. These temperature dependences are determined, without any interaction effects, by the Bose-factor for optical excitations of anharmonic phonons with the nonequally spaced energy levels.

4 pages, 4 figures