Einstein Modes in the Phonon Density of States of the Single-Filled Skutterudite Yb$_{0.2}$Co$_{4}$Sb$_{12}$

Measurements of the phonon density of states by inelastic neutron \emph{time-of-flight} scattering and specific heat measurements along with first principles calculations, provide compelling evidence for the existence of an Einstein oscillator ("\emph{rattler}") at $ω_{E1} \approx$ 5.0 meV in the filled skutterudite Yb$_{0.2}$Co$_{4}$Sb$_{12}$. Multiple dispersionless modes in the measured density of states of Yb$_{0.2}$Co$_{4}$Sb$_{12}$ at intermediate transfer energies (14 meV $\leq$ \emph{$ω$} $\leq$ 20 meV) are exhibited in both the experimental and theoretical \emph{density-of-states} of the Yb-filled specimen. A peak at 12.4 meV is shown to coincide with a second Einstein mode at \emph{$ω_{E2} \approx$} 12.8 meV obtained from heat capacity data. The local modes at intermediate transfer energies are attributed to altered properties of the host CoSb$_{3}$ cage as a result of Yb-filling. It is suggested that these modes are owed to a complementary mechanism for the scattering of heat-carrying phonons in addition to the mode observed at $ω_{E1} \, \approx$ 5.0 meV. Our observations offer a plausible explanation for the significantly-higher \textit{dimensionless figures of merit} of filled skutterudites, compared to their parent compounds.