Anharmonic phonons in type I clathrates

A systematic study on the anharmonicity of phonons is made for thermoelectric single crystal type-I clathrates based on their heat capacity $C_{p}$ at low temperatures (T) down to 360\,mK. The low-T linear terms $^{obs}\gamma T$ of $C_{p}$, including the tunneling-term of the atoms accommodated in the host cages ($\gamma_{ph} T$=$\alpha T$), and the Sommerfeld itinerant-electron term ($\gamma_{e} T$) are successfully separated through careful measurements of sigle crystals with various carrier concentrations. The values of the density of anharmonic potentials are deduced. The effective mass (m${*}$) enhancement is also determined from $\gamma_{e}$ values and the electron-phonon interaction strength ($\lambda$) can be evaluated from these values. It is shown that both the thermal conductivities ($\kappa$'s) and the electron-phonon interaction strengths ($\lambda$'s) are quantitatively in good agreement with the $\alpha$ parameters deduced from the present experiments. The boson peaks observed at low energy excitations are disucssued in relation to the $\alpha$ values.