Lattice dynamics in Bi₂Te₃ and Sb₂Te ₃: Te and Sb density of phonon states

The lattice dynamics in Bi₂Te₃ and Sb ₂Te₃ were investigated both microscopically and macroscopically using 121Sb and 125Te nuclear inelastic scattering, x-ray diffraction, and heat capacity measurements. In combination with earlier inelastic neutron scattering data, the element-specific density of phonon states was obtained for both compounds and phonon polarization analysis was carried out for Bi₂Te₃. A prominent peak in the Te specific density of phonon states at 13meV, that involves mainly in-plane vibrations, is mostly unaffected upon substitution of Sb with Bi revealing vibrations with essentially Te character. A significant softening is observed for the density of vibrational states of Bi with respect to Sb, consistently with the mass homology relation in the long-wavelength limit. In order to explain the energy mismatch in the optical phonon region, a ∼20% force constant softening of the Sb-Te bond with respect to the Bi-Te bond is required. The reduced average speed of sound at 20K in Bi₂Te₃, 1.75(1)km/s, compared to Sb₂Te₃, 1.85(4)km/s, is not only related to the larger mass density but also to a larger Debye level. The observed low lattice thermal conductivity at 295K, 2.4Wm^-1K^-1 for Sb₂Te ₃ and 1.6Wm^-1K^-1 for Bi₂Te ₃, cannot be explained by anharmonicity alone given the rather modest Grüneisen parameters, 1.7(1) for Sb₂Te₃ and 1.5(1) for Bi₂Te₃, without accounting for the reduced speed of sound and more importantly the low acoustic cutoff energy.