Lattice instability and elastic dispersion due to the rattling motion in the type-I clathrate Ba ₈Ga ₁₆Sn ₃₀

To investigate the off-center rattling motion and its charge-carrier dependence in type-I clathrate compounds, we carried out ultrasonic measurements on type-I Ba ₈Ga ₁₆Sn ₃₀ and a reference compound, K ₈Ga ₈Sn ₃₈. We found elastic softening of C ₄₄ originating from a lattice instability due to the off-center rattling motion of Ba atom in Ba ₈Ga ₁₆Sn ₃₀. Elastic softening below 1 K suggests that the lattice instability remains at very low temperatures. We also found ultrasonic dispersion which has no mode selectivity. No-mode-selective ultrasonic dispersion in Ba ₈Ga ₁₆Sn ₃₀ would be caused by a strong electron-phonon coupling. No charge-carrier dependence is observed between n-type and p-type Ba ₈Ga ₁₆Sn ₃₀. The significant softening on the bulk modulus in Ba ₈Ga ₁₆Sn ₃₀ contrasts to the continuous hardening in K ₈Ga ₈Sn ₃₈, indicating the central role of the rattling motion in the softening.