The off-center rattling of Nd rare-earth ions in the filled skutterudite compound NdOs₄Sb₁₂ has been investigated by ultrasonic measurement. The longitudinal C₁₁ mode for frequencies between 34 and 253 MHz shows a marked frequency dependence in elastic constant and ultrasonic attenuations at two different temperatures centered at around 45 and 15 K. The relaxational frequency dependence of ultrasonic dispersion reveals a thermally activated Γ₂₃-type off-center motion of Nd-ions, involving local charge fluctuations with Γ₂₃ symmetry in the (OsSb₃)₄ cage. An attempt time τ_0,(1)=7.5×10^-12 s and an activation energy E₁=337 K were obtained from fits to the dispersion at around 45 K. The presence of another dispersion at lower temperatures of around 15 K implies that the rattling in NdOs₄Sb₁₂ has an additional low-energy excitation characterized by a lower activation energy E₂∼67 K with an attempt time τ_0,(2)=5.1×10^-11 s.

J. Phys. Soc. Jpn. 77 (2008) 074607.

Figure (a) Relative change in elastic constant ΔC₁₁/C₁₁ as function of temperature at frequencies of 34, 108, 180, and 253 MHz. (b) Solid lines show calculations of ΔC₁₁/C₁₁ using Landau-Khalatnikov theory. Dotted lines indicate the higher-frequency limit of the elastic constant C_∞ and the low frequency limit C₀. Arrows indicate the temperatures that satisfy the resonant condition of ω ∼ 1/τ_i. (c) Temperature dependence of ultrasonic attenuation coefficient α₁₁ at frequencies of 34, 108, 180, and 253 MHz. Solid lines are theoretical fits using the parameters.