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.

A variety of thermodynamic and transport measurements were made on high-quality single crystals of the Pr-based filled skutterudite compound PrFe₄As₁₂. Abrupt features in magnetization, ac susceptibility, specific heat, resistivity, thermoelectric power, and ultrasonic velocity reveal the onset of long range ferromagnetic order below Theta_C=18 K. The low-temperature magnetic susceptibility is characterized by a Curie–Weiss law with an effective moment of 3.52µ_B/f.u. and a saturation magnetization of 2.3µ_B/f.u., which is consistent with a magnetic Γ₅ triplet ground state. A gaplike reduction of the large electronic specific heat coefficient of 340 mJ/mol K² and several other features point to a strongly correlated electron behavior that is likely coupled to a change in magnetic and/or structural order near T*~12 K. Furthermore, this complex magnetic state is found to be strongly field dependent, as evidenced by a change in the easy axis at low fields and an additional contribution to thermal conductivity appearing only at high fields.

Phys. Rev. B 77 (2008) 144432. (Editor's Suggested).

Figure : A comparison of low-temperature specific heat, electrical resistivity, magnetization, ac susceptibility,
thermopower, and ultrasound data that are used to correlate features that are observed at the ferromagnetic ordering temperatureTheta_c = 18 K and the characteristic temperature T*= 12 K and T' = 10 K.

Upper: Temperature derivative of resistivity and electronic plus magnetic contributions to specific heat, which shows a striking resemblance of the temperature dependence of each throughout the entire range.

Middle: Low-field (5 mT) dc magnetization and the imaginary part of the ac susceptibility, highlighting the coincidence of both the irreversibility temperature in M(T) and the peak in Chi_ac(T) with T*.

Lower* Zero-field thermoelectric power and relative change in the elastic constant ΔC₄₄/C₄₄ as a function of temperature for PrFe₄As₁₂.