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.

Elastic constant measurements down to 0.48 K and in magnetic fields up to 11 T were performed on a single crystal of the filled skutterudite compound PrOs₄As₁₂. The longitudinal C_L111=C_B+4C₄₄/3 mode shows Curie-type softening below ~25 K, which is explained in terms of the quadrupole susceptibility modified by a crystalline electric field with a Γ₄⁽²⁾ ground state. A detailed H-T phase diagram for H || [111] is compiled with the elastic anomalies, which appear on the boundaries of two ordered phases at temperatures below 2.3 K and in fields below 3 T. The intermediate phase between 2 and 2.5 T assumes the aspect of antiferroquadrupolar ordering.

Phys. Rev. B 77 (2008) 094435,

also on J. Phys. Soc. Jpn. 77 (2008) Suppl. A, pp. 225-228.

Figure : Magnetic field vs. Temperature (H-T) phase diagram of PrOs₄As₁₂ with fields (a) H || [111] and (b) H || [1-10]. Data points are determined by a feature of elastic anomalies; upward or downward in C_L111 vs. H (solid circles and squares), C_L111 vs. T (open circles and squares); minimum in C_L111 vs. H (times), C_L111 vs. T (plus). Error bars on the markers indicate roughly estimated transition width. Solid lines are guides to the eyes, separating the PM region (phase I), AFM region (phase III) and unknown ordered phase II and II'.

We have performed dilatometric measurements by the capacitance method on tetragonal rare earth compounds DyB₂C₂ and HoB₂C₂ that show antiferro-quadrupole (AFQ) ordering. The tetragonal structure is invariant across the paramagnetic phase to the AFQ phase at T_Q=24.7 K in DyB₂C₂. In the case of intermediate phase IV of HoB₂C₂, between T_C1=5.9 K and T_C2=5.0 K, the lattice length along the [101] direction reveals an abrupt increase, while the lengths along the [100] and [110] directions shrink slightly. This lattice distortion is described in terms of triclinic strain ε_yz = ε_zx≠0 indicating the spontaneous ferro-quadrupole moment <O_yz>= <O_zx>≠0. A plausible model, based on an octupole ordering <T_x>=<T_y>=<T_z>≠0, in phase IV of HoB₂C₂, is argued.

J. Phys. Soc. Jpn. 74 (2005) 1666.

(*This research was performed at Niigata University in 2004.)