Ultrasonic dispersion in the hexagonal ferromagnet Nd₃Ru₄Al₁₂

The rare-earth ferromagnet Nd₃Ru₄Al₁₂ has Curie temperature T_C = 39 K and crystallizes in the hexagonal Nd₃Ru₄Al₁₂-type structure (space group P6₃/mmc), which is a non-caged structure. A previous measurement of the elastic moduli has shown an upturn around 10 K in the temperature dependence of the longitudinal modulus C₃₃. The upturn is not caused by any phase transition. To investigate the origin of the upturn in Nd₃Ru₄Al₁₂, we have measured the temperature dependence of C₃₃ at various ultrasonic frequencies. The temperature of the upturn increases with increasing ultrasonic frequency indicating the ultrasonic dispersion, and it does not change under applied magnetic fields. These results suggest that the upturn originates from the rattling effect at one of the aluminium sites in the crystal structure. Assuming a Debye-type relaxation for the elastic modulus and an Arrhenius-type relaxation time for the rattling, the activation energy was estimated as E = 115 K and the relaxation time as τ₀ = 1.5 × 10^-13 s. (author)