Ultrasonic Dispersion in the Hexagonal Ferromagnet Nd₃Ru₄Al₁₂

Abstract

The rare-earth ferromagnet Nd 3 Ru 4 Al 12 has Curie temperature T C = 39 K and crystallizes in the hexagonal Gd 3 Ru 4 Al 12-type structure (space group P6 3 /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 C 33. The upturn is not caused by any phase transition. To investigate the origin of the upturn in Nd 3 Ru 4 Al 12 , we have measured the temperature dependence of C 33 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  0 = 1.5  10-13 s.