Renormalized motion of dysprosium atoms filling boron cages of DyB ₆

The lattice dynamics of DyB ₆ are investigated by an inelastic X-ray scattering technique. The measured phonon modes are dominated by the motion of Dy ions in oversized boron cages. These soften remarkably as temperature is decreased, with the energy of the longitudinal phonon for the propagation vector q ₁ = (1=2;0;0) decreasing by 29% from 300K down to the phase transition temperature of 31 K. The dispersion relation curves show kinklike anomalies at q _k = (0:38;0:38;0). The observed phenomena are very similar to those previously observed in GdB ₆ [Iwasa et al: Phys. Rev. B 84 (2011) 214308]. We note analogous phonon anomalies in the heavier rare-earth hexaboride systems, owing to the interplay between the motion of rare-earth atoms and the electronic state, particularly characterized by the Friedel oscillation.