Universality of anharmonic motion of heavy rare-earth atoms in hexaborides

Phonons of TbB6 are studied by inelastic X-ray scattering and compared with those of GdB₆ and DyB₆. Measured low-lying phonon modes located near 6 meV soften distinctly with decreasing temperature, particularly the longitudinal phonon that is dominated by the motion of Tb ions at q1 =( 1/2; 0; 0). The magnitude and temperature dependence of phonon energy are between those of GdB₆ and DyB₆. We derive a Landau-type free-energy expansion with respect to the atomic displacement in TbB₆, and discuss a general feature among these three compounds. The systematic variation in the phonon characteristics of these hexaborides and the first-order-like instability indicate the universality of the anharmonic motion of heavy rare-earth atoms in RB₆ (R = Gd, Tb, and Dy).