Valence-lattice interaction on YbPd

An intermediate valence compound YbPd undergoes successive structural transitions at 105 K and 125 K. The recent inelastic X-ray scattering measurement have revealed softening of longitudinal acoustic (LA) mode around X point, q =(0, 0, 0.5). We have attempted to reproduce this softening from first-principles calculations. The calculated results with fixed valence Yb do not show any anomaly in the LA mode around X. To include valence change in the lattice vibrations, the nearest-neighbor valence-lattice interaction has been added. The interaction reduces the energy of the LA mode around X as observed by the experiment. This soft mode leads to the structure below 105 K. On the other hand, the lowest energy is found at the slightly different wavevector, q =(0.1, 0.1, 0.5). This wavevector corresponds to the superlattice reflection observed by the experiment in the intermediate incommensurate phase between 105 K and 125 K. Therefore, the successive structural transitions of YbPd can be correctly reproduced by including this valence-lattice interaction.