Lattice instability coupled with valence degrees of freedom in valence fluctuation compound YbPd

Inelastic x-ray scattering (IXS) was used to examine the valence fluctuation compound YbPd at 300 K in the $\Gamma -X$, $\Gamma -M, X-M$, and X-R directions. The obtained spectra and determined phonon dispersion relations demonstrate lattice instabilities related to the successive transitions and correlations between phonon spectra and valence degrees of freedom in YbPd. The low-lying branches in the phonon dispersion relations as well as the broadened linewidths of the IXS spectra observed around the longitudinal $X$ point provide supporting evidence of correlation between a valence-lattice interaction and the successive transitions in YbPd. X-ray absorption spectroscopy was also performed in order to discuss correlations between lattice instabilities and Yb valence degrees of freedom in YbPd.

Figure 1

(a) Brillouin zone of a CsCl-type structure isostructural with YbPd. (b) IXS spectra of YbPd taken with high-resolution setup along the Γ-$X$($L$) direction at 300 K. Open circles depict experimental data. Dashed curves depict contributions of the longitudinal acoustic modes.

Figure 2

Phonon dispersion relation of YbPd taken in the Brillouin zone of (4+ξ 0 0) at 300 K. Closed circles (open squares) depict the data taken with the high-resolution (normal) setup. Solid curves are guides to the eye.

Figure 3

IXS spectra of YbPd at 300 K taken with the normal setup along the (a) X($L$)-$R$ and (b) X($L$)-$M$ directions. Open circles depict experimental data. Dashed curves depict the contribution of the lowest modes in each direction.

Figure 4

Phonon dispersion relations of YbPd at 300 K. Open circles are data points obtained by IXS. Solid curves are guides to the eye. Dashed curves are the calculated results reported in Ref. [20].

Figure 5

Phonon dispersion relations (upper panel) and excitation linewidths (lower panel) in various directions around (4.5 0 0) at 300 K. Solid curves are guides to the eye.

Figure 6

Temperature dependence of the IXS spectra of YbPd at the $X$($L$) point of (4.50 0.00 0.00). The gray regions correspond to the elastic contribution at each temperature.

Figure 7

Temperature dependence of the quasielastic linewidth at the $X$($L$) point of (4.50 0.00 0.00).

Figure 8

Yb $L_{\mathrm{III}}$-edge x-ray absorption spectrum of YbPd at 300 K.

Figure 9

Temperature dependence of average Yb valence in YbPd estimated from the Yb $L_{\mathrm{III}}$-edge x-ray absorption spectra.