Softening of bond-stretching phonon mode in Ba${}_{1-x}$K${}_x$BiO${}_3$ at the metal-insulator transition

The dispersion of phonons in Ba${}_{1-x}$K${}_x$BiO${}_3$ along the ($3+q$, 0, 0) direction in reciprocal space was determined for $x=0$, 0.30, 0.37, and 0.52 using high-resolution inelastic x-ray scattering. The observed phonon energies near $\Gamma$ were in good agreement with published optical data. It was found that two high-energy modes strongly soften near $q=0.25$ when the system becomes metallic ($x>0.35$). There was no softening in the insulating phase, even at $x=0.30$, very near the metal-insulator transition. This suggests that the phonon softening is linked to the appearance of the Fermi surface.

Figure 1

A typical IXS spectrum for the BaBiO${}_3$ system at various $q$ values. Open circles show experimental data with their statistical error bars. Lines below the spectrum show the pseudo-Voigt fitting for elastic scattering and each phonon mode indicated by a short bar. Solid black lines show the total fitting of the experimental data.

Figure 2

Potassium content dependence of phonon energies for various modes at $q~0.1$ in ($3+q$,0,0) momentum (filled symbols). Open symbols are the other experimental data for LO phonon modes from Raman and optical spectroscopies.[28, 29, 30] Dashed horizontal lines are guides for the eye.

Figure 3

High-energy part of the IXS spectra of the BKBO system for the four compositions. The number beside the data shows the $q$ value in ($3+q$,0,0) momentum. Open symbols show experimental data and solid lines show the fitting result. Short vertical bars on the data indicate the positions of the phonon peaks. Dashed vertical lines are guides for the eye, to track the phonon dispersions. Data were plotted by a shift in the vertical axis to distinguish the different $q$ patterns.

Figure 4

Phonon branches of the BKBO system in the (100) direction for four values of $x$ (filled symbols and double circles) and data from neutron scattering studies[21, 22] for comparison (open symbols). Dashed lines are guides for the eye.