Phonon density of states and oxygen-isotope effect in ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$

The phonon densities of states (DOS) of insulating ${\mathrm{BaBiO}}_3$ and superconducting ${\mathrm{Ba}}_{0.6}$ ${\mathrm{K}}_{0.4}$ ${\mathrm{BiO}}_3$ and the variation of the phonon spectrum of the superconducting compound upon oxygen-isotope ${(}^{16}$O, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$) substitution are determined by inelastic neutron scattering (INS) and molecular-dynamics (MD) simulations. The MD simulations are carried out with an effective interaction potential which includes steric effects, Coulomb interactions, and the charge-dipole interactions due to the electronic polarizability of ${\mathrm{O}}^{2\mathrm{-}}$. The MD results are in good agreement with the INS experiments and electron-tunneling measurements. Partial DOS of Ba, K, Bi, and O in ${\mathrm{BaBiO}}_3$ and ${\mathrm{Ba}}_{0.6}$ ${\mathrm{K}}_{0.4}$ ${\mathrm{BiO}}_3$ are also determined from MD simulations. In the superconducting material, the phonon spectrum softens and is comprised of broad bands around 15, 30, and 60 meV. The partial DOS reveal that phonons above 20 meV are due to oxygen vibrations, whereas phonons below 20 meV are due to Ba, K, and Bi. The reference oxygen-isotope-effect exponent, ${\mathrm{\alpha }}_{\mathrm{O}}$r=-∂ ln〈ω〉/∂ ln${\mathit{M}}_{\mathrm{O}}$, of ${\mathrm{Ba}}_{0.6}$ ${\mathrm{K}}_{0.4}$ ${\mathrm{BiO}}_3$ is determined to be ${\mathrm{\alpha }}_{\mathrm{O}}$r=0.42±0.05 from the mass (${\mathit{M}}_{\mathrm{O}}$) variation of the first moment of the phonon DOS, ${}_{\mathrm{O}}{}^{16}{}_{}{}^{}\mathrm{〉}$ and ${}_{\mathrm{O}}{}^{18}{}_{}{}^{}\mathrm{〉}$.