Oxygen phonon branches in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$

We report results of inelastic neutron scattering measurements of phonon dispersions in optimally doped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.95}$ and compare them with model calculations. The focus is on the in-plane oxygen bond-stretching phonon branches. The study of these modes is complicated by anticrossings with c-axis-polarized branches; such effects are interpreted through lattice-dynamical shell-model calculations. The in-plane anisotropy of the bond-stretching phonons was firmly ascertained from measurements on a detwinned sample. Studying not only the in-plane modes involving in-phase motion for the two Cu-O layers within a unit cell but also those with opposite-phase motion was of great help for establishing a clear experimental picture. The measurements confirm that the in-plane oxygen bond-stretching phonon branches disperse steeply downwards from the zone center in both the a and the b directions indicating a strong electron-phonon coupling. For the b-axis-polarized bond-stretching phonons, there is an additional feature of considerable interest: a sharp local frequency minimum was found to develop on cooling from room temperature to $T=10\mathrm{}\mathrm{K}$ at wave vector $\mathbf{q}\approx 0.27$ r.l.u.