Superconductivity-induced phonon softening in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ observed by inelastic neutron scattering

Inelastic neutron scattering yielded the first information on superconductivity-induced frequency shifts for q≠0 phonons in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathit{x}}$. For branches starting from the Raman-active mode at 340 ${\mathrm{cm}}^{\mathrm{-}1}$ (10.2 THz), the shifts were found to decrease only slowly with increasing momentum transfer (x=7.0) or even exhibit a maximum at finite (x=6.92) when going along the [100] and [010] directions. They were independent of q in the [001] direction. The shifts were much smaller for the ${\mathit{A}}_{\mathit{u}}$ mode at 307 ${\mathrm{cm}}^{+1\mathrm{}}$ and the ${\mathit{E}}_{\mathit{u}}$ mode at 343 ${\mathrm{cm}}^{\mathrm{-}1}$ and for q≠0 phonons related to these modes.