Bond-Stretching-Phonon Anomalies in Stripe-Ordered ${\mathrm{La}}_{1.69}{\mathrm{Sr}}_{0.31}{\mathrm{NiO}}_4$

We report a neutron scattering study of bond-stretching phonons in ${\mathrm{La}}_{1.69}{\mathrm{Sr}}_{0.31}{\mathrm{NiO}}_4$, a doped antiferromagnet in which the added holes order in diagonal stripes at $45°$ to the Ni-O bonds. For the highest-energy longitudinal optical mode along the bonds, a softening of $20\%$ is observed between the Brillouin zone center and the zone boundary. At $45°$ to the bonds, a splitting of the same magnitude is found across much of the zone. Surprisingly, the charge-ordering wave vector plays no apparent role in the anomalous dispersions. The implications for related anomalies in the cuprates are discussed.