Phonon anomalies and critical fluctuations associated with charge stripes in La$_{1.67}$Sr$_{0.33}$NiO$_4$

We will report inelastic neutron scattering measurements of the spectrum of charge excitations in the stripe-ordered phase of La$_{2-x}$Sr$_{x}$NiO$_{4}$ ($x = \frac{1}{3} $). We identified clear signature of charge stripes at low energies in the nickelates. Our results imply that dynamic stripes are critical fluctuations associated with the stripe-ordering transition. We also observed a phonon anomaly correlated with dynamic stripes above the static-ordering transition, which occurs at 241~K. Our results elucidate the nature of dynamic charge stripes and their signature in the neutron spectra.