Low-energy dispersion of dynamic charge stripes in La$_{1.75}$Sr$_{0.25}$NiO$_{4}$ observed with inelastic neutron scattering*

The dynamic stripe correlations have been the subject of intense research, owing to the possible links with high-T$_{c}$ superconductivity. In light of a recently published, direct observation of charge-stripe fluctuations in La$_{2-x}$Sr$_{x}$NiO$_{4}$ using inelastic neutron scattering\footnote{S. Anissimova, $et$ $al.$, Nat. Commun. 5, 3467 (2014)}, we did a follow-up neutron experiment on a $x$=0.25 sample to characterize the low-energy dispersion of these dynamic charge stripes using the HYSPEC instrument at the Spallation Neutron Source. The scattering signals are collected in the vicinity of a charge-order peak with a large wave vector (4.4, 3, 0), where dynamic spin-stripe correlations are negligible. Mapping the low-energy charge-stripe fluctuations in a wide temperature range, we observe a finite dispersion along the stripe-modulation direction at T$\geq$160K where the charge stripes become disordered, while the steep dispersion in the orthogonal direction is not resolved.