  The insulator-to-metal transition continues to be a challenging subject,
especially when electronic correlations are strong. In layered compounds, such
as La2-xSrxNiO4 and La2-xBaxCuO4, the doped charge carriers can segregate into
periodically-spaced charge stripes separating narrow domains of
antiferromagnetic order. Although there have been theoretical proposals of
dynamically fluctuating stripes, direct spectroscopic evidence of charge-stripe
fluctuations has been lacking. Here we report the detection of critical lattice
fluctuations, driven by charge-stripe correlations, in La2-xSrxNiO4 using
inelastic neutron scattering. This scattering is detected at large momentum
transfers where the magnetic form factor suppresses the spin fluctuation
signal. The lattice fluctuations associated with the dynamic charge stripes are
narrow in q and broad in energy. They are strongest near the charge stripe
melting temperature. Our results open the way towards the quantitative theory
of dynamic stripes and for directly detecting dynamical charge stripes in other
strongly-correlated systems, including high-temperature superconductors such as
La2-xSrxCuO4.
