Anisotropic dispersion of charge stripe fluctuations in La$_{1.75}$Sr$_{0.25}$NiO$_4$*

It has recently been demonstrated that charge stripe fluctuations can be detected in La$_{2-x}$Sr$_x$NiO$_4$ by inelastic neutron scattering at temperatures close to the charge-ordering transition [1]. The next step is to characterize the dispersion of these excitations. To do this, we have studied a crystal with $x=0.25$ using the HYSPEC instrument at the Spallation Neutron Source. The clearest picture has been obtained at a temperature of 160 K, where spin order is absent while the charge order is weak but finite. The effective observation window is limited to $E < 8$ meV, as acoustic phonons dispersing from neighboring Bragg peaks obscure the weak signal of interest at higher energies. Measuring about the charge-order peak at wave vector (4.4,3,0), where $a^*=1.159$~\AA$^{-1}$, we observe a dispersion with a velocity of $\sim20$ meV-\AA\ along the stripe-modulation direction, but no clear dispersion in the orthogonal direction. The detected velocity has the scale of lattice, rather than purely electronic, excitations. \par\noindent [1] S. Anissimova {\it et al.}, Nat. Commun. {\bf 5}, 3467 (2014).