  Following previous works reporting an anomalous behavior of several
zone-center optical phonons across the magnetic transition of square lattice
iridates Sr2IrO4 and Sr3Ir2O7, we have investigated the lattice dynamics as a
function of momentum in these materials by means of high-resolution inelastic
x-ray scattering (IXS). The observed phonon energies and scattering intensities
across the Brillouin zone are in excellent agreement with ab-initio lattice
dynamical calculations based on non-magnetic density-functional-perturbation
theory (DFPT). Our results do not evidence any renormalization of the phonons
at finite momentum across the magnetic transition of Sr2IrO4. The only
anomalous behavior was detected for the in-plane polarized
longitudinal-acoustic phonon branch in Sr3Ir2O7, which anomalously softens
towards low temperatures and might be related to anisotropic negative thermal
expansion in this compound. No anomalies related to potential charge ordering
were observed.
