Neutron scattering study of soft phonons and diffuse scattering in insulating La$_{1.95}$Sr$_{0.05}$CuO$_{4}$

Soft phonons and diffuse scattering in insulating La$_{2-x}$Sr$_{x}$CuO$_4$ ($x=0.05$) have been studied by the neutron scattering technique. The X-point phonon softens from high temperature towards the structural transition temperature $T_{s}=410$ K, and the Z-point phonon softens again below 200 K. The Z-point phonon softening persists to low temperature, in contrast to the behavior observed in the superconducting $x=0.15$ compound, in which the Z-point phonon hardens below $T_c$. The diffuse scattering associated with the structural phase transition at 410 K appears at commensurate positions. These results highlight interesting differences between superconducting and insulating samples.