Neutron scattering study of soft optical phonons in ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$${\mathrm{Sr}}_{\mathrm{x}}$${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$

The soft optical phonons associated with the tetragonal-to-orthorhombic structural phase transition in ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$ have been investigated using inelastic-neutron-scattering techniques. Single crystals with Sr concentration of x=0, 0.08, and 0.14 were studied. Both branches of the doubly degenerate X-point phonon which go soft at the tetragonal-to-orthorhombic transition have been observed in the orthorhombic phase. In all three samples one branch hardens, while the other remains relatively soft with behavior indicative of a further incipient structural phase transition. We identify the hard and soft branches of the orthorhombic phase as zone center and zone-boundary phonons, respectively. The zone-center mode has $A_g$ symmetry and is, consequently, Raman active. The relation of these measurements to other structural properties and to the superconductivity in ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$ is discussed.