  Comprehensive inelastic neutron-scattering measurements were performed to
study the soft optical phonons in La2-xSrxCuO4 at x=0.10, 0.12 and 0.18. We
found at x=0.18 that the softening of Z-point phonon, suggesting incipient
structural transition from the low-temperature orthorhombic (LTO) to
low-temperature tetragonal (LTT) phase, breaks at Tc, which is consistent with
the previous report by Lee et al. for the optimally doped x=0.15 sample. As for
x=0.10 and 0.12, on the other hand, the softening continues even below Tc. It
is thus clarified that the breaking of soft phonon is characteristic of
La2-xSrxCuO4 in the optimally and overdoped regions. In the course of studying
the soft phonons, we discovered that a central peak remains above the LTO to
high-temperature tetragonal (HTT) phase transition at Ts1 and splits into
incommensurate components along the (1 1 0)HTT direction at higher
temperatures. This is a common feature for both x=0.12 and 0.18 and their
temperature dependences of the splitting 2d can be scaled by using a
renormalized temperature T/Ts1. In the high temperature limit, d saturates
around d ~ 0.12 r.l.u., which value is close to the splitting of incommensurate
magnetic signals. This implies that the incipient lattice modulation starts
appearing at very high temperature. Details of this modulation and its
relations with other properties are, however, not yet clarified.
