Soft phonon and the central peak at the structural phase transition in SrTiO₃

The continuous displacive phase transition in SrTiO₃ near T_c ≈ 105 K is characterized by a central elastic peak observed in neutron-scattering experiments above T_c, i.e., before the associated soft phonon mode becomes overdamped upon cooling. The origin of this central peak remains unresolved. Here we present inelastic x-ray scattering results on the cubic-to-tetragonal phase transition in SrTiO₃. We quantitatively compare the soft phonon mode and central peak in two differently grown SrTiO₃ samples with well-characterized defect concentrations and discuss the results in relation to thermodynamic and transport probes such as specific heat and thermal conductivity. Our results show that the soft mode evolves similarly in both samples, although the central peak intensity differs by a factor of four, suggesting that the local crystal properties that are insensitive to the collective lattice excitations are likely responsible for the central elastic line in SrTiO₃. High momentum and milli-electronvolt energy resolution of our inelastic x-ray sacattering measurements allow us to separate the elastic intensity of the central peak from low-energy quasielastic phonon scattering, revealing anisotropic correlation lengths on cooling toward T_c.