X-ray scattering study of the spin-Peierls transition and soft phonon behavior in TiOCl

We have studied the S=1 2 quasi-one-dimensional antiferromagnet TiOCl using single crystal x-ray diffraction and inelastic x-ray scattering techniques. The Ti ions form staggered spin chains which dimerize below Tc1 =66 K and have an incommensurate lattice distortion between Tc1 and Tc2 =92 K. Based on our measurements of the intensities, wave vectors, and harmonics of the incommensurate superlattice peaks, we construct a model for the incommensurate modulation. The results are in good agreement with a soliton lattice model, though some quantitative discrepancies exist near Tc2. The behavior of the phonons has been studied using inelastic x-ray scattering with ∼2 meV energy resolution. For the first time, a zone-boundary phonon which softens at the spin-Peierls temperature TSP has been observed. Our results show reasonably good quantitative agreement with the Cross-Fisher [Phys. Rev. B. 19, 402 (1979)] theory for the phonon dynamics at wave vectors near the zone boundary and temperatures near TSP. However, not all aspects of the data can be described, such as the strong overdamping of the soft mode above TSP. Overall, our results show that TiOCl is a good realization of a spin-Peierls system, where the phonon softening allows us to identify the transition temperature as TSP = Tc2 =92 K.