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 T-c1=66 K and have an incommensurate lattice distortion between T-c1 and T-c2=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 T-c2. The behavior of the phonons has been studied using inelastic x-ray scattering with similar to 2 meV energy resolution. For the first time, a zone-boundary phonon which softens at the spin-Peierls temperature T-SP 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 T-SP. However, not all aspects of the data can be described, such as the strong overdamping of the soft mode above T-SP. 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 T-SP=T-c2=92 K.