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

Abstract

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 ${T}_{c1}=66\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and have an incommensurate lattice distortion between ${T}_{c1}$ and ${T}_{c2}=92\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. 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 $\ensuremath{\sim}2\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ energy resolution. For the first time, a zone-boundary phonon which softens at the spin-Peierls temperature ${T}_{\mathit{SP}}$ 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 ${T}_{\mathit{SP}}$. However, not all aspects of the data can be described, such as the strong overdamping of the soft mode above ${T}_{\mathit{SP}}$. 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 ${T}_{\mathit{SP}}={T}_{c2}=92\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.