Evidence for Lattice Effects at the Charge-Ordering Transition in (TMTTF)${}_2$X

Abstract

High-resolution thermal expansion measurements have been performed for exploring the mysterious "structureless transition" in (TMTTF)${}_2$X (X = PF${}_6$ and AsF${}_6$), where charge ordering at $T_{CO}$ coincides with the onset of ferroelectric order. Particularly distinct lattice effects are found at $T_{CO}$ in the uniaxial expansivity along the interstack $\text{c*}$-direction. We propose a scheme involving a charge modulation along the TMTTF stacks and its coupling to displacements of the counteranions X${}^{-}$. These anion shifts, which lift the inversion symmetry enabling ferroelectric order to develop, determine the 3D charge pattern without ambiguity. Evidence is found for another anomaly for both materials at $T_{int}$ $\simeq$ 0.6 $\cdot$ $T_{CO}$ indicative of a phase transition related to the charge ordering.