Exploring the Charge-Ordering Transition in (TMTTF)${}_2$X via Thermal Expansion Measurements

We report results of high-resolution measurements of the \emph{c${}^{\ast }$}-axis expansivity (${\alpha }_{c^{\ast }}$) at the charge-ordering (CO) transition for the quasi-1D (TMTTF)${}_2$X compounds with X = SbF${}_6$ and Br and make a comparison with previous results for the X = PF${}_6$ and AsF${}_6$ salts. For X = SbF${}_6$, due to the screening of the long-range Coulomb forces, a sharp $\lambda$-type anomaly is observed at $T_{CO}$, which contrasts with the step-like mean-field anomaly at $T_{CO}$ for PF${}_6$ and AsF${}_6$, where CO occurs in the Mott-Hubbard charge-localized regime. For the latter two salts, a negative contribution to ${\alpha }_{c^{\ast }}$ is observed above $T_{CO}$. This feature is assigned to the anions’ rigid-unit modes, which become inactive for $T$ $<$ $T_{CO}$. Our ${\alpha }_{c^{\ast }}$ results for the X = Br salt, where such rigid-unit modes are absent, reveal no traces of such negative contribution, confirming the model based on the anions’ rigid-unit modes for the X = PF${}_6$ and AsF${}_6$ salts.