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Register a new userExploring the Charge-Ordering Transition in (TMTTF)$_2$X via Thermal Expansion Measurements
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We report results of high-resolution measurements of the emph{c$^*$}-axis expansivity ($alpha_{c^{*}}$) 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 $alpha_{c^{*}}$ is observed above $T_{CO}$. This feature is assigned to the anions rigid-unit modes, which become inactive for $T$ $<$ $T_{CO}$. Our $alpha_{c^{*}}$ 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.
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Charge-ordering phenomena have been highly topical over the last few years. A phase transition towards a charge ordered state has been observed experimentally in several classes of materials. Among them, many studies have been devoted to the family of quasi-one dimensional organic charge-transfer salts (TMTTF)$_2$X, where (TMTTF) stands for tetramethyltetrathiafulvalene and X for a monovalent anion (X = PF$_6$, AsF$_6$ and SbF$_6$). However, the relationship between the electron localization phenomena and the role of the lattice distortion in stabilizing the charge-ordering pattern is poorly documented in the literature. Here we present a brief overview of selected literature results with emphasis placed on recent thermal expansion experiments probing the charge-ordering transition of these salts.
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 $textbf{textit{c*}}$-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.
Using a combination of Density Functional Theory, mean-field analysis and exact diagonalization calculations we reveal the emergence of a dimerized charge ordered state in TMTTF$_2$-PF$_6$ organic crystal. The interplay between charge and spin order leads to a rich phase diagram. Coexistence of charge ordering with a structural dimerization results in a ferroelectric phase, which has been observed experimentally. The tendency to the dimerization is magnetically driven revealing TMTTF$_2$-PF$_6$ as a multiferroic material.
Using one- and two-dimensional NMR spectroscopy applied to $^{13}$C spin-labeled (TMTTF)$_2$AsF$_6$ and (TMTTF)$_2$PF$_6$, we demonstrate the existence of an intermediate charge-ordered phase in the TMTTF family of charge-transfer salts. At ambient temperature, the spectra are characteristic of nuclei in equivalent environments, or molecules. Below a continuous charge-ordering transition temperature T$_{co}$, the spectra are explained by assuming there are two inequivalent molecules with unequal electron densities. The absence of an associated magnetic anomaly indicates only the charge degrees of freedom are involved and the lack of evidence for a structural anomaly suggests that charge/lattice coupling is too weak to drive the transition.
The itinerant quasi-ferromagnetic metal MnSi has been studied by detailed thermal expansion measurements under pressures and magnetic fields. A sudden decrease of the volume at the critical pressure Pc ~1.6 GPa has been observed and is in good agreement with the pressure variation of the volume fraction of the spiral magnetic ordering. This confirms that the magnetic order disappears by a first order phase transition. The energy change estimated by the volume discontinuity on crossing Pc is of similar order as the Zeeman energy of the transition from the spiral ground state to a polarized paramagnetic one under magnetic field. In contrast to the strong pressure dependence of the transition temperature, the characteristic fields are weakly pressure dependent, indicating that the strength of the ferromagnetic and the Dzyaloshinskii-Moriya interactions do not change drastically around Pc. The evaluated results of the thermal expansion coefficient and the magnetostriction are analyzed thermodynamically. The Sommerfeld coefficient of the linear temperature term of the specific heat is enhanced just below Pc. The magnetic field-temperature phase diagrams in the ordered and paramagnetic phases are also compared. Comparison is made with other heavy fermion compounds with first order phase transition at 0 K.
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