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.
We report a study of the 16.5 GHz dielectric function of hydrogenated and deuterated organic salts (TMTTF)$_2$PF$_6$. The temperature behavior of the dielectric function is consistent with short-range polar order whose relaxation time decreases rapidly below the charge ordering temperature. If this transition has more a relaxor character in the hydrogenated salt, charge ordering is strengthened in the deuterated one where the transition temperature has increased by more than thirty percent. Anomalies in the dielectric function are also observed in the spin-Peierls ground state revealing some intricate lattice effects in a temperature range where both phases coexist. The variation of the spin-Peierls ordering temperature under magnetic field appears to follow a mean-field prediction despite the presence of spin-Peierls fluctuations over a very wide temperature range in the charge ordered state of these salts.
We have investigated the charge ordering phase of the quasi one dimensional quantum antiferromagnet (TMTTF)$_2X$ ($X=$ SbF$_6$, AsF$_6$ and PF$_6$) using high fields/frequencies electron paramagnetic resonance. In addition to the uniform displacement of the counter anions involved in the charge order phase, we report the existence of a superlattice between the spin chains in the direction $c$, caused by the space modulation of the charge order. When the field is high enough, the magnetic decoupling of the spin chains allows us to estimate the interaction between the chains, $J_c<1$~mK, three orders of magnitude lower than expected from the mean field theory.
Using a combination of density functional theory and dynamical mean field theory we show that electric polarization and magnetism are strongly intertwined in (TMTTF)$_2$-$X$ (X$=$PF$_6$, As$F_6$, and SbF$_6$) organic crystals and they originate from short-range Coulomb interactions. Electronic correlations induce a charge-ordered state which, combined with the molecular dimerization, gives rise to a finite electronic polarization and to a ferroelectric state. We predict that the value of the electronic polarization is enhanced by the onset of antiferromagnetism showing a sizable magnetoelectric leading to a multiferroic behavior of (TMTTF)$_2$-$X$ compounds.
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.
We report an ultrasonic study of the magneto-elastic coupling of the hydrogenated and deuterated (TMTTF)$_2$PF$_6$ organic salts. For both salts the temperature dependence of the longitudinal velocity along the c* axis displays a monotonic stiffening of the $C_{33}$ compressibility modulus upon cooling. Below the characteristic temperature scale 40 K the modulus stiffening becomes markedly enhanced, in concomitance with the reduction of spin degrees of freedom previously seen in magnetic measurements as low dimensional precursors of the spin-Peierls transition. The magneto-elastic coupling appears to be much weaker in the hydrogenated salt due to the highly inhomogeneous elastic behavior induced by the proximity of the charge ordering transition to the spin-Peierls phase. For the deuterated salt, an important anomaly in the ultrasound velocity is observed below the spin-Peierls transition temperature $T_{rm SP}$ in agreement with scaling of the elastic deformation with the spin-Peierls order parameter. In spite of the weakly inhomogeneous character of the spin-Peierls phase transition, the magnetic field dependence of $T_{rm SP}$ is well captured with the mean-field prediction for the lattice distorted Heisenberg spin chain.