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Article

Comprehensive Optical Investigations of Charge Order in Organic Chain Compounds (TMTTF)2X

1
Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
2
Dip. Chimica Generale ed Inorganica, Chimica Analitica e Chimica Fisica, Università di Parma, Parco Area delle Scienze, 43124-I Parma, Italy
*
Author to whom correspondence should be addressed.
Crystals 2012, 2(2), 528-578; https://doi.org/10.3390/cryst2020528
Submission received: 2 March 2012 / Revised: 30 April 2012 / Accepted: 1 May 2012 / Published: 23 May 2012
(This article belongs to the Special Issue Molecular Conductors)

Abstract

: Charge ordering in the (TMTTF)2X salts with centrosymmetric anions ( X = PF 6 , AsF 6 , SbF 6 ) leads to a ferroelectric state around 100 K. For the first time and in great completeness, the intra- and intermolecular vibrational modes of (TMTTF)2X have been investigated by infrared and Raman spectroscopy as a function of temperature and pressure for different polarizations. In this original paper, we explore the development and amount of charge disproportionation and the coupling of the electronic degrees of freedom to the counterions and the underlying lattice. The methyl groups undergo changes with temperature that are crucial for the anion cage formed by them. We find that the coupling of the TMTTF molecules to the hexafluorine anions changes upon cooling and especially at the charge-order transition, indicating a distortion of the anion. Additional features are identified that are caused by the anharmonic potential. The spin-Peierls transition entails additional modifications in the charge distribution. To complete the discussion, we also add the vibrational frequencies and eigenvectors based on ab-initio quantum-chemical calculations.

1. Introduction

The physics of the one-dimensional organic compounds (TMTCF)2X (with C = Se, S and X being a monovalent anion such as PF 6 , AsF 6 , SbF 6 , Br, or Cl O 4 ) is an active research topic for already three decades [18]. The phase diagram presented in Figure 1 is a sort of summary of the findings on these materials. Nevertheless, in recent years it became obvious that some very fundamental issues of the coupling of spin, charge and lattice degrees of freedom—albeit occasionally addressed in some very early papers—are not understood in sufficient depth and require more detailed and comprehensive studies. Especially the charge-ordered state of the Fabre salts (TMTTF)2X still bears some mystery.

First indications of a phase transition at TCO = 157 K in (TMTTF))2SbF6 were provided by thermopower and transport measurements [9], but it took another 15 years before one- and two-dimensional 13C spin labeled NMR spectroscopy could prove charge disproportionation developing for T < TCO [1015]. Dielectric permittivity measurements on several of these TMTTF salts finally yielded evidence for ferroelectric behavior of purely electronic origin [1622]. The ferroelectric state is associated with the charge order and results from the loss of inversion symmetry relating the molecules on the chain. X-ray investigations, however, failed to give evidence for a doubling of the unit cell or other lattice effects associated with that phase transition [2325]. Calculations based on the extended Hubbard Hamiltonian could reproduce the charge-ordered state [26,27], however, the coupling to the lattice—seen by 19F NMR spectroscopy [13] or as an anomaly in the thermal expansion [28]—is necessary to describe the complete phase diagram [2931]. A recent neutron scattering study indicates that charge ordering at TCO drives a uniform displacement of the anions mainly directed along the a-axis [32]. It results in an alternation of charge rich (ρ0 + δ) and charge poor molecules (ρ0δ). It was proposed that charge order in adjacent stacks occurs in phase, in contrast to the broken translational symmetry observed in other charge-ordered linear chain compounds [33,34]. ESR experiments, however, strongly suggest that in the charge-ordered regime two inequivalent magnetic TMTTF chains coexist [35], most probably due to the loss of translational invariance in the bc plane. The increase of mosaicity around TCO [36] supports the development of ferroelectric domains in the nanometer scale.

According to stoichiometry, the (TMTTF)2X compounds should form metallic compounds with a three-quarter-filled conduction band, but due to their strong electronic interaction, the systems become insulating upon cooling. Below approximately 250 K a minimum in resistivity marks a localization of the charge due to on-site Coulomb interaction U; the characteristic temperatures are listed in Table 1. Except (TMTTF)2ClO4, all Fabre salts develop a charge-ordered phase below T < TCO, as can be seen by a kink in ρ(T) [Figure 2b] [7,37,38], nuclear magnetic resonance (NMR) [10,11,15,39], electron spin resonance (ESR) [35,40], dielectric [18,20,22], and optical measurements [4145]. While the magnetic properties at ambient temperature can be described as an antiferromagnetic chain according to the S = 1/2 Heisenberg model, the systems either exhibit a transition to an antiferromagnetic ground state or to a spin-Peierls state at low temperatures (Table 1) [4648].

Charge order is supposed to be driven by the effective Coulomb repulsion V between neighboring molecules with respect to the bandwidth W = 2t. Since both parameters depend on the intersite distance, the charge-order transition temperature TCO can be tuned by applying physical [13,4953] as well as by chemical pressure [7,37]. As an example, the temperature-dependent resistivity of (TMTTF)2SbF6 is plotted in Figure 2b with increasing hydrostatic pressure up to 10 kbar. The charge-order transition is seen as a change in slope of ρ(T) that shifts from TCO = 157 K at ambient pressure to approximately 125 K at 5 kbar and well below 100 K at 10 kbar. The weak but crucial coupling between adjacent chains leads to a transverse overlap integral t that significantly influences the electronic properties when approaching the dimensional crossover to a higher-dimensional metal.

The crystals develop a Drude-like optical response also for Eb as external or internal pressure increases [54,55]. However, there is no simple and not even a monotonous relation between the interstack distance (given by the unit cell parameter b) and the charge-ordering transition TCO [37]. Even more delicate is the interaction between the TMTTF molecules and the anions which are incorporated in a cavity formed by six methyl groups as shown in Figure 2a. In the case of tetrahedral or linear anions with no inversion symmetry, the orientation of the anions becomes ordered as the temperature decreases below TAO. But even for centrosymmetric anions like PF 6 , AsF 6 or SbF 6 the electronic properties of the compounds are strongly influenced by the link between the sulphur atom on the TMTTF and the ligand of the anions. In Figure 2c the dependence of TCO on the shortest distance between the sulfur atoms and the fluorine or oxygen atoms in the anions is plotted for TMTTF salts with different hexaflourines.

In order to gain more insight into the charge disproportionation of (TMTTF)2X salts, we have performed comprehensive optical investigations of the infrared and Raman active vibrational features around the phase transitions. Most sensitive are the ν3(ag) Raman mode and the antisymmetric molecular vibration ν28(b1u) probed along the c-direction (Figure 3). We also observe the low-frequency intermolecular vibrational modes of the TMTTF molecules that are seen in the Raman spectra and become infrared active due to charge disproportionation.

2. TMTTF Molecule and Vibrational Modes

In the present paper, we relate our assignments of the vibrational modes to the nomenclature proposed by Meneghetti and coworkers [59] where the molecular structure of TMTTF is assumed to have D2h symmetry. According to the character table for the D2h point group (Table 2), there are eight different irreducible representations whereas only the antisymmetric b1u, b2u and b3u modes are infrared active and the symmetric ag, b1g, b2g, b3g are Raman active. The au species is neither Raman nor infrared active. A complete list of the vibrational modes is given in Tables A1 (gerade modes) and A2 (ungerade modes) of the Appendix. Bases on ab-initio quantum-chemical calculations we calculated the frequencies and intensities of the molecular modes of the neutral TMTTF and fully ionized TMTTF+. Of interest are the Raman active ag modes getting also infrared active by electron-molecular vibrational (emv) coupling to the electronic background. They arise in the spectra as Fano-resonances when overlapped to an electronic continuum.

Compared to conventional metals and semiconductors, the building blocks of synthetic metals are large molecules, a fact which has appreciable effects on the vibrational and electronic properties. In general, we can distinguish two sorts of electron-phonon interaction: a coupling to lattice phonons which is normally found in any kinds of solid, and a coupling of the electrons to intramolecular vibrations of the organic molecules which form the conducting layer. Within the framework of the tight-binding description of electrons, the difference between these two effects is that the coupling to lattice vibrations modulates the transfer integrals t, while the coupling to intramolecular vibrations modulates the on-site energy ε [60]. The energy of these two kinds of phonons is also distinct: due to the comparably heavy molecules, the lattice modes are observed below approximately 200 cm−1 for these crystals, while the intramolecular vibrations of TMTTF, which show the strongest coupling constants, lie between 500 and 1700 cm−1. In the Appendix we give complete lists of the intramolecular vibrations and their infrared intensities (Tables A1,A2).

The coupling of electrons to molecular vibrations was first observed and described for one-dimensional systems, but later extended to two dimensions (for a review see for example References [61,62]). The interaction takes place via a modulation of the HOMO energy; for one dimension in the presence of a symmetry break the emv-interaction induces oscillations of the conduction-electron density along the stacking direction with the frequency of the phonons [6367]; hence the excitations couple to the external infrared radiation. In this context symmetry break means that the molecular units should not lie at the inversion centers. It was shown for one-dimensional systems that if the occupied molecular orbital is non-degenerate, the linear emv-coupling is possible only to the totally-symmetric ag vibrational modes of the molecule [68], which normally are infrared forbidden.

The highest occupied molecular orbital (HOMO) of a neutral TMTTF molecule is drawn in Figure 4 where the highest charge density can be found between the C=C double bonds. They are mostly effected by a change of the ionicity of the molecule. These bonds are mainly involved in the vibrational ν3, ν4 and ν28 modes mentioned in the previous Section 1 (for more details see Appendix). They can be used to detect the onset of the charge ordering as well as a gauge for the charge disproportionation.

Concerning the crystal structure, all Fabre salts are isostructural consisting of stacks of the planar organic molecules TMTTF along the a-axis that are separated in the c-direction by monovalent anions. In the b-direction, the distance of the stacks is comparable to the van der Waals radii. Due to the triclinic symmetry P 1 ¯ (Ci), b′ denotes the projection of the b-axis perpendicular to a, and c* is normal to the ab-plane. The symmetry analysis for the lattice phonons can be found in Section 5.1.

3. Experimental Details

Single crystals of the charge-transfer salts (TMTTF)2X [tetramethyltetrathiafulvalene (TMTTF)] with X = PF 6 , AsF 6 , and SbF 6 were grown by electrochemical methods as described previously [37,47]. The needle-shaped single crystals are several millimeters long in the a-direction and less than a millimeter wide in the other crystal orientations. For our optical investigations we used naturally grown surfaces of single crystals. The in-plane infrared reflection spectra R(ν) of (TMTTF)2PF6 and (TMTTF)2AsF6 crystals were measured for light polarized along the a and b′-axes utilizing a Bruker IFS 113V Fourier-transform spectrometer in the frequency range 40 cm−1 < ν < 10, 000 cm−1 at temperatures 5 K < T < 300 K. The crystals were placed either in a He exchange gas cryostat or a cold-finger cryostat. For the reflectivity along the third direction (Ec*) we used IR microscope HYPERION attached to a Bruker IFS 66v/s and a Bruker Vertex 80 Fourier transform spectrometer. The microscope is purged with nitrogen to reduce the atmospheric absorption bands. Here the reflectivity spectra were collected in a frequency range from 500 to 8000 cm−1 with a resolution of 0.5 cm−1 at temperatures from 290 down to 10 K. From the frequency dependent reflectivity we derived the real part of the optical conductivity σ1(ν) and the dielectric loss 2(ν) by Kramers–Kronig analysis, using our DC resistivity data [37] for the low-frequency extrapolation and previously published data on (TMTTF)2PF6 for the high-frequency extrapolation [6972]. More details on the data analysis can be found in References [62,73].

Raman spectra on (TMTTF)2X ( X = PF 6 , AsF 6 ) single crystals have been measured using four different excitation energies: the λ = 568, 647, 676 and 752 nm line from a Kr+ laser. Laser line was focused onto a smooth part of the crystal by a 20× magnification objective and the scattered radiation was analyzed with a Renishaw 1000 spectrometer equipped with ultra-steep long-pass filter. Next premonochromator has been used for low-frequency spectra. The 647 and the 676 nm lines are almost resonant with the first localized electronic excitation of the (TMTTF)2+ system occurring around 15,000 cm−1 in the perpendicular polarization (b′-direction) [70]. The 568 and 752 nm lines are both out of resonance, and in particular the laser line at 752 nm can be used to study polarization dependence and to measure Raman scattering excited with light polarized along the stack (a-axis) due to the very low background signal. The 568 nm line has the serious drawback to be strongly resonant with the TMTTF+ cationic species [74], therefore spectra are totally dominated by TMTTF+ bands probably originating from impurities crystallized on the sample surface. For temperature dependent measurements, the crystals were attached to a cold finger cryostat. Heating of the sample by laser irradiation can amount to as much as 10 K at low temperatures; it was accounted by for recalibration.

4. Molecular Vibrations

The spectral range from 200 to 3000 cm−1 is dominated by intramolecular vibrations of the TMTTF molecules and of the hexafluoride anions. The modes involving the covalent C=C bonds are most sensitive for the charge on the molecules and will be used to obtain information about the charge disproportionation. The vibrations of the terminal methyl groups give indications on the coupling between the anions and the TMTTF molecules via the weak CH⋯F interactions. Also the vibrational modes of the anions are changed by distortion of the octahedrons.

4.1. High-Energy Raman Spectra: Molecular Vibrations

Raman spectra excited with the 647 nm line have been measured with the incident light polarized perpendicular to the a-axis to fully exploit resonance effects. Figure 5a contains the room temperature spectra of (TMTTF)2PF6 and (TMTTF)2AsF6. They are characterized by a strong fluorescence background and by the three most strongly coupled molecular vibrations, ν3(ag) = 1599 cm−1, ν4(ag) = 1474 cm−1 and ν10(ag) = 502 cm−1. In addition we can identify an overtone of the ν10(ag) mode around 1000 cm−1 and a shoulder on the low energy side of the ν3(ag) band that could be assigned to the ν28(b1u) = 1580 cm−1 molecular mode.

In the right panel of Figure 5 the polarization-dependent Raman spectra are presented as measured with the λ = 752 nm laser line. The (b′, b′)-polarization spectrum (incident and scattered light both polarized perpendicular to the a-axis) is characterized by the same three coupled molecular vibrations present in the 647 nm spectra, while these bands are totally absent in the (a, a)-polarization (incident and scattered light both polarized parallel to the a-axis).

In both polarization directions in the range between 800 cm−1 and 1000 cm−1 several small peaks occur which can be assigned to combination and overtone modes. The weak peak at 800 cm−1 can be assigned to the combination of the ν10(ag) and the ν11(ag) modes whereas the feature at around 1000 cm−1 is related to the aforementioned first overtone of ν10(ag). The intermediate mode at 930 cm−1 can be identified as the ν8(ag) mode. A weak and very broad spectral feature can also be identified in the (a, a)-polarization around 1300 cm−1: its shape and bandwidth seem to indicate a vibronic or electronic origin, however its assignment to the vibronic anti-phase combination of ν4(ag) modes is questionable due to symmetry arguments and energy difference with the corresponding infrared signal (where it shows up at around 1200 cm−1 for the polarization Ea).

In order to investigate the charge disproportionation among the TMTTF molecules at the charge-ordering transition, we have performed Raman experiments on (TMTTF)2PF6 and (TMTTF)2AsF6 as a function of temperature. In Figure 6 we display the temperature evolution of the (TMTTF)2AsF6 Raman spectra measured with the 647 nm laser line. The splitting of the ν3(ag) mode can be clearly seen below T = 100 K; it is a fingerprint of the disproportionation of charge between the two TMTTF molecules in the unit cell.

In Raman spectra, the ν3(ag) mode is the best choice to gain information on the molecular charge distribution since it shows a large and linear ionicity shift and is only weakly coupled to the electronic system [59,75]; in Figure 3 the shift of the vibrational frequency is plotted as a function of (positive) charge per TMTTF molecule. On the contrary the ν4(ag) mode, which has the strongest e-ph coupling constant, cannot provide a reliable estimate of the ionicity in charge-ordered non-centrosymmetric one-dimensional systems [76]. Particularly, the ν4(ag) mode in our spectra of (TMTTF)2AsF6 and (TMTTF)2PF6 (Figures 6,7) remains almost fixed around 1479 cm−1, which corresponds to an average charge of ρ0 = +0.5e, and does not show any splitting. Yamamoto and Yakushi explained these phenomena as the combined effects of the electron-phonon perturbation and of the ionicity shift [77,78].

A careful inspection of our (TMTTF)2AsF6 spectra evidences that the ν3(ag) band gains intensity on lowering the temperature; down to T = 120 K the band slightly narrows, but then broadens when cooled further to 100 K. At that point the band splits abruptly reaching Δν = 7 cm−1 already at T = 95 K. As demonstrated in Figure 8, the amplitude of the splitting increases slightly on lowering the temperature further and reaches its maximum value of Δν = 12 cm−1 at 30 K. According to

2 δ = Δ ν 72 cm 1 / e
obtained from Figure 3 the charge imbalance is calculated to ρrichρpoor = 2δ = 0.17 e for (TMTTF)2AsF6. There are interesting differences of how the intensity of the two components assigned to the ν3(ag) mode evolves with temperature. Both exhibit comparable intensities in the 85 K spectrum right below TCO; upon cooling the lower-energy component becomes stronger, while the higher-energy suddenly loses intensity and almost disappears at the lowest temperature (Figure 6).

This behavior is anomalous because in the framework of centrosymmetric dimeric system the higher-energy component should correspond to the Raman-active in-phase mode combination, while the lower energy to the infrared-active out-of-phase combination. Obviously charge order breaks the inversion symmetry, nevertheless for a small charge imbalance these general considerations should remain valid; i.e., the higher-energy component should have the higher Raman intensity.

In Figure 7 the Raman spectra of (TMTTF)2PF6 are shown for various temperatures as indicated. The observations are very similar as for the (TMTTF)2AsF6 salt including the anomalous intensity evolution of the ν3(ag) features. In the case of (TMTTF)2PF6 the ν3(ag) mode splits between T = 70 and 65 K; it grows from 4 cm−1 to 7.5 cm−1 when cooled down to 20 K (corresponding to 2δ = 0.10e, according to Equation 1), suffering a small flection at the lowest temperatures (see Figure 8) due to the spin-Peierls transition at TSP = 19 K. We will come back to this point in Section 6.

Two observations should be noted at this point: In both compounds a weak spectral feature occurs around 1580 cm−1 which we assign to the Raman-active anti-phase combination of the ν28(b1u) mode; its temperature dependence can be followed in Figure 9. This mode is very sensitive to the charge distribution in TMTTF systems and can best be followed by infrared measurements performed with the polarization Ec, as discussed in more detail in Section 4.2. From Figure 10 it is seen that upon cooling, the mode first shifts to higher frequencies, before it splits at TCO. The stronger low-energy peak then softens as the temperature decreases further. Unfortunately it is quite hard to follow the frequency evolution and splitting of this ν28(b1u) mode in our Raman data, since it appears as a shoulder in the high temperature spectra and exhibits only a weak and broad profile at low temperature. Nevertheless its identification by Raman measurements offers a useful internal check for our infrared analysis, presented in the the following Section 4.2.

The second observation refers to the three clear and sharp bands that occur at 1427, 1446 and 1459 cm−1 in the charge-ordered state. They can be safely assigned to CH-bending mode of methyl groups and will be discussed in more detail in Section 4.3. Their appearance below TCO implies some kind of ordering of the TMTTF methyl groups due to the interaction with the anions which could possibly stabilize the 4kF -charge-density-wave charge-ordered state [79].

4.2. Mid-Infrared Vibrational Spectroscopy of Charge-Sensitive Modes

First indications for charge disproportionation from optical measurements have been obtained by in-plane reflection measurements [4244]. In Figure 11 the optical conductivity of (TMTTF)2AsF6 and (TMTTF)2PF6 is plotted for different temperatures as indicated. The data are obtained from reflection experiments performed on the ab-plane that are dominated by the response of the conduction electrons. At elevated temperatures, a dip is observed around 1600 cm−1 that is caused by the electron-molecular vibrational (emv) coupled ν3(ag) mode. This Raman mode is not infrared active by itself, but via coupling to the electronic background it becomes visible as an antiresonance in the polarization along the stacking direction. The temperature dependence of the minima (indicated by arrows in Figure 11) is plotted in Figure 8 together with the Raman peaks. In the right panel also the corresponding charge disproportionation of (TMTTF)2AsF6 and (TMTTF)2PF6 is plotted as a function of temperature.

As pointed out by several scholars [41,59,80,81], the antisymmetric ν28(b1u) stretching mode is probably the most sensitive local probe for charge disproportionation as it involves the outer C=C bonds of the fulvalene rings where most of the charge is accumulated as visualized in Figure 4. Although Hirose et al. were able to observe this mode in their in-plane reflection measurements [41], a better and more direct approach consists in measuring in the perpendicular direction, i.e., Ec where the electric field is mainly along the molecular axis and the background signal due to conduction electrons is lower.

In the optical conductivity presented in Figure 10 a strong mode is seen that splits as the temperature drops below TCO. The peaks can be assigned to charge-rich (ρ0 + δ) and charge-poor (ρ0δ) TMTTF molecules. There is a very good agreement with the weak ν28(b1u) feature observed in the Raman spectra (Figure 9), as far as the frequencies and the temperature dependence is concerned.

The analysis of the spectral weight and width of the modes observed in the infrared spectra is not straightforward, since the modes overlap, are strongly distorted and are influenced by the electronic contributions. Nevertheless, in our spectra the intensity of the lower-frequency peak is always stronger than the high-frequency one due to the higher intrinsic intensity of this mode in the cationic TMTTF+ species. A comprehensive analysis has been performed for the two-dimensional BEDT-TTF conductors and superconductors [82,83] that in principle could also be applied to all systems based on TTF moiety and its derivatives.

Following Meneghetti et al. [59], the resonance frequency of the ν28(b1u) mode occurs at 1627 cm−1 for neutral TMTTF and at 1547 cm−1 for TMTTF+ (cf. Table A2). Assuming a linear shift of the resonance frequency with the ionicity of the molecule, the charge disproportionation 2δ can be calculated from the difference Δν of the resonance frequencies:

2 δ = Δ ν 80 cm 1 / e

In Figure 12 the temperature dependence of the peak position and the charge disproportionation is plotted for (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6. The low temperature values are listed in Table 3. Two interesting observations should be noted: (i) if the charge imbalance 2ρ(T) is taken as a sort of order parameter, its temperature dependence basically follows the mean-field behavior for (TMTTF)2PF6 while it becomes more abrupt when going to (TMTTF)2SbF6 with the tendency towards a first-order transition. From a broad maximum in 1(T) observed in the 35–50 K temperature range [16], the possibility of local charge order and/or ferroelectric domains has been inferred [84]. In our experiments we do not see any indications of an additional phase transition down to T = 20 K; (ii) In all three salts, the lower frequency peak of the ν28(b1u) mode pair rapidly moves towards lower frequency due to the continuous depletion of charge, but then the peak position reverses its temperature behavior and slightly shifts toward higher frequencies. The effects seems to be beyond what might be explained by thermal contraction. Interestingly, the temperature dependence of the split totally symmetric ν3(ag) mode does not exhibit such a behavior, as demonstrated in Figure 8.

Finally, we would like to point out that our local probe of the C=C bonds is a direct measure of the charge per TMTTF molecule; thus the plots in Figure 8 and Figure 12 give the temperature dependence of the charge-order amplitude, which can be considered as the order parameter of this phase. In contrast to the results inferred from 13C-NMR spectra [13], we do not see any suppression of the charge disproportionation at lower temperatures. However, looking at the temperature dependence of the ν3(ag) mode displayed in Figure 6 for the example of (TMTTF)2AsF6, we can see that the intensity of the high-frequency peak gets weaker on the expense of the low-frequency peak as the temperature decreases. At T = 20 K is is only visible as a shoulder. The intensity of the charge-order-split modes is discussed by Girlando in detail [82] and it would be worth to dwell on this issue further.

4.3. Methyl Groups

There is an ongoing discussion about the involvement of the anions in the charge-order transition of TMTTF and BEDT-TTF salts and about further changes of the lattice [8587]. The anions are located in a cavity formed by the methyl groups of the adjacent TMTTF molecules, thus we expect that the pure methyl vibrations are most sensitive to changes of the anions in that cage due to the sizeable F⋯H interaction. Already in 1984 Kistenmacher discussed the role of the cavity and anion size and their interaction for the isostructural TMTSF salts [88,89]. There are four methyl groups closest to the anions which are located in the bc*-plane, and another two in the ac*-plane. These six methyl groups determine three sets of three-fold symmetry axes close to the symmetry axes of the octahedron. The four closest CH3 groups delimit two sets of two-fold symmetry axes which are close to the axes of the octahedron. In addition, the interaction to the fluorine atoms form weak hydrogen bond networks with the closest methyl groups (Figure 2) that become particularly effective at low temperatures [90,91].

Two effects are envisioned: (i) the motion of the anions slows down as the temperature is reduced and eventually it locks into a fixed position. This seems to be rather a pre-requirement of charge order than a consequence; (ii) The charge disproportionation among the TMTTF molecules modifies the interaction between the organic stacks and the anions; the various motions of the methyl groups become affected in different ways, but also the symmetry of the anions is broken and hence the degeneracy of vibrations lifted.

According to our ab-initio quantum-chemical calculations listed in Tables A1 and A2, we expect C–C–H bending modes (β-CH3 modes) at around 930 and 1020 cm−1, H–C–H bending modes (α-CH3 modes) between 1400 and 1440 cm−1 and C–H stretching vibrations (ν-CH3 modes) located between 2850 and 2970 cm−1. As illustrated in Figure A2 through Figure A5, most of these vibrations happen within the ab-plane, but can also include out-of-plane motions.

For light polarized parallel to the b′-direction three pronounced modes are detected around 935, 1090 and 1445 cm−1 that not only become stronger upon cooling but also show very distinct temperature dependences best demonstrated in the dielectric losses 2(ν) displayed in Figure 13 for (TMTTF)2AsF6 (upper frames) and (TMTTF)2PF6 (lower frames). At room temperature a broad feature is recognized around 938 cm−1 that can be ascribed to the C–C–H bending vibration. These β-CH3 modes consist of movements of the hydrogens in opposite directions causing the methyl group to bend; it involves a motion of the outer carbon atoms as depicted in Figures A2(g,h), A3(f), A4(e,f) and A5(c). As the temperature is lowered the band shifts down to 932 cm−1 for (TMTTF)2AsF6 (934 cm−1 for (TMTTF)2PF6) and narrows significantly. The observation is confirmed by measurements with Ec* displayed in Figure 14. We relate the softening of the 923 cm−1 mode to the slowing down of the anion motion, which allows the methyl groups to relax. The most dramatic change occurs when going from T = 20 K to 13 K; on the high-energy wings two peaks can be identified that split into four when cooled further to T = 6 K. It is tempting to assign these novel sub-features to spin-Peierls transition at TSP = 13 K; we will come back to this point in Section 6. In the case of (TMTTF)2PF6 the narrowing seems to be more gradual. The mode is also observed for the electric field polarized in c*-direction as demonstrated in Figure 14 for the example of (TMTTF)2PF6.

The 1090 cm−1 mode becomes more pronounced upon cooling and splits for low temperatures (middle frame of Figure 13); the behavior is very similar for (TMTTF)2AsF6 and (TMTTF)2PF6. We tentatively assigned the mode to the antisymmetric ν31(b1u) vibration (β-CH3) which mainly involves the terminal C–CH3 groups [Figure A3(f)], very similar to the totally symmetric ν7(ag) [Figure A2(g)] that appears in approximately the same frequency range; in the room-temperature Raman spectra (Figure 5) it shows up only as a very small peak. For Ec* we also observe this mode (Figure 14), but no double structure of similar emphasis. The temperature evolution is somewhat different compared to the modes discussed above in Section 4.2 where mainly the charge disproportionation is probed via the C=C bond stretching. There are indications that the 1090 cm−1 mode separates already well above TCO, and once developed, the two peaks basically do not change any more in strength and position. For Ec* we find only minor indications of this mode with a similar temperature dependence. In the line of previous observations by 1H NMR [9294], we suggest that the rapid motion of the CH3 groups is locked around 150 K. A clear splitting for T < TCO can be observed for the C–C–H bending mode located at 1003 cm−1 (Figure 14); at T = 10 K the peaks are at 1000 and 1007 cm−1 for (TMTTF)2PF6. Note, the presence of this mode as well as its splitting is also observed as an antiresonance in the Ea spectra of (TMTTF)2PF6 and (TMTTF)2AsF6 (not shown).

Finally the H–C–H bending vibrations [α-CH3, most likely ν29(b1u) or ν46(b2u)] are observed at 1440 cm−1; with decreasing temperature they exhibits a hardening up to 1446 cm−1. At low temperatures just above TCO the band splits and a minor satellite mode is clearly seen at the low-energy side at 1440 cm−1 for both compounds. Basically no change happens for T < TCO any more (Figure 13). These observations are supported by our Raman experiments presented in Figures 6,7 where three peaks are identified at 1427, 1446 and 1459 cm−1. We can safely assign those features to the H–C–H bending modes. For the polarization Ec* the 1441 cm−1 peak becomes stronger upon cooling with basically no shift in frequency; however, an antiresonance dip is observed at 1447 cm−1 for low temperatures as seem in the right panel of Figure 14. A weak satellite peak seems to develop and shift down to 1427 cm−1 for T = 10 K. We conclude that at the charge-order transition the coupling of the methyl groups to the anions is modified in addition to the pure temperature effect via thermal contraction of the lattice.

A second H–C–H bending mode at 1393 cm−1 is more pronounced; it becomes very narrow (and slightly softer) at low temperatures and it is accompanied by two satellite peaks on each side. Note that for Ea, a feature can be recognized at 1385 cm−1, which is related to the α-CH3 modes ν30(b1u) or ν47(b2u) [Figures A3(e) and A4(d)]. It splits with cooling far above the transition temperatures for all three compounds investigated in our study. From Figure 15 it is obvious that the line shape is asymmetric and significantly broadened at room temperature, indicating that there are different molecular sites present. With increasing anion size, the asymmetry decreases. It is also noteworthy that the strength of the peaks, the onset and the splitting drop with increasing TCO, which can be directly related to the interaction of the anion with the methyl group. These modes involve a particularly strong movement of the CH3 carbon atom in the direction of the anions and thus modifies the cavity size. Its pressure dependence will be examine in more detail in Section 4.5.

Recently Janokowski et al. [95] observed modifications of the CH3 bands in (o-DMTTF)2X upon cooling that they relate to the hydrogen bonding of halide anions with the methyl groups which influences the CH3 vibrational modes. The splitting of the modes is taken as evidence for breaking the symmetry which yields a small non-equivalence of different hydrogen bonds. However, one has to keep in mind that the cavities formed by the methyl group is cushion-like. This soft and flexible interface allows for a certain amount of disorder [91]. There is no free rotation of the anions at high temperatures [96], but also no complete order at low temperatures.

4.4. Anions

In a next step we will look at the anions themselves, i.e., at the molecular vibrations of the pnicogen hexafluorides. Free octahedral ions have Oh point group symmetry and 15 vibrational modes that can be represented as [97]

Γ = a 1 g + e g + 2 t 1 u + t 2 g + t 2 u .

Three of these modes ν1(a1g), ν2(eg), and ν5(t2g) are Raman active, ν3(t1u) and ν4(t1u) are infrared active; the t2u mode is inactive. The ν4(t1u) vibration commonly shows up as a very strong feature in the in-plane reflectivity spectra of TMTCF salts [6972]. As sketched on the right side of Figure 16, for the ν3(t1u) mode the plane of the central pnictide and four fluorine nuclei moves in one direction while the apical fluorine nuclei move the opposite way. In the case of ν4(t1u) the apical nuclei are not involved, and the central pnictide vibrates opposite to the four fluorine nuclei. Both modes are threefold degenerate. Upon cooling, the vibrational motion of the anions slows down and the octahedra eventually lock into a fixed position determined by the cavity that is formed by the methyl groups of the neighboring molecules. A first distortion of this cave occurs from the enormous thermal contraction. In the course of charge ordering, the inversion symmetry is broken and the unbalanced Coulomb attraction exerted by the charge-rich TMTTF molecules causes another distortion of the anions that lifts the degeneracy. It turns out that in addition to the cavity of the methyl groups, the interaction of the sulfur atoms to the anions [37,98] is also important, as depicted in Figure 2.

In Figure 16 the conductivity spectra of (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6 are presented in the narrow range around the ν4(t1u) mode of the octahedral ions.

At room temperature, the vibrational features are located at ν4(t1u) = 837 cm−1 for (TMTTF)2PF6, at 699 cm−1 for (TMTTF)2AsF6 and at 654 cm−1 for (TMTTF)2SbF6. As the temperature approaches TCO upon cooling, a shoulder starts to develop that finally becomes a satellite peak. The overall behavior is similar for the three compounds, but they differ in important details. In the case of PF 6 the mode develops a shoulder at the lower-frequency wing that becomes a separate peak upon cooling. It is not clear whether the separate peak at 848 cm−1 also belong to the anion vibration since it does not change much with temperature. The spectral weight of the satellite peaks is much smaller than the principal mode. The later one shifts to higher frequencies as the temperature is reduced, while the two small modes above and below exhibit a slight softening. The temperature dependence starts at room temperature and gradually develops upon cooling with basically no indications of the charge order transition. Similar observations are made for (TMTTF)2AsF6 and (TMTTF)2SbF6. Since the arsenic atom is heavier than phosphorous, the corresponding mode appears slightly below 700 cm−1 for (TMTTF)2AsF6. Upon cooling a shoulder develops at higher energies (707 cm−1) with an onset well above TCO and no appreciable shift. This observation implies a distortion that is more related to the lattice modification upon cooling rather than charge order. This is supported by our pressure-dependent measurements discussed in the subsequent Section 4.5 where we follow the mode up to 5.2 GPa. The SbF 6 anion behaves similarly as AsF 6 ; a minor mode grows around 664 cm−1 as the temperature is reduced, with no obvious modification at TCO. The major peak at 655 cm−1, however, exhibit a slight broadening and eventually splitting for low temperatures.

Unfortunately, our results do not allow us to reliably determine a particular methyl group being responsible for the anion distortion. Due to motion and missing alignment of the anions axes with respect to the crystallographic directions even at low temperatures, we cannot identify a particular contact that cause the distortion. The fact that we mainly observe the anion mode in the polarization Ec* is caused by the lower out-of-plane electronic contribution.

At elevated temperatures the octahedral anions move rapidly, seen by the broader vibrational features of the anions and methyl groups. From the splitting of the mode at high temperatures we conclude that the distortion is present at all temperatures. Also from NMR experiments it is concluded that at high temperatures the anions are highly disordered and might even rotate, but the rotation of the methyl groups is also important for the coupling [13,92,93,99]. Yu et al. suggested that a suppression of the anion motion effects the charge disproportionation [13]. Rather, our findings point towards a distortion of the anions by lattice contraction and charge order. As pointed out above (Section 4.1, Table 3, Figures 5,2) the charge disproportionation is not reduced when the temperature is lowered and the anions stop rotating. The coupling seems to be strongest for (TMTTF)2PF6 where the splitting below TCO is most pronounced; for (TMTTF)2SbF6 the charge order seems to have a minimum influence.

The slowing down of the anions motion softens the methyl group vibrations. Around T ≈ 150 K the anion position locks in; the ν31(b1u) and other β-CH3 modes [involving also the outer carbon atoms of TMTTF and in particular the methyl groups, as depicted in Figure A3(f)] split, indicating two well distinct methyl groups vibrations. For T < TCO these modes are modified due to the redistribution of charge and coupling to the anions. The lifted degeneracy of anion vibrations indicates the distortion of the octahedra. We conclude that the coupling of the hexafluoride anions to the TMTTF methyl groups forming the cavities (despite the cushion-like softness) changes with temperature but is also affected by the charge order. There mutual interaction modifies the anions as well as the TMTTF molecules.

These findings are corroborated by quantum-chemical calculations based on the low-temperature crystal structure [100] which reveal a deformation of the wave-function of the TMTTF molecules by the anion potential. The distance between TMTTF and PF 6 and SbF 6 anions decreases as the temperature is reduced; interestingly thermal contraction is not remarkable for the Br-salt. However, the gradual change was seen in the whole temperature, and was continuous through the charge-order temperature. It causes an anomalous temperature behavior of the g-tensor with a continuous rotation of the principal axes around the a axis when T decreases from room temperature to 20 K [100]. At the charge-order transition temperature TCO the charge disproportionation on the TMTTF molecules leads to two non-equivalent couplings between the anions and the TMTTF molecules. This broken inversion symmetry of the (TMTTF)2X crystals causes a modification of the spin distribution on the molecules and rotates the g-tensor around the molecular axis. At the domain boundary two inequivalent magnetic sites interact and cause additional contributions to the ESR linewidth [35].

4.5. Pressure Dependence of Molecular Vibrations

In order to obtain additional information of the coupling between the anions to the TMTTF molecules and in particular to the CH3 groups, we have performed pressure-dependent optical reflection measurements on (TMTTF)2PF6 and (TMTTF)2AsF6. The experiments were performed at room temperature using a diamond anvil cell as discussed in more detail in References [54,55,101]. In Figure 17 we plot the pressure dependence of some vibrational features. It is interesting to note that hydrostatic pressure mainly affects the a-direction; X-ray studies under pressure reveal that the b and c-axes change only by 4.7% and 4.0% with pressure up to 27 kbar, while the crystals shrinks by 7.1% along the a-axis [102]. The cavities containing the anions get distorted.

The pressure dependence of the optical conductivity is shown in Figure 17 for selected frequency ranges. Most pronounced is the shift of the CCH bending mode at 915 cm−1 that moves by more than 25 cm−1 as the pressure increases to 50 kbar, indicating a significant hindering of the vibration. The mode at 1082 cm−1, for which we have suggested the assignment ν31(b1u) above, exhibits a very similar pressure dependence. On the contrary, the peak 998 cm−1 basically remains unchanged in frequency and just becomes smeared out until it has disappeared. It is interesting to note that for moderate pressure, the peak shifts to lower energies, in contrast to most other modes. The most pronounced modification upon applying high pressure is found for the ν47(b2u) = 1385.5 cm−1 mode, which involves the CH bending vibrations of the methyl groups [symmetric α-CH3 vibration, sketched in Figure A4(d)]. The mode develops a shoulder at 1397 cm−1 that becomes a well developed double peak when going up to 52 kbar. From the crystal structure displayed in Figure 2a we see that within the bc*-plane two sorts of methyl groups can be distinguished, one more directed along the c-axis, the other more along the b-direction. The application of pressure strongly affects the coupling of the CH3 groups, but differently for both sorts. Methyl groups form a soft cushion surrounding the anions that is squeezed upon pressure, getting stiffer and denser. However, not all of them are affected equally, leading to a broadening and splitting of the modes.

The pressure dependence of two other peaks in the (TMTTF)2AsF6 spectra are worth mentioning. First the fingerprint of the ν3(ag) mode close to 1600 cm−1 for which the temperature dependence was already discussed in Section 4.2. Its broadening with pressure with some indication of splitting may be seen as evidence that the two molecules per unit cell are influenced differently.

The most interesting behavior is presented in the left frame of Figure 18, where the anion vibrational mode is seen. Upon application of high hydrostatic pressure, the mode shifts to higher frequencies, becomes broad and finally exhibits two satellite peaks left and right to the main maximum at 717 cm−1, separated by approximately ±8 cm−1. The threefold degeneracy of the ν4(t1u) mode is lifted as the hexafluoride anion becomes distorted at high pressure. This implies that the motion of the anions is stopped by the methyl groups and eventually the strong pressure completely breaks the degeneracy.

4.6. Anharmonicity in One-Dimensional Organic Conductors

The Raman spectra illustrated in Figure 5 reveal modes that originate from combinations and overtones of fundamental modes. These modes can be relocated in the infrared spectra along the stacking direction exhibiting a splitting below TCO and delivering further information about charge ordering and the electronic potential.

In Figure 19 we plot the temperature dependence of a mode at 805 cm−1 that is a combination of the emv-coupled ν11(ag) and ν10(ag) modes. It can be observed as a peak or dip depending on electronic background (cf. Section 2). The occurrence of the higher-frequency peaks throughout the entire temperature range indicates that here we deal with an anharmonic electronic potential of the TMTTF+0.5 molecule. Both modes are members of the same symmetry species ag, consequential the combination (ν11 + ν10) mode possess the same symmetry as the fundamental ones; i.e., it is Raman active and simultaneously becomes infrared-activated via emv-coupling. This symmetry consideration holds for all modes discussed in this Section.

The ν11 and the ν10 modes involve the stretching of the CS bond and the bending of the CCH3 bond; both modes are quite sensitive to changes of the ionicity. Beside the ν4 mode, the ν10 has the highest coupling constant [75] which are listed in Table 4. In the Raman spectra displayed in Figure 5b, the (ν11 + ν10) mode is also present as a weak peak at 800 cm−1. According to Meneghetti et al. [59] the maximum value of the splitting between a neutral and a positive charged molecule is Δν = 50 cm−1 resulting for (TMTTF)2PF6 in 2δ = 0.14 e and for (TMTTF)2AsF6 in 2δ = 0.20 e (in analogy to Equations (1) and (2)).

A similar observation can be made for the first overtone of the ν10 mode which is also visible in all Raman spectra (Figure 5) at 1000 cm−1 where it appears as an asymmetric broad peak. In the infrared spectra (Figure 20), the single asymmetric peak at room temperature evolutes into two dips after cooling below TCO = 67 K for (TMTTF)2PF6, for instance. In the case of the two other compounds, (TMTTF)2AsF6 and (TMTTF)2SbF6, we can actually identify a doubling of the splitting at very low temperatures, indicating that four different sites exists in the unit cell, although the other modes do not support this conclusion. The maximum amplitude of the mode splitting is Δν = 48 cm−1 at the lowest temperature yielding a charge imbalance of 0.14e for (TMTTF)2PF6, 0.19e for (TMTTF)2AsF6 and 0.26e for (TMTTF)2SbF6, which is also in good agreement with the values listed in Table 3. In Figure 21 we plot the spectra of the compounds, (TMTTF)2PF6 and (TMTTF)2AsF6, measured for the polarization Ea. For (TMTTF)2SbF6 the spectra were too noisy to identify any vibrational features in this spectral range. At higher frequency a vibrational feature is observed at 1805 cm−1 that splits very similarly to the emv-coupled ν3(ag) mode. At this point, no fundamental vibrational mode should exist, but it can be assigned to the combination mode of ν4 + ν11. Depending on the electronic background, emv-coupled modes can show up either as dips or as peaks in the conductivity spectra (cf. Section 2).

Beside the mentioned and charge sensitive modes, two broad features can be noticed in the lower and upper panels of Figure 22 in the frequency ranges between 1800 cm−1 and 2000 cm−1 and between 2600 cm−1 and 2800 cm−1. The feature located at around 1900 cm−1 is basically not apparent at room temperature, but gets really pronounced at the charge order transition. It can be ascribed to the combination mode of the two strongest emv-coupled ν4 and ν10 modes. The intensity clearly scales with the charge disproportionation increasing with the anion size.

The highest anomaly is located at 2750 cm−1 and cannot be related to the aforementioned methyl vibrations which are found between 2850 and 3000 cm−1. The feature is already present at room temperature where it manifests as a weak dip that is strongest for (TMTTF)2SbF6. Its strength increases with the anion size from (TMTTF)2PF6 to (TMTTF)2SbF6. At TCO the mode gains intensity. According to the theoretical calculations and the infrared and Raman measurements by Meneghetti et al. [59], no fundamental mode can be assigned to the resonance.

Hence it can be related to the overtone of ν4(ag) being strongly coupled to the transition band. One can exclude that the resonance arise from the overlap of different transition bands. This dip-like optical structure also appears in two-dimensional organic conductors [103,104] as well in other one-dimensional systems [95,106] with and without a charge-order state.

In the literature of organic conductors not much attention has been devoted to these features and anharmonicity in general. Very recently Yamamoto et al. [103,105] considered these anomalies and provided a first explanation of the spectral structure by applying a model of a diatomic dimer systems including emv-coupling. It reveals that the overtone of strongly coupled modes get activated by charge disproportionation. Taking into account higher order terms of the vibronic perturbation, they receive two terms describing the anharmonicity effect. One term is connected to the charge-transfer matrix which is present in all systems leading to a non-zero activation of the combination and overtones in any system, whereas the second term includes the charge disproportionation strongly contributing to the activation of higher modes. Both terms compete with each other, however, with increasing charge disproportionation the influence of the charge-transfer term diminishes.

If we consider now our one-dimensional system, we have a finite contribution of the charge transfer that leads to the activation of the higher modes at all temperatures, which is the main reason why we see the effect in all three compounds. But as soon as the systems enters the charge-order phase, the charge-separation term takes over. For (TMTTF)2PF6, the system has a low charge imbalance, thus the contribution of the second term is marginal; therefore the strength of the features is very similar above and below TCO. But the situation changes if we go to (TMTTF)2SbF6 where the charge disproportionation is 2δ = 0.3e; here the second term dominates and a huge change sets in below TCO. According to Yamamoto et al. [103] the maximum influence of the second term is at 0.85e, implying that for such kind of charge-ordered system the effect must be even stronger. To support this interpretation, it would be desirable to conduct an infrared study on the new synthesized organic salt (TMTTF)2TaF6 [107] where the transition temperature is at TCO = 175 K, connected with a larger charge imbalance. Here we could show that from the overtones and the combination modes we can gain further insight into the electronic interaction; in general they can be used to observe the onset of the charge ordering.

5. Low-Energy Spectroscopy: Lattice Phonons

Our investigations of the intramolecular vibrations presented above provide clear evidence that charge disproportionation between the organic molecules occurs in various (TMTTF)2X salts, as summarized in Table 3. We also provided a complex picture of the coupling to the anions and the important influence of the methyl groups forming a soft cavity around the octahedra. The next question now is the charge-order pattern, i.e., the lattice symmetry of the charge distribution. To that end we extended our Raman experiments down to low-energy (20–200 cm−1) and supplemented the findings with far-infrared reflection data, reaching down to 40 cm−1.

5.1. Symmetry Analysis

First let us analyze the symmetry of the unit cell and vibrational modes of the (TMTTF)2X salts crystallized in the triclinic P 1 ¯ space. Following Krauzman et al. [108] and based on careful structure analysis, the stack dimerization can be neglected and a pseudo-monoclinic unit cell approximated with C2h symmetry. In the spectral region below 200 cm−1 at most 15 lattice modes are expected: 6 due to the rigid translations and rotations of the anions and 9 due to the (TMTTF)2 dimer degrees of freedom. In a first approximation we can describe the dimer degrees of freedom as the three anti-phase rigid translations (Ta, Tb, Tc), three in-phase and three anti-phase librations (3R+, 3R) of the two TMTTF moieties. Within the C2h symmetry six dimer modes are Raman active (Ag, Bg) and three are infrared active (Au, Bu) as schematically represented in Table 5, together with their corresponding polarization dependence. The anion translations are also infrared active and have Au symmetry (translation along a-axis), and Bu symmetry (translations perpendicular to the a axis), while the three anion rotations are Raman active with one Ag and two Bg symmetry modes. We note that rotations and libration modes owe their Raman intensity uniquely from the rigid rotations of the molecular dielectric tensor; therefore they usually have very weak intensity and can hardly be observed. This is especially true for octahedral anions where the dielectric tensor has more or less a spherical symmetry.

Summarizing, the analysis reveals that two dimer translation modes (Tb and Tc) are expected in the Ag Raman spectra, which probe the diagonal components of the polarizations tensor (aa, bb′ and cc polarization); and one dimer translation (Ta) in the Bg spectrum characterized by off-diagonal elements of the tensor (ab′ and ac crossed polarization). Instead, anion translations can be detected in the infrared spectra, in particular the mode with Au symmetry in the spectra polarized along the a-axis, and the two modes with Bu symmetry in the spectra polarized along the b′-direction.

5.2. Far-Infrared Spectra

In Figure 23 the far-infrared reflectivity spectra of (TMTTF)2AsF6 and (TMTTF)2PF6 are plotted for two different polarizations: Ea and Eb′. When the temperature is reduced below TCO = 102, and 67 K, respectively, three vibrations become infrared active due the charge disproportionation between charge rich (ρ0 + δ) and charge poor (ρ0δ) molecules. In a first attempt these modes are assigned to the three anti-phase translation modes in the a, b and c-direction. As inversion symmetry is lost in the charge-ordered state, a permanent dipole moment develops (electronic ferroelectricity) with a charge distribution ⋯ + − + − + −. For (TMTTF)2AsF6 the strong Ta(Bg symmetry) mode develops at 85 cm−1 when probed along the stacking direction; in the perpendicular polarization, two vibrational features are observed: at 54 cm−1 [Tb(Ag)] and 66 cm−1 [Tc(Ag)]. In the (TMTTF)2PF6 compound we find two modes for Ea at 68 and 83 cm−1 [Ta(Bg)], and one at 54 cm−1 [Tb(Ag)] in the perpendicular direction. The comparison with our Raman spectra will support and advance the assignment.

The rather strong band observed in (TMTTF)2PF6 at 68 cm−1 cannot be satisfactorily assigned at this point. We suggest that the 68 cm−1 band is probably the internal vibration, known as “boat-mode” [109]. This low-frequency mode is infrared active for Ea but also has a Raman counterpart, as demonstrated in Figure 24. It strongly couples to the charge-order transition because it describes the distortion mode which links neutral TMTTF (boat conformation) and TMTTF+ (flat conformation). Thus this modes can modulate the charge transfer between molecules in weakly charge-ordered system, such (TMTTF)2PF6. In strong charge-ordered system, such as (TMTTF)2AsF6, it is not observed, probably hindered by the strong band at 85 cm−1. We may want to point out the 75 cm−1 feature also observed in (TMTTF)2AsF6 as a very weak shoulder that might the analogue to the 68 cm−1 in (TMTTF)2PF6 [110]. In (TMTTF)2AsF6 the charge disproportionation is more stable and the mode is not strong enough to move the charge between molecules and develop an oscillating dipole moment. In Section 6 we suggest a relation to the spin-Peierls transition since it splits for T < TSP as demonstrated in Figure 25.

An interesting development can be identified around 110 cm−1 (Figure 26); for T < TCO a mode starts to grow and becomes quite strong as the temperature is reduced further. In order to make the development more transparent, the ratios R ( T = 6 K ) R ( T = 70 K ) and R ( T = 20 K ) R ( T = 70 K ) is plotted in the right panel. The assignment of this feature is not clear at this point. Either it is a ν54(b2u) which we calculate to show up at 102 cm−1 for the ionized and at 95 cm−1 for the neutral molecule [111]. Alternatively we can assigned the 110 cm−1 mode to the harmonic of Tb(Ag). This implies some anharmonicity also for the lattice potential. For (TMTTF)2AsF6 we do not observe any feature at that frequency.

Finally, we would like to note that none of these infrared bands can be assigned to translational modes involving anion motion against the (TMTTF)2 dimer. In fact, they always show up below TCO when inversion symmetry is removed, while anion translations should already be infrared active even in centrosymmetric systems. The fact that these translational ionic modes are missing in the infrared spectra has been also reported for the isostructural Bechgaard (TMTSF)2X salts by Eldridge et al. [112], whose band assignments was supported by isotope-substitution shifts. Of course, we cannot rule out the possibility that these modes occur at energies lower than 40 cm−1 due to their massive ionic components and the relatively large and soft anion cages.

5.3. Low-Frequency Raman Spectra

Polarized Raman spectra of (TMTTF)2AsF6 collected with the 752 nm laser line at different temperatures are displayed in Figure 27. In (a, a) polarization a strong Ag band occurs around 48 cm−1 at room temperature which shows a large thermal shift up to 60 cm−1 on cooling to T = 120 K. For the polarization (b, a) two weaker Bg bands are observed around 41 and 77 cm−1; the very weak band located at 77 cm−1 is further confirmed by the resonant Raman spectra reported in Figure 28, where this mode gains strong resonance enhancement from the 647 nm laser line and shifts up to 84 cm−1 on cooling at T = 80 K. In resonant conditions the scattering mechanism is mainly governed by the electron-phonon interaction term; therefore we can safely assign this Bg band to the translation mode Ta, that is a Peierls-like phonon, which is able to modulate the overlap between molecular orbitals. The strong Ag band at 48 cm−1 is assigned to another translation mode (Tb or Tc), while the Bg band around 41 cm−1 might be assigned to one of the librations ( R b + , R c + ) according to Table 5; however, it is more likely that the feature belongs to a low-frequency internal mode (molecular vibration) because it exhibits only a very small thermal shift. In contrast to lattice vibrations, molecular vibrations are only weakly affected by the thermal lattice contraction.

In Section 5.2 we have seen that lattice modes of (TMTTF)2X become infrared active in the ferroelectric charge-ordered state. In Figure 29 we plot the representative Raman spectra of (TMTTF)2AsF6 at low temperature (T = 15 K). In the left panel we compare spectra obtained on two samples and with different laser power, while in the right panel we report polarized Raman spectra measured with two different laser lines [resonant (λ = 647 nm) and nearly resonant (676 nm)]. Five sharp bands are observed below 100 cm−1, and a cluster of broad bands around 110–130 cm−1. In Table 6 we summarize their frequencies and polarization dependences.

The mode observed around 83 cm−1 in Raman spectra (ab′-polarization) has already been assigned to the Ta translation mode, in agreement with its infrared polarization parallel to the a-axis (see Figure 23). The Ag Raman bands at 53 and 65 cm−1 correspond to infrared bands observed for the perpendicular polarization (Eb′-axis). The correspondence of the strong Raman band at 65 cm−1, assigned to a translation mode (Tb or Tc), to the weaker infrared band along the b′-axis suggests a smaller projection along this direction; therefore we identify the 65 cm−1 mode as the Tc translation mode. Correspondingly the mode at 53 cm−1 is assigned to the remaining translation mode, Tb. The third translation (Ta) corresponds to the dimerization mode and shows up as a strong feature around 85 cm−1 in the infrared spectra for a polarization.

In order to support our phonon assignments, we have performed density functional (DFT) calculations on a ( TMTTF ) 2 + dimer, using the PBE0 hybrid functional which performs well on dimeric noncovalent interactions [113]. The vibrational analysis have been performed relaxing the dimer coordinates to the equilibrium geometry, by imposing only the constraint on intra-dimer distance (fixed at the crystal value of 3.416 Å) to simulate the crystal packing effect along the a-direction. The mode represented in Figure 30, with a strong Peierls-like Ta character, is calculated at 82 cm−1 in perfect agreement with experiments, while Tb and Tc translation modes are calculated at 66 and 19 cm−1, respectively.

Although in our analysis we have focussed on (TMTTF)2AsF6, similar observations have been made on (TMTTF)2PF6 (see Table 7). In Figure 24 the low-temperature Raman spectra are compared to each other. Some differences in the spectra should be noted, for example, a new infrared and Raman band occurs around 68 cm−1 which could not be assigned ultimately but might be a signature of the intramolecular out-of plane vibration related to the boat configuration of the TMTTF molecules [109], as discussed in the previous Subsection 5.2. This low-frequency mode is linked to the charge transfer and not observed in strongly charge-ordered systems, such as (TMTTF)2AsF6. The main conclusions drawn for (TMTTF)2AsF6, however, can be safely extended also to (TMTTF)2PF6.

6. Spin-Peierls Transition

(TMTTF)2AsF6 and (TMTTF)2PF6, both undergo a spin-Peierls transition at TSP = 13 and 19 K, respectively. ESR experiments [46,47] clearly show the susceptibility to vanish exponentially as the triplet state forms and the lattice exhibit a tetramerization of the TMTTF chains. We can rule out a ⋯ + − − + + − − + ⋯ charge-distribution, since spin susceptibility does not exhibit a jump at TSP related to such a rearrangement and symmetry change as observed below the discontinuous anion ordering transition in TMTTF salts with tetrahedral anions, such as Cl O 4

, BF 4 or ReO 4 . The transition from a 4kF charge-ordered state to the 2kF ground state happens due to order in the spin sector in the case of a spin-Peierls transition, while the anion order also affects the charge sector. Since this Peierls transition involves changes in the lattice, we have carefully investigated the temperature dependence of the low-frequency modes.

As demonstrated in Figure 25 the 75 cm−1 mode of (TMTTF)2AsF6 identified already in Figure 23 splits when the temperature is lowered and T < TSP. It is not clear whether this mode is related to the feature observed in the low-temperature Raman spectra at 74 cm−1. Note, there is basically no change detected for the Tc mode at 66 cm−1. In addition, we see a small band to evolve at 461 cm−1 as the temperature decreases below TSP.

There is theoretical and experimental evidence of a coexistence of charge order and spin-Peierls lattice distortion [10,11,2931,42,44,79,114] with different options of the actual charge and spin patterns. In particular in both (TMTTF)2AsF6 and (TMTTF)2PF6 we do see a coupling of both types of ordering. The double peak found at 455 cm−1 can be assigned to the intramolecular ν35(b1u) mode. This basically implies that the spin-lattice coupling at TSP also leads to a variation of the charge distribution on the TMTTF molecules due to the tetramerization. This might also be the reason for the anomaly observed for the ν3(ag) mode at T < TSP. From Figure 11 it is clearly seen that the higher-frequency mode of (TMTTF)2AsF6 shifts down again for the lowest temperature. Similar observations are made in our Raman spectra summarized in Figure 8. Interestingly, the behavior for (TMTTF)2PF6 seems to be the opposite. There also seems to be a significant variation in the coupling to the anions at TSP as previously discussed on experimental and theoretical grounds [13,29]. Nakamura and collaborator [15,39,41] observe in their 13C-NMR spectra taken on (TMTTF)2AsF6 that the split peaks combine into one broad peak below TSP and interpret this as indication of a sizeable charge redistribution from charge rich to poor sites. From our vibrational spectra, we estimate this effect much smaller, not exceeding 20% of 2δ (Figure 8).

In the spectral range around 1400–1450 cm−1 we observe a reduction of the reflectivity in (TMTTF)2PF6 and (TMTTF)2AsF6 when the spin-Peierls phase is entered at TSP = 19 and 13 K, respectively, as displayed in Figure 31. In addition, a small absorption feature builds up at 1410 cm−1, which is better seen either in the reflectivity ratio R(T = 13 K) : R(T = 20 K) (right frame of Figure 31) or dielectric absorption 2(ν), plotted in Figure 32 for both examples.

The feature is robust and linked to the spin-Peierls phase, as proven by repeated temperature cycling. It also shows up in (TMTTF)2AsF6 below TSP = 13 K. Also the dielectric loss 2(ν) is slightly reduced in the spin-Peierls phase, but around 1410 cm−1 the mode can be clearly identified. The stronger feature around 1398 cm−1 has been discussed in Figures 14,15 and assigned to the C–H–C bending motion of the methyl groups; it changes upon entering the charge-ordered phase.

It is tempting to assign this 1410 cm−1 feature to the ν4(ag) mode that becomes activated due to the tetramerization. Commonly this mode is present in the infrared spectra around 1300 cm−1 (at room temperature) due to emv-coupling; i.e., independent and well above any long-range order. As seen from Table 4, the mode has the strongest emv-coupling constant. It is observed in our Raman spectra as a very strong peak at 1474 cm−1 (cf. Figure 5) but does not show any splitting upon charge-ordering. Below TSP the stacks are tetramerized, which could make the ν4(ag) vibrations infrared active. Low-temperature optical investigations on (TMTTF)2SbF6, compared to the spin-Peierls systems, could give valuable information in this regard. For the coupling between charge order and spin-Peierls transition, see also the reviews by Pouget [91,114].

7. Conclusions

The optical investigations of the quasi-one-dimensional charge-order systems (TMTTF)2X by Raman and infrared spectroscopy yield an enormous wealth of information on the charge disproportionation amplitude and symmetry, and about the molecular interactions which may trigger the ferroelectric phase transition.

Molecular vibrations are the most suitable local probe to follow directly the charge imbalance as a function of temperature and pressure. From the totally symmetric ν3(ag) mode observed by Raman spectroscopy and the asymmetric ν28(b1u) mode observed by infrared spectroscopy, we extract the temperature dependence of the charge disproportionation and find approximately a mean-field behavior (Figures 8,12). At low temperatures 2δ amounts to 0.15e, 0.19e and 0.29e for (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6, respectively. This is significantly lower than previous estimates from NMR experiments, as summarized in Table 3.

A careful analysis of the vibrational features involving the methyl groups of TMTTF and the hexafluoride anions evidences the important mutual coupling that is modified at the charge-order transition in addition to the usual change with temperature. The splitting of the C–C–H bending modes at 1000 cm−1 and at 1080 cm−1 reveals a modification of the coupling to the anions related to the broken inversion symmetry. The anions become distorted and the degeneracy of their ν4(t1u) mode is lifted. This is more an effect of temperature (e.g., thermal contraction) than charge order.

Additional features are identified that are caused by the anharmonic potential. The spin-Peierls transition entails additional modifications in the charge distribution. To complete the discussion, we also add the vibrational frequencies and eigenvectors based on ab initio quantum-chemical calculations.

From the analysis of our infrared and Raman spectra we have obtained an almost complete understanding of the lattice dynamics of the (TMTTF)2X systems. Above the ferroelectric transition temperature a Peierls-like mode Ta, characterized by a strong resonant behavior, have been identified in Raman spectra. Below the transition, in the charge-ordered state, this mode becomes also infrared active with polarization along the a-axis and marks the loss of the dimer inversion symmetry due to the site-charge redistribution. Similarly, the identification of the other translation modes, Tb and Tc, in infrared and Raman spectra completes the picture and confirm the original hypothesis of a charge-ordered state with a ⋯· + − + − + − ⋯ charge-distribution pattern.

Appendix

We used the GAMESS package [116,117] for the ab initio quantum chemical calculations. The ground state structure of the cation as well as the structure of the neutral molecule were optimized with the hybrid DFT-B3LYP functional and the 6-31+G(d,p) basis set yielding good results for organic molecules [118]. The calculations were carried out for the isolated molecule with the C1 and the D2h symmetry suggested by Meneghetti et al. [59]. For the optimization we used the standard grid and a tight geometry optimization. The analysis of the cation and the neutral molecule symmetry—after the optimization with the initial symmetry C1—resides in the C2 symmetry whereas by increasing the tolerance parameters yielding also the D2h symmetry. Our findings support Meneghetti and coworkers who assumed that the original geometry only deviates partially from the D2h symmetry. All received vibrational frequencies are positive verifying that the equilibrium structure has been obtained.

The neutral molecule distorts in a boat-like confirmation (left panel Figure A1) and the cation exhibits a flat structure (right panel Figure A1) being often observed in other organic molecules [119121]. The D2h symmetry for the cation results in four imaginary frequencies, respectively in one imaginary frequency for the neutral molecule indicating that the equilibrium ground state geometry for both is C2 and not D2h.

Figure A1. On the left picture, the boat-like equilibrium geometry of the TMTTF0 molecule.
Figure A1. On the left picture, the boat-like equilibrium geometry of the TMTTF0 molecule.
Crystals 02 00528f33 1024

In Tables A1,A2 we report the calculated and the experimentally determined frequencies [59] of the gerade and ungerade modes, respectively, for TMTTF0 and TMTTF+ with the C2 symmetry. We used two different scaling factors for the high-frequency vibrations 0.9679 (above 1300 cm−1) and for the low-frequency modes 1.01 which has been actually determined for the triple-ζ basis set 6-311+G(d,p) [122]. The ag, au, b3g and b3u modes in D2h reduce to A modes in C2. The B modes in C2 correlate with b1g, b1u, b2g and b2u. For better comparison with the results of Meneghetti et al. [59] and further clarification, we sorted the normal modes according to the eight irreducible representations of the D2h group.

Table A1. Calculated frequencies (in cm−1) and infrared intensities (given in D2 amu−1Å−2) of the gerade molecular modes of TMTTF0 and TMTTF+. The experimental values are extracted from [59]. The corresponding eigenvectors of the modes are displayed in Figure A2. The following abbreviations are used: Int.: Intensity, asym: asymmetric, sym: symmetric, def: deformation, ip: in-plane, oop: out-of-plane, tor: torsion, str: stretching, brea: breathing, bend: bending.
Table A1. Calculated frequencies (in cm−1) and infrared intensities (given in D2 amu−1Å−2) of the gerade molecular modes of TMTTF0 and TMTTF+. The experimental values are extracted from [59]. The corresponding eigenvectors of the modes are displayed in Figure A2. The following abbreviations are used: Int.: Intensity, asym: asymmetric, sym: symmetric, def: deformation, ip: in-plane, oop: out-of-plane, tor: torsion, str: stretching, brea: breathing, bend: bending.
Symmetry LabelTMTTF0TMTTF+Mode description

νexpνcalcνscaledInt.νexpνcalcνscaledInt.
agν12, 9233, 1423, 0410.41273, 1673, 0560.1161ν-CH3 asym
ν23, 0342, 9370.02913, 0542, 9560.0994ν-CH3 sym
ν31, 6391, 6901, 6360.00361, 5671, 6221, 5700outer, inner C=C str
ν41, 5381, 5961, 5450.00361, 4181, 4921, 4440.0021outer, inner C=C str
ν51, 4321, 5021, 4540.24441, 4471, 4000α-CH3 asym
ν61, 4341, 3880.0061, 4361, 3910.0015α-CH3 sym
ν71, 0921, 1031, 1140.0511, 1041, 1011, 1120β-CH3
ν89349409490.0189419369450.0008β-CH3
ν95605535580.0135665635690S–C–CH3 str
ν104944955000.01975235245300C–S–C str
ν112773133160.0362983113140.0018CH3 sci
ν122172112130.01142282222240rings def ip

b1gν203, 0832, 9840.2383, 1113, 0110.0353ν-CH3 asym
ν211, 4821, 4340.02461, 4791, 4310.0656α-CH3 asym
ν221, 0631, 0730.0051, 0631, 0740.0017β-CH3
ν235075120.00065115160.0002rings def oop
ν241761780.06521511530.0002rings def oop, CH3 tor
ν251451470.0051211220.0002rings def oop, CH3 tor

b2gν373, 0822, 9830.21873, 1133, 0130.0361ν-CH3 asym
ν381, 4881, 4400.41051, 4871, 4390.0418α-CH3 asym
ν391, 0471, 0570.00141, 0481, 0580.0024β-CH3
ν405175220.11325075120.0001rings def oop
ν412612630.00092962990.0004rings def oop
ν421511530.020698990rings def oop, CH3 tor
ν4360610.068473740.0018rings def oop, CH3 tor

b3gν553, 1333, 0320.123, 1583, 0570.0079ν-CH3 asym
ν563, 0312, 9340.02053, 0522, 9530.0651ν-CH3 sym
ν571, 4931, 4450.03431, 4841, 4360.1928α-CH3 asym
ν581, 4171, 3710.00151, 4191, 3740.0453α-CH3 sym
ν591, 1881, 2000.00041, 1941, 2070β-CH3
ν601, 1181, 1290.03051, 1261, 1360β-CH3
ν619859950.00321, 0381, 0490S–C str inner, β-CH3
ν627437510.00727637700S–C str outer
ν634734780.00074744790ring def ip
ν643853890.00733873910C–CH3 str
ν652462590.01112362390.0002ring def ip
Table A2. Calculated frequencies (in cm−1) and infrared intensities (given in D2amu−1Å−2) of the ungerade modes of TMTTF0 and TMTTF+. The experimental values are extracted from [59]. The eigenvectors are sketched in Figures A3A5. The following abbreviations are used: Int.: Intensity, asym: asymmetric, sym: symmetric, def: deformation, ip: in-plane, oop: out-of-plane, tor: torsion, str: stretching, brea: breathing, bend: bending.
Table A2. Calculated frequencies (in cm−1) and infrared intensities (given in D2amu−1Å−2) of the ungerade modes of TMTTF0 and TMTTF+. The experimental values are extracted from [59]. The eigenvectors are sketched in Figures A3A5. The following abbreviations are used: Int.: Intensity, asym: asymmetric, sym: symmetric, def: deformation, ip: in-plane, oop: out-of-plane, tor: torsion, str: stretching, brea: breathing, bend: bending.
Symmetry LabelTMTTF0TMTTF+Mode description

νexpνcalcνscaledInt.νexpνcalcνscaledInt.
auν133, 0822, 9830.42423, 1113, 0110.0447ν-CH3 asym
ν141, 4831, 4350.10071, 4801, 4320.0551α-CH3 asym
ν151, 0641, 0740.00281, 0631, 0730.0003β-CH3
ν165055100.00165015060ring def oop
ν171771790.02981471490.0006ring def oop
ν181451460.02261171180.0034def oop, C3 tor
ν1966670.001143430.0054def oop

b1uν262, 9123, 1423, 0410.87012, 9233, 1663, 0650.1837ν-CH3 asym
ν272, 8483, 0342, 9361.74662, 8483, 0532, 9560.2383ν-CH3 asym
ν281, 6271, 6821, 6280.2081, 5471, 6021, 5518.6833outer C=C str
ν291, 4371, 5021, 4540.37731, 4381, 4911, 4430.0307α-CH3 asym
ν301, 3741, 4331, 3870.0011, 4371, 3910.0857α-CH3 sym
ν311, 0901, 1011, 1120.66161, 0951, 0961, 1080.0616β-CH3, S–C str
ν329359419500.08429359309391.2806ν-CH3 asym, S–C str
ν337807787860.91688288218290.6553C–S str
ν345565455510.05735575515560.1366rings brea asym
ν354394354400.3564684764800.5027rings brea asym
ν362363073100.0763063090.0039C=C–CH3 bend

b2uν442, 9903, 1323, 0320.252, 9733, 1593, 0570.028ν-CH3 asym
ν452, 8483, 0322, 9341.9552, 8533, 0522, 9540.1876ν-CH3 sym
ν461, 4371, 4931, 4450.4031, 4381, 4841, 4360.2372α-CH3 asym
ν471, 3851, 4181, 3720.0151, 3991, 4201, 3740.0894α-CH3 sym
ν481, 1831, 1921, 2030.51251, 1851, 1971, 2090.0754β-CH3
ν491, 1091, 1200.39851, 1091, 1200.2273β-CH3
ν508538610.03338759079170.1686C–S str, β-CH3
ν517477457530.02247687647710.0041C–S str, C=C–CH3 bend
ν524794840.114834880.0384C–CH3 str
ν533323373410.133593453480.0466def ip, C=C–CH3 bend
ν5480810.0683840.0093def ip

b3uν663, 0832, 9840.43, 1123, 0120.0566ν-CH3 asym
ν671, 4881, 4410.43281, 4871, 4391.02α-CH3 asym
ν681, 0481, 0580.00211, 0491, 0590.0188β-CH3
ν692772800.16033233260.1897def ip
ν702742780.020382792820.0463def oop
ν711501510.11576760.0142def oop, CH3 tor
ν7234350.066746470.069def oop

In order to illustrate the movement of the atoms within the TMTTF molecule for the most important vibrational modes, their eigenvectors are plotted in Figure A2 and Figure A3 through Figure A5, for the gerade and ungerade modes, respectively.

Figure A2. Eigenvectors of the twelve totally symmetric (ag) intramolecular modes of TMTTF. (a) ν1(ag) mode; (b) ν2(ag) mode; (c) ν3(ag) mode; (d) ν4(ag) mode; (e) ν5(ag) mode; (f) ν6(ag) mode; (g) ν7(ag) mode; (h) ν8(ag) mode; (i) ν9(ag) mode; (j) ν10(ag) mode; (k) ν11(ag) mode; (l) ν12(ag) mode.
Figure A2. Eigenvectors of the twelve totally symmetric (ag) intramolecular modes of TMTTF. (a) ν1(ag) mode; (b) ν2(ag) mode; (c) ν3(ag) mode; (d) ν4(ag) mode; (e) ν5(ag) mode; (f) ν6(ag) mode; (g) ν7(ag) mode; (h) ν8(ag) mode; (i) ν9(ag) mode; (j) ν10(ag) mode; (k) ν11(ag) mode; (l) ν12(ag) mode.
Crystals 02 00528f34 1024Crystals 02 00528f34a 1024
Figure A3. Eigenvectors of the eleven ungerade (b1u) intramolecular modes of TMTTF. (a) ν26(b1u) mode; (b) ν27(b1u) mode; (c) ν28(b1u) mode; (d) ν29(b1u) mode; (e) ν30(b1u) mode; (f) ν31(b1u) mode; (g) ν32(b1u) mode; (h) ν33(b1u) mode; (i) ν34(b1u) mode; (j) ν35(b1u) mode; (k) ν36(b1u) mode.
Figure A3. Eigenvectors of the eleven ungerade (b1u) intramolecular modes of TMTTF. (a) ν26(b1u) mode; (b) ν27(b1u) mode; (c) ν28(b1u) mode; (d) ν29(b1u) mode; (e) ν30(b1u) mode; (f) ν31(b1u) mode; (g) ν32(b1u) mode; (h) ν33(b1u) mode; (i) ν34(b1u) mode; (j) ν35(b1u) mode; (k) ν36(b1u) mode.
Crystals 02 00528f35 1024
Figure A4. Eigenvectors of the eleven ungerade (b2u) intramolecular modes of TMTTF. (a) ν44(b2u) mode; (b) ν45(b2u) mode; (c) ν46(b2u) mode; (d) ν47(b2u) mode; (e) ν48(b2u) mode; (f) ν49(b2u) mode; (g) ν50(b2u) mode; (h) ν51(b2u) mode; (i) ν52(b2u) mode; (j) ν53(b2u) mode; (k) ν54(b2u) mode.
Figure A4. Eigenvectors of the eleven ungerade (b2u) intramolecular modes of TMTTF. (a) ν44(b2u) mode; (b) ν45(b2u) mode; (c) ν46(b2u) mode; (d) ν47(b2u) mode; (e) ν48(b2u) mode; (f) ν49(b2u) mode; (g) ν50(b2u) mode; (h) ν51(b2u) mode; (i) ν52(b2u) mode; (j) ν53(b2u) mode; (k) ν54(b2u) mode.
Crystals 02 00528f36 1024
Figure A5. Eigenvectors of the seven ungerade (b3u) intramolecular modes of TMTTF. (a) ν66(b3u) mode; (b) ν67(b3u) mode; (c) ν68(b3u) mode; (d) ν69(b3u) mode; (e) ν70(b3u) mode; (f) ν71(b3u) mode; (g) ν72(b3u) mode.
Figure A5. Eigenvectors of the seven ungerade (b3u) intramolecular modes of TMTTF. (a) ν66(b3u) mode; (b) ν67(b3u) mode; (c) ν68(b3u) mode; (d) ν69(b3u) mode; (e) ν70(b3u) mode; (f) ν71(b3u) mode; (g) ν72(b3u) mode.
Crystals 02 00528f37 1024Crystals 02 00528f37a 1024

Acknowledgments

Many valuable discussions with S. Brown, N. Drichko, A. Girlando, A. Pashkin, J.-P. Pouget and E. Rose are acknowledged. We thank G. Untereiner for the crystal growth and sample preparation. The project was supported by the Deutsche Forschungsgemeinschaft (DFG) and by the Carl-Zeiss-Stiftung. We would like to thank the bwGRiD [115] for providing the computational resources.

Classification: PACS 75.25.Dk, 71.20.Ps 74.70.Kn, 78.30.-j, 63.20.-e

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Figure 1. The phase diagram of the quasi one-dimensional TMTTF and TMTSF salts, first suggested by Jérome and coworkers [2] and further supplemented by many groups over the years [5]. For the different compounds with centrosymmetric anions the ambient-pressure position in the phase diagram is indicated. Going from the left to the right, the materials get less one-dimensional due to the increasing interaction in the second and third direction. At low temperatures various broken symmetry ground states develop. Here loc stands for charge localization, CO for charge ordering, SP for spin-Peierls, AFM for antiferromagnet, SDW for spin density wave, and SC for superconductor. While some of the boundaries are clear phase transitions, the ones indicated by dashed lines are better characterized as a crossover. The position in the phase diagram can be tuned by external or chemical pressure.
Figure 1. The phase diagram of the quasi one-dimensional TMTTF and TMTSF salts, first suggested by Jérome and coworkers [2] and further supplemented by many groups over the years [5]. For the different compounds with centrosymmetric anions the ambient-pressure position in the phase diagram is indicated. Going from the left to the right, the materials get less one-dimensional due to the increasing interaction in the second and third direction. At low temperatures various broken symmetry ground states develop. Here loc stands for charge localization, CO for charge ordering, SP for spin-Peierls, AFM for antiferromagnet, SDW for spin density wave, and SC for superconductor. While some of the boundaries are clear phase transitions, the ones indicated by dashed lines are better characterized as a crossover. The position in the phase diagram can be tuned by external or chemical pressure.
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Figure 2. (a) Two views on the crystal structure of (TMTTF)2SbF6 illustrate the confinement of the octahedral anions in a cavity formed by methyl groups (gray) of the surrounding TMTTF molecules. Also shown are the closest connections between the fluorine (green) and sulphur atoms (yellow). The right panels demonstrate the shift of the charge-order transition temperature TCO as a function physical and chemical pressure; (b) Temperature dependence of the DC resistivity of (TMTTF)2SbF6 measured along the b-direction at different values of hydrostatic pressure as indicated. TCO is seen as a kink in ρ(T) that shifts to low temperatures as pressure increases; (c) Dependence of TCO on the shortest distance between the ligands of the anions (F or O) and sulfur atoms in TMTTF. The structural data are taken from References [23,5658]; cf. also Reference [37].
Figure 2. (a) Two views on the crystal structure of (TMTTF)2SbF6 illustrate the confinement of the octahedral anions in a cavity formed by methyl groups (gray) of the surrounding TMTTF molecules. Also shown are the closest connections between the fluorine (green) and sulphur atoms (yellow). The right panels demonstrate the shift of the charge-order transition temperature TCO as a function physical and chemical pressure; (b) Temperature dependence of the DC resistivity of (TMTTF)2SbF6 measured along the b-direction at different values of hydrostatic pressure as indicated. TCO is seen as a kink in ρ(T) that shifts to low temperatures as pressure increases; (c) Dependence of TCO on the shortest distance between the ligands of the anions (F or O) and sulfur atoms in TMTTF. The structural data are taken from References [23,5658]; cf. also Reference [37].
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Figure 3. Sketch of the totally symmetric ag modes ν3 and ν4 and the asymmetric ν28(b1u) stretching modes of the TMTTF molecule that mainly involve the central and outer C=C bonds. In the right frame, we show the linear shift of the intramolecular vibrations ν3(ag) and ν28(b1u) with the charge per TMTTF molecule obtained from optical spectroscopy by Meneghetti et al. [59].
Figure 3. Sketch of the totally symmetric ag modes ν3 and ν4 and the asymmetric ν28(b1u) stretching modes of the TMTTF molecule that mainly involve the central and outer C=C bonds. In the right frame, we show the linear shift of the intramolecular vibrations ν3(ag) and ν28(b1u) with the charge per TMTTF molecule obtained from optical spectroscopy by Meneghetti et al. [59].
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Figure 4. Contour plot for the HOMO orbital of a neutral TMTTF molecule. The charge is mainly located on the sulfur atoms and the three C=C double bonds.
Figure 4. Contour plot for the HOMO orbital of a neutral TMTTF molecule. The charge is mainly located on the sulfur atoms and the three C=C double bonds.
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Figure 5. (a) Room temperature Raman spectra of (TMTTF)2X ( X = PF 6 , AsF 6 ) single crystals measured with the λ = 647 nm; (b) Polarized room temperature Raman spectra of (TMTTF)2AsF6 measured with the λ = 752 nm. In parentheses the components of the polarizations tensor probed in the experiment.
Figure 5. (a) Room temperature Raman spectra of (TMTTF)2X ( X = PF 6 , AsF 6 ) single crystals measured with the λ = 647 nm; (b) Polarized room temperature Raman spectra of (TMTTF)2AsF6 measured with the λ = 752 nm. In parentheses the components of the polarizations tensor probed in the experiment.
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Figure 6. Raman spectra of (TMTTF)2AsF6 as a function of temperature. The data are taken with λ = 647.2 nm for the polarization (b, b′). Most obvious is the splitting of the ν3(ag) mode around 1600 cm−1 and the evolution of three features between 1425 and 1460 cm−1 as the temperatures drops below TCO = 102 K. For T = 95 K the two Lorentzian contributions are plotted separately to demonstrate the decomposition.
Figure 6. Raman spectra of (TMTTF)2AsF6 as a function of temperature. The data are taken with λ = 647.2 nm for the polarization (b, b′). Most obvious is the splitting of the ν3(ag) mode around 1600 cm−1 and the evolution of three features between 1425 and 1460 cm−1 as the temperatures drops below TCO = 102 K. For T = 95 K the two Lorentzian contributions are plotted separately to demonstrate the decomposition.
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Figure 7. Raman spectra of (TMTTF)2PF6 as a function of temperature. Similar to the spectra of (TMTTF)2AsF6, the ν3(ag) mode around 1600 cm−1 splits as the temperature drops below TCO = 67 K and three features evolve between 1425 and 1460 cm−1 that can be assigned to bending modes of the methyl groups. For T = 13 K we plot the different contributions separately.
Figure 7. Raman spectra of (TMTTF)2PF6 as a function of temperature. Similar to the spectra of (TMTTF)2AsF6, the ν3(ag) mode around 1600 cm−1 splits as the temperature drops below TCO = 67 K and three features evolve between 1425 and 1460 cm−1 that can be assigned to bending modes of the methyl groups. For T = 13 K we plot the different contributions separately.
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Figure 8. Left two panels: Temperature evolution of the peak frequencies of the ν3(ag) mode of (TMTTF)2X obtained from our Raman (open circles) and infrared spectra (filled squares). The corresponding charge disproportionation 2δ is plotted in the right panel as a function of temperature.
Figure 8. Left two panels: Temperature evolution of the peak frequencies of the ν3(ag) mode of (TMTTF)2X obtained from our Raman (open circles) and infrared spectra (filled squares). The corresponding charge disproportionation 2δ is plotted in the right panel as a function of temperature.
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Figure 9. Raman spectra of (TMTTF)2AsF6 and (TMTTF)2PF6 as a function of temperature. The spectral features observed on the low-frequency wing of the strong ν3(ag) band is assigned to the molecular ν28(b1u) mode and followed by the solid line. The decomposition of the T = 20 K spectrum illustrates the different contributions to the fit.
Figure 9. Raman spectra of (TMTTF)2AsF6 and (TMTTF)2PF6 as a function of temperature. The spectral features observed on the low-frequency wing of the strong ν3(ag) band is assigned to the molecular ν28(b1u) mode and followed by the solid line. The decomposition of the T = 20 K spectrum illustrates the different contributions to the fit.
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Figure 10. The optical conductivity of (TMTTF)2X with X = PF 6 ( T C O = 67 K ), AsF 6 ( T C O = 102 K ) and SbF 6 ( T C O = 157 K ) recorded along the c-direction for different temperatures as indicated. The conductivity was shifted by a constant factor for better clarification. Below TCO, the ν28(b1u) mode splits in two components as shown by the two black arrows. It is interesting to note that in the case of (TMTTF)2SbF6 the modes have a strong Fano shape.
Figure 10. The optical conductivity of (TMTTF)2X with X = PF 6 ( T C O = 67 K ), AsF 6 ( T C O = 102 K ) and SbF 6 ( T C O = 157 K ) recorded along the c-direction for different temperatures as indicated. The conductivity was shifted by a constant factor for better clarification. Below TCO, the ν28(b1u) mode splits in two components as shown by the two black arrows. It is interesting to note that in the case of (TMTTF)2SbF6 the modes have a strong Fano shape.
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Figure 11. Mid-infrared conductivity σ1(ν) of (TMTTF)2AsF6 and (TMTTF)2PF6 for light polarized parallel to the molecular stacks (Ea) in the spectral region of the emv coupled totally symmetric intramolecular ν3(ag) mode for temperatures above and below TCO. The curves are displaced by a constant factor to avoid overlap. The arrows indicate the positions of the antiresonance dips.
Figure 11. Mid-infrared conductivity σ1(ν) of (TMTTF)2AsF6 and (TMTTF)2PF6 for light polarized parallel to the molecular stacks (Ea) in the spectral region of the emv coupled totally symmetric intramolecular ν3(ag) mode for temperatures above and below TCO. The curves are displaced by a constant factor to avoid overlap. The arrows indicate the positions of the antiresonance dips.
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Figure 12. (a) Position of the peaks for the (TMTTF)2X with X = SbF 6 , AsF 6 and PF 6 as a function of T recorded along the c axis; (b) Temperature dependence of the charge dispropotionation probed by the splitting of the ν28 mode. The charge imbalance 2δ is estimated from the difference of the two resonance frequencies by Equation 2.
Figure 12. (a) Position of the peaks for the (TMTTF)2X with X = SbF 6 , AsF 6 and PF 6 as a function of T recorded along the c axis; (b) Temperature dependence of the charge dispropotionation probed by the splitting of the ν28 mode. The charge imbalance 2δ is estimated from the difference of the two resonance frequencies by Equation 2.
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Figure 13. Dielectric losses 2(ν) of (TMTTF)2AsF6 and (TMTTF)2PF6 for light polarized perpendicular to the molecular stacks (Eb′) in the upper and lower frames, respectively. In the left panels the C–C–H bending vibration is observed around 935 cm−1. The antisymmetric ν31(b1u) mode located around 1090 cm−1 at room temperature splits as T drops below TCO = 102 and 67 K, respectively. The right panels show the temperature dependence of the H–C–H bending modes.
Figure 13. Dielectric losses 2(ν) of (TMTTF)2AsF6 and (TMTTF)2PF6 for light polarized perpendicular to the molecular stacks (Eb′) in the upper and lower frames, respectively. In the left panels the C–C–H bending vibration is observed around 935 cm−1. The antisymmetric ν31(b1u) mode located around 1090 cm−1 at room temperature splits as T drops below TCO = 102 and 67 K, respectively. The right panels show the temperature dependence of the H–C–H bending modes.
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Figure 14. Temperature dependence of the vibrational modes observed in the optical conductivity of (TMTTF)2PF6 for the polarization direction Ec. The curves are shifted for clarity reasons.
Figure 14. Temperature dependence of the vibrational modes observed in the optical conductivity of (TMTTF)2PF6 for the polarization direction Ec. The curves are shifted for clarity reasons.
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Figure 15. Temperature dependence of the infrared active α-CH3 mode measured along the Ea for (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6 single crystals. Two distinct peaks develops above TCO reflecting the interaction of methyl group and the fluorine atoms of the anion.
Figure 15. Temperature dependence of the infrared active α-CH3 mode measured along the Ea for (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6 single crystals. Two distinct peaks develops above TCO reflecting the interaction of methyl group and the fluorine atoms of the anion.
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Figure 16. Vibrational spectra of (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6 in the range of the anion vibrational mode ν4(t1u) obtained with light polarized perpendicular to the ab-plane. The curves for different temperatures are vertically displaced for clarity reasons. As the temperature is reduced below TCO, the modes split by about 7.5 cm−1 due to the distortion of the octahedra. The right side contains a sketch of the two infrared active normal modes of vibration of the octahedral M F 6 ions (where M = P, As, and Sb is shown by the red sphere and the fluorine atoms by the blue dots). While ν3(t1u) is around 500 cm−1 and falls outside the mid-infrared range, the ν4(t1u) mode is seen around 650 to 840 cm−1.
Figure 16. Vibrational spectra of (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6 in the range of the anion vibrational mode ν4(t1u) obtained with light polarized perpendicular to the ab-plane. The curves for different temperatures are vertically displaced for clarity reasons. As the temperature is reduced below TCO, the modes split by about 7.5 cm−1 due to the distortion of the octahedra. The right side contains a sketch of the two infrared active normal modes of vibration of the octahedral M F 6 ions (where M = P, As, and Sb is shown by the red sphere and the fluorine atoms by the blue dots). While ν3(t1u) is around 500 cm−1 and falls outside the mid-infrared range, the ν4(t1u) mode is seen around 650 to 840 cm−1.
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Figure 17. Pressure dependence of the optical conductivity of (TMTTF)2AsF6 measured at room temperature for Ea. The spectral range of those features is enlarged that are related to vibrations of the TMTTF methyl groups.
Figure 17. Pressure dependence of the optical conductivity of (TMTTF)2AsF6 measured at room temperature for Ea. The spectral range of those features is enlarged that are related to vibrations of the TMTTF methyl groups.
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Figure 18. Pressure dependence of the optical conductivity of (TMTTF)2AsF6 measured at room temperature for Ea. The 700 cm−1 mode is related to the AsF 6 vibration, while the 1600 cm−1 peak is related to the asymmetric C=C stretching vibration of the TMTTF molecule.
Figure 18. Pressure dependence of the optical conductivity of (TMTTF)2AsF6 measured at room temperature for Ea. The 700 cm−1 mode is related to the AsF 6 vibration, while the 1600 cm−1 peak is related to the asymmetric C=C stretching vibration of the TMTTF molecule.
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Figure 19. Infrared spectra of (TMTTF)2PF6 and (TMTTF)2AsF6 as function of temperature measured along the stacking direction (Ea). For the two compounds the clear splitting of the antiresonance combination mode ν11(ag) + ν10(ag) is visible. In the case of (TMTTF)2SbF6 the data were too noisy to present here. The spectra are shifted with a constant value for clarification. In the lower panel the same mode is presented, for the example of (TMTTF)2PF6, but measured for E polarized perpendicular to the ab-plane. It is interesting to note that the two peaks observed for Ec* spectra become dips in the Ea polarization due to the emv interaction with the electronic background with a clear Fano shape at elevated temperatures. In the case of (TMTTF)2AsF6 peaks are observed also for the light polarized parallel to the stacks.
Figure 19. Infrared spectra of (TMTTF)2PF6 and (TMTTF)2AsF6 as function of temperature measured along the stacking direction (Ea). For the two compounds the clear splitting of the antiresonance combination mode ν11(ag) + ν10(ag) is visible. In the case of (TMTTF)2SbF6 the data were too noisy to present here. The spectra are shifted with a constant value for clarification. In the lower panel the same mode is presented, for the example of (TMTTF)2PF6, but measured for E polarized perpendicular to the ab-plane. It is interesting to note that the two peaks observed for Ec* spectra become dips in the Ea polarization due to the emv interaction with the electronic background with a clear Fano shape at elevated temperatures. In the case of (TMTTF)2AsF6 peaks are observed also for the light polarized parallel to the stacks.
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Figure 20. Temperature-dependent infrared spectra for the 2ν10 mode obtained for (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6 with Ea. The arrows indicate the evolution of the resonance with decreasing temperature.
Figure 20. Temperature-dependent infrared spectra for the 2ν10 mode obtained for (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6 with Ea. The arrows indicate the evolution of the resonance with decreasing temperature.
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Figure 21. Mid-infrared conductivity σ1(ν) of (TMTTF)2PF6 and (TMTTF)2AsF6 for light polarized parallel to the molecular stacks (Ea) in the vicinity of the emv-coupled totally symmetric intramolecular ν3(ag) mode for temperatures above and below TCO. The curves are displaced by a constant factor to avoid overlap. The arrows indicate the positions of the antiresonance dips. In the case of (TMTTF)2SbF6 the spectra were too noisy to identify any clear feature.
Figure 21. Mid-infrared conductivity σ1(ν) of (TMTTF)2PF6 and (TMTTF)2AsF6 for light polarized parallel to the molecular stacks (Ea) in the vicinity of the emv-coupled totally symmetric intramolecular ν3(ag) mode for temperatures above and below TCO. The curves are displaced by a constant factor to avoid overlap. The arrows indicate the positions of the antiresonance dips. In the case of (TMTTF)2SbF6 the spectra were too noisy to identify any clear feature.
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Figure 22. Temperature dependence of the infrared spectra of (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6 obtained from reflection measurements along the stacking direction (Ea). In the upper and lower panels, two distinct features are highlighted marking the combination mode of ν4 + ν10 and the first overtone of 2ν4, respectively.
Figure 22. Temperature dependence of the infrared spectra of (TMTTF)2PF6, (TMTTF)2AsF6 and (TMTTF)2SbF6 obtained from reflection measurements along the stacking direction (Ea). In the upper and lower panels, two distinct features are highlighted marking the combination mode of ν4 + ν10 and the first overtone of 2ν4, respectively.
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Figure 23. Far-infrared reflectivity spectra of (TMTTF)2AsF6 (upper panels) and (TMTTF)2PF6 salts (lower panels) measured at different temperatures with the polarization parallel (Ea, left panels) and perpendicular (Eb′, right panels) to the stacks. As T drops below TCO strong vibrational features develop at 54, 66, 75 and 85 cm−1 in the case of (TMTTF)2AsF6, and at 54, 68, and 83 cm−1 for (TMTTF)2PF6. The excitations are mainly related to the translational lattice modes Ta, Tb and Tc sketched on the right side for the example of a TMTTF dimer.
Figure 23. Far-infrared reflectivity spectra of (TMTTF)2AsF6 (upper panels) and (TMTTF)2PF6 salts (lower panels) measured at different temperatures with the polarization parallel (Ea, left panels) and perpendicular (Eb′, right panels) to the stacks. As T drops below TCO strong vibrational features develop at 54, 66, 75 and 85 cm−1 in the case of (TMTTF)2AsF6, and at 54, 68, and 83 cm−1 for (TMTTF)2PF6. The excitations are mainly related to the translational lattice modes Ta, Tb and Tc sketched on the right side for the example of a TMTTF dimer.
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Figure 24. Raman spectra of (TMTTF)2PF6 compared to (TMTTF)2AsF6 measured with λ = 647 nm laser line in the (b, b′)-polarization at T = 15 K. For the assignment of the modes, confer with Table 7.
Figure 24. Raman spectra of (TMTTF)2PF6 compared to (TMTTF)2AsF6 measured with λ = 647 nm laser line in the (b, b′)-polarization at T = 15 K. For the assignment of the modes, confer with Table 7.
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Figure 25. The absorption spectra exhibit the temperature-development of the 75 cm−1 lattice mode in (TMTTF)2AsF6 on the left side. In the right panel, a weak band develops at 461 cm−1 that might be a satellite of the double structure seen at 452 and 457 cm−1.
Figure 25. The absorption spectra exhibit the temperature-development of the 75 cm−1 lattice mode in (TMTTF)2AsF6 on the left side. In the right panel, a weak band develops at 461 cm−1 that might be a satellite of the double structure seen at 452 and 457 cm−1.
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Figure 26. Far-infrared reflectivity spectra of (TMTTF)2PF6 at different temperatures obtained for Eb′ polarized light. A feature at 110 cm−1 gradually develops as the temperature is reduced below TCO. On the right side the reflectivity at T = 6 and 20 K is normalized to the T = 70 K values.
Figure 26. Far-infrared reflectivity spectra of (TMTTF)2PF6 at different temperatures obtained for Eb′ polarized light. A feature at 110 cm−1 gradually develops as the temperature is reduced below TCO. On the right side the reflectivity at T = 6 and 20 K is normalized to the T = 70 K values.
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Figure 27. Low-frequency Raman spectra of (TMTTF)2AsF6 in the polarization (a, a) and (b, a) obtained at different temperatures using the λ = 752 nm laser line. Note the different intensity scale: Bg spectra are two times weaker than Ag ones.
Figure 27. Low-frequency Raman spectra of (TMTTF)2AsF6 in the polarization (a, a) and (b, a) obtained at different temperatures using the λ = 752 nm laser line. Note the different intensity scale: Bg spectra are two times weaker than Ag ones.
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Figure 28. Unpolarized resonant Raman spectra of (TMTTF)2AsF6 as a function of temperature taken with λ = 647 nm.
Figure 28. Unpolarized resonant Raman spectra of (TMTTF)2AsF6 as a function of temperature taken with λ = 647 nm.
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Figure 29. Left panel: λ = 647 nm Raman spectra of (TMTTF)2AsF6 at 15 K. Laser power has been reduced in order to minimize sample heating. Right panel: Polarized Raman spectra at 15 K.
Figure 29. Left panel: λ = 647 nm Raman spectra of (TMTTF)2AsF6 at 15 K. Laser power has been reduced in order to minimize sample heating. Right panel: Polarized Raman spectra at 15 K.
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Figure 30. The Peierls-like mode of Ta character represents the vibrations of the TMTTF molecules against each other; it is calculated at 82.3 cm−1 using DFT method.
Figure 30. The Peierls-like mode of Ta character represents the vibrations of the TMTTF molecules against each other; it is calculated at 82.3 cm−1 using DFT method.
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Figure 31. Reflectivity of (TMTTF)2PF6 and (TMTTF)2AsF6 measured for the polarization Ea at different temperatures as indicated. In both compounds the overall value of R(ν) does not increase any more for T < 20 K; in a narrow range between 1400 and 1450 cm−1 the reflectivity even drops and shows evidence for some mode that develops for T < TSP. The mode around 1410 cm−1 is enhanced in the reflectivity ratio R(T = 13 K)/R(T = 20 K), shown for the example of (TMTTF)2PF6, in the right panel.
Figure 31. Reflectivity of (TMTTF)2PF6 and (TMTTF)2AsF6 measured for the polarization Ea at different temperatures as indicated. In both compounds the overall value of R(ν) does not increase any more for T < 20 K; in a narrow range between 1400 and 1450 cm−1 the reflectivity even drops and shows evidence for some mode that develops for T < TSP. The mode around 1410 cm−1 is enhanced in the reflectivity ratio R(T = 13 K)/R(T = 20 K), shown for the example of (TMTTF)2PF6, in the right panel.
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Figure 32. The dielectric losses 2(ν) of (TMTTF)2PF6 and (TMTTF)2AsF6 exhibit a feature around 1410 cm−1 (indicated by the arrows) that builds up when the temperature drops below TSP = 19 and 13 K, respectively. The measurements have been performed with light polarized parallel to the stacks.
Figure 32. The dielectric losses 2(ν) of (TMTTF)2PF6 and (TMTTF)2AsF6 exhibit a feature around 1410 cm−1 (indicated by the arrows) that builds up when the temperature drops below TSP = 19 and 13 K, respectively. The measurements have been performed with light polarized parallel to the stacks.
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Table 1. Transition temperatures for charge localization Tρ and charge order TCO of various Fabre salts (TMTTF)2X. TSP indicates the spin-Peierls transition temperature and TN is the temperature of the antiferromagnetic ordering, determined by transport and magnetization measurements [37,46].
Table 1. Transition temperatures for charge localization Tρ and charge order TCO of various Fabre salts (TMTTF)2X. TSP indicates the spin-Peierls transition temperature and TN is the temperature of the antiferromagnetic ordering, determined by transport and magnetization measurements [37,46].
CompoundTρ (K)TCO (K)TSP (K)TN (K)
(TMTTF)2PF62506719
(TMTTF)2AsF625010213
(TMTTF)2SbF62401578
Table 2. The analysis of the symmetry species and their polarization-dependent activity for the D2h point group of the TMTTF molecule.
Table 2. The analysis of the symmetry species and their polarization-dependent activity for the D2h point group of the TMTTF molecule.
D2h
Symmetrypolarization
InfraredRaman
agxx, yy, zz
b1gxy
b2gxz
b3gyz
au
b1uz
b2uy
b3ux
Table 3. The charge disproportionation 2δ is defined as the difference between charge rich site ρ0 +δ and charge poor sites ρ0δ. First estimates are based on magnetic measurements; here we add the values obtained from our infrared and Raman investigations conducted at low temperatures as indicated in brackets. 2ν10(ag) indicates the first harmonic of the totally symmetric ν10 mode that appears around 1000 cm−1.
Table 3. The charge disproportionation 2δ is defined as the difference between charge rich site ρ0 +δ and charge poor sites ρ0δ. First estimates are based on magnetic measurements; here we add the values obtained from our infrared and Raman investigations conducted at low temperatures as indicated in brackets. 2ν10(ag) indicates the first harmonic of the totally symmetric ν10 mode that appears around 1000 cm−1.
Compound2δ [e]
NMRν28(b1u) IR2ν10(ag) IRν3(ag) IRν3(ag) Raman
(TMTTF)2PF60.28 [39]0.15 (10 K)0.14 (10 K)0.12 (30 K)0.10 (20 K)
(TMTTF)2AsF60.33 [15]0.21 (30 K)0.19 (30 K)0.26 (20 K)0.17 (20 K)
0.50 [11]
0.16 [41]0.11 [41]
(TMTTF)2SbF60.50 [12]0.29 (40 K)0.26 (40 K)
Table 4. The emv-coupling constants for ag modes of the TMTTF molecule calculated by Pedron et al. [75].
Table 4. The emv-coupling constants for ag modes of the TMTTF molecule calculated by Pedron et al. [75].
Modeν3ν4ν7ν8ν9ν10ν11ν12
Frequency (cm−1)1, 6391, 5381, 092934560494277217
gi (cm−1)2429682422421614848181
Table 5. Analysis of the (TMTTF)2 lattice modes using the approximated C2h unit cell.
Table 5. Analysis of the (TMTTF)2 lattice modes using the approximated C2h unit cell.
C2h
Symmetry
Lattice ModesPolarization
Ag T b , T c , R a +aa, bb′, cc, bc
Bg T a , R b + , R c +ab′, ac
Au R a a
Bu R b , R c b′, c
Table 6. Experimental frequencies and assignments of the (TMTTF)2AsF6 lattice modes obtained from our Raman and infrared measurements at room temperature and T ≈ 15 K. Here Sym. denotes the symmetry of the modes and Pol. their polarization.
Table 6. Experimental frequencies and assignments of the (TMTTF)2AsF6 lattice modes obtained from our Raman and infrared measurements at room temperature and T ≈ 15 K. Here Sym. denotes the symmetry of the modes and Pol. their polarization.
300 K
15 K
Assignment
Raman
Raman
infrared
ν (cm−1)Sym.ν (cm−1)Pol.ν (cm−1)Pol.
41Bg43ab R b + or int.
53bb54bTb
48Ag65aa, bb66bTc
74bb75a
77Bg83ab85aTa
Table 7. Experimental frequencies and assignments of the (TMTTF)2PF6 lattice modes obtained from our Raman and infrared measurements at room temperature and T ≈ 15 K. Here Pol. denotes the polarization used.
Table 7. Experimental frequencies and assignments of the (TMTTF)2PF6 lattice modes obtained from our Raman and infrared measurements at room temperature and T ≈ 15 K. Here Pol. denotes the polarization used.
15 K
Assignment
Raman
Infrared
ν (cm−1)Pol.ν (cm−1)Pol.
42ab R b + or int.
54bb54bTb
60
66aa, bbTc
6968a
82ab83aTa

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Dressel, M.; Dumm, M.; Knoblauch, T.; Masino, M. Comprehensive Optical Investigations of Charge Order in Organic Chain Compounds (TMTTF)2X. Crystals 2012, 2, 528-578. https://doi.org/10.3390/cryst2020528

AMA Style

Dressel M, Dumm M, Knoblauch T, Masino M. Comprehensive Optical Investigations of Charge Order in Organic Chain Compounds (TMTTF)2X. Crystals. 2012; 2(2):528-578. https://doi.org/10.3390/cryst2020528

Chicago/Turabian Style

Dressel, Martin, Michael Dumm, Tobias Knoblauch, and Matteo Masino. 2012. "Comprehensive Optical Investigations of Charge Order in Organic Chain Compounds (TMTTF)2X" Crystals 2, no. 2: 528-578. https://doi.org/10.3390/cryst2020528

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