Charge Fluctuations in the Dimer-Mott Insulating State of (rac-DM-EDT

Article pubs.acs.org/JPCC

Charge Fluctuations in the Dimer-Mott Insulating State of (rac-DMEDT-TTF)2PF6 Iwona Olejniczak,*,† Arkadiusz Fra̧ckowiak,† Krzysztof Ptaszyński,† Flavia Pop,‡ and Narcis Avarvari‡ †

Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Poznań, Poland Laboratoire Moltech Anjou, UMR 6200 CNRS, Universite d’Angers, UFR Sciences, Bât. K, 2 Bd. Lavoisier, 49045 Angers, France

‡

S Supporting Information *

ABSTRACT: Low-dimensional molecular conductors are known to display various insulating ground states that result from significant electronic correlations, depending on the degree of dimerization. Of particular interest are intermediate systems where the interplay between dimer-Mott and chargeordered phases is observed. Here we report an optical study of (rac-DM-EDTTTF)2PF6, a weakly dimerized organic conductor that is based on the chiral DM-EDT-TTF donor molecule. Variable-temperature infrared reflectance spectra clearly demonstrate a quasi-one-dimensional response together with a metal−insulator phase transition at 110 K. Both the broadening of the chargesensitive vibrational ν2 mode observed in Raman spectra and the strong EMVactivated ν3 mode in the reflectance spectra polarized in the stack direction suggest the charge fluctuations to develop in the insulating state. Significant modification of the hydrogen-bonding type interaction between the conducting DM-EDT-TTF layer and the PF6 anions is detected below 110 K. We suggest that the low-temperature insulating state in (rac-DM-EDT-TTF)2PF6 should be regarded as a coexistence of the dimer-Mott state and fluctuating charge-order.

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INTRODUCTION In the field of low-dimensional molecular conductors, significant electronic correlations result in various insulating ground states that can be coupled with charge, spin, and lattice degrees of freedom.1 In weakly dimerized quarter-filled compounds with one hole per two donor molecules, the charge is localized due to intersite Coulomb repulsion V, leading to the insulating charge-ordered (CO) phase, as observed in θ-(BEDT-TTF)2RbZn(SCN)4 [BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene].2 On the other hand, the dimer-Mott (DM) insulating state is realized in dimerized systems that are effectively half-filled, with the on-site electron repulsion U as the most important parameter,3 and a typical example is κ-(BEDT-TTF)2Cu[N(CN)2]Cl.4 It has been suggested that both the magnetic fluctuations in the vicinity of the Mott transition and charge fluctuations in the vicinity of the CO phase can be relevant for superconductivity.5−8 It is also known that charge degrees of freedom that exist within a dimer unit can constitute electronic ferroelectricity that is of current interest in the solid state physics due to possible applications.9−11 In fact, charge-order-driven ferroelectricity has been suggested based on dielectric measurements in (TMTTF)2X salts [TMTTF: tetramethyltetrathiafulvalene],12 α-(BEDT-TTF) 2 I 3 , 13 β′-(BEDT-TTF) 2 ICl 2 , 14 κ-(BEDTTTF)2Cu[N(CN)2]Cl,15 and a quantum spin liquid (QSL) candidate κ-(BEDT-TTF)2Cu2(CN)3,16−19 even in the absence of a clear spectroscopic evidence for charge-ordered states.20−22 Despite these findings we are still lacking a comprehensive picture of the interplay between dimer-Mott and chargeordered phase that unquestionably exists. Of particular interest © 2017 American Chemical Society

are therefore intermediate systems which can be located between the 1/4-filled and effectively 1/2-filled. Recently, dimer-Mott instability has been discovered in the chargeordered dimerized organic salt β-(meso-DMBEDT-TTF)2PF6,23 whereas a possibility of dynamic charge fluctuations has been discussed in the case of another QSL candidate κ-(BEDTTTF)2Ag2(CN)3.24 With this paper, we present the (rac-DMEDT-TTF)2PF6 organic conductor, which we consider a good candidate for investigations of charge order effects within the dimer-Mott insulating state. (rac-DM-EDT-TTF)2PF6 [DM-EDT-TTF = dimethyl-ethylenedithio-tetrathiafulvalene] belongs to a quickly growing family of low-dimensional conductors, which were synthesized by an approach involving controlled introduction of chirality into tetrathiafulvalene-derived radical.25−34 Unsymmetrical donor molecules in chiral conductors are arranged in a headto-tail manner, and the resulting materials are usually classified as two-dimensional (2D) layered molecular conductors. In some cases chiral conductors display unusual electrical and magnetic properties,35−37 or new functionalities, as in the case of two enantiopure salts ((S,S)-DM-EDT-TTF)2ClO4 and ((R,R)-DM-EDT-TTF)2ClO4 that were recently demonstrated to display an electrical magneto-chiral anisotropy effect.38 The molecular conductor (rac-DM-EDT-TTF)2PF6, that is of interest here, crystallizes in the triclinic system, centrosymmetric space group P1.̅ There are two DM-EDT-TTF donor Received: August 11, 2017 Revised: September 19, 2017 Published: September 19, 2017 21975

DOI: 10.1021/acs.jpcc.7b08037 J. Phys. Chem. C 2017, 121, 21975−21984

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The Journal of Physical Chemistry C molecules (Figure 1a) in the unit cell, one (R,R)-DM-EDTTTF enantiomer, and one (S,S)-DM-EDT-TTF enantiomer,

that is based on another unsymmetrical, but achiral, tetrathiafulvalene derivative; both materials have quite similar room temperature structures, the same space group, almost the same unit cell parameters, and the same anion. As expected for a weakly dimerized quarter-filled organic conductor, (rac-DM-EDT-TTF)2PF6 displays metallic conductivity at room temperature and undergoes the metal− insulator (MI) phase transition at TMI = 110 K on lowering the temperature. The structure does not change between room temperature and 100 K apart from the usual thermal contraction. Consequently, quasi-one-dimensional (Q1D) Fermi surfaces of (rac-DM-EDT-TTF)2PF6, that consist of significantly warped open lines, do not change much. Chargeor spin-density-wave instabilities have been ruled out as a possible origin of the transition. Within the correlated picture, that is therefore more appropriate for (rac-DM-EDTTTF)2PF6, we could expect two kinds of electronic localizations, a charge-ordered state characteristic for a regular/ weakly dimerized stack of donor molecules that involves the presence of charge-rich and charge-poor molecules, or a dimerMott state in the presence of significant dimerization, with one hole localized on a dimer and donor molecules equally charged +0.5. Taking into account no change in symmetry of the crystal structure of (rac-DM-EDT-TTF)2PF6 and lack of evidence for differently charged donor molecules from preliminary Raman study, the dimer-Mott ground state was recently suggested for this material.30 With the present paper we report a detailed infrared and Raman spectroscopic study of (rac-DM-EDT-TTF)2PF6. The optical conductivity spectra display a quasi-one-dimensional response together with clear signatures of the 110 K metal− insulator phase transition. Unusual broadening of a CC stretching mode observed in the Raman spectra below 110 K suggests the presence of charge fluctuations. Our goal is to provide more understanding of the charge distribution in the dimer-Mott insulating state of the (rac-DM-EDT-TTF)2PF6 molecular conductor.

Figure 1. (a) Molecular structure of DM-EDT-TTF, (b) Simplified molecular arrangement of the conducting layer of (rac-DM-EDTTTF)2PF6 with five different transfer integrals; here t1 and t2 are the intradimer and interdimer transfer integrals in the stack direction, and t5 denotes the largest interstack interaction, t2/t1 ≈ 0.8 and t5/t1 ≈ 0.1.30 Dimers are marked out in the structure.

related by an inversion center.30 All fluorine atoms of the anion are involved in short H···F contacts with vinyl, ethylene, and methyl H atoms of DM-EDT-TTF. The donor molecules are arranged into parallel weakly dimerized stacks along the a-b direction considerably coupled in the interstack a + b direction, with five different donor···donor interactions in the conducting layer (Figure 1b). Such structure resembles a β-type arrangement of BEDT-TTF salts.39 In fact, a similar structure of the conducting layer is found in β-(meso-DMBEDT-TTF)2PF6,40

Figure 2. Polarized reflectance (a,b) and optical conductivity (c,d) spectra in the conducting plane of (rac-DM-EDT-TTF)2PF6 (E∥a−b denotes polarization along the stacking direction, and E∥a + b denotes polarization perpendicular to the stacking direction), at several temperatures between 300 and 10 K. The insets in panels (c) and (d) demonstrate comparison between conductivity spectra in the metallic (300 K) and insulating (10 K) states, in the broad frequency range. As one can notice, spectral weight builds up in the insulating phase at about 1100 cm−1 in both polarization directions. 21976


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EXPERIMENTAL SECTION Single crystalline samples of (rac-DM-EDT-TTF)2PF6 were obtained by electrocrystallization.30 The average size of elongated plates was 1 × 0.2 × 0.05 mm3. The optical axes of the samples were determined in infrared measurements as those displaying the largest anisotropy. The spectra were measured in the two directions, nearly parallel to the stacking axis (E∥a-b) and to the interstack axis (E∥a + b). The polarized reflectance spectra were recorded in the frequency range 700− 10000 cm−1 with a resolution of 4 cm−1 employing a Bruker Equinox 55 FT-IR spectrometer equipped with a Hyperion 1000 infrared microscope and a set of suitable polarizers. The absolute values of the optical reflectance were obtained using an aluminum mirror. The optical conductivity was calculated from the reflectance spectra through a Kramers−Kronig analysis.41 In the low-frequency range the data were extrapolated assuming a constant value for the insulating response and the HagenRubens behavior for the metallic response. Beyond the highfrequency limit the data were extrapolated to zero assuming a ω−2 behavior up to 106 cm−1 and a ω−4 behavior for higher frequencies. Raman spectra were measured with backscattering geometry from 1400 to 1600 cm−1 with the electrical vector of the laser beam parallel to the a + b axis, using a Raman LABRAM HR800 spectrometer equipped with a microscope, and two excitation lines, λ = 488 and 514.5 nm. The intensity of the laser beam was reduced to less than 0.1 mW to avoid sample overheating. The spectra were measured with a spectral resolution 2 cm−1. The temperature dependence of both the optical reflectance and Raman spectra was obtained using a continuous-flow coldfinger cryostat from Oxford Instruments. To achieve good thermal contact, the single crystals were mounted with vacuum grease. The spectra were taken for several temperatures from 300 to 10 K. Raman spectra with 488 nm excitation measured at 300, 200, 110, 70, and 10 K have already been published in ref 30 and are reproduced here for comparison and comprehensive discussion. The distances R between molecular centers in the crystal structure were estimated based on the structural data,30 taking into account the central part of the DM-EDT-TTF molecule including the TTF moiety with the two additional S atoms.

in the stack direction (Figure 2c) consists of a broad electronic band that ranges between 700 and 3000 cm−1. This lowfrequency electronic feature grows with lowering the temperature from 300 to 10 K into a rather sharp band centered at about 1100 cm−1, with most of the intensity increased below about 120 K. The vibrational modes of the DM-EDT-TTF donor molecule, activated via electron-molecular vibration (EMV) coupling with the electronic background,44 are also enhanced in the insulating phase. At the same time, the optical conductivity spectra polarized in the interstack direction (Figure 2d), while considerably lower, are characterized by a similar electronic band that appears at 1100 cm−1 below 110 K. Another electronic feature at about 7000 cm−1 together with the normally infrared active vibrational modes observed below about 1200 cm−1, display weak temperature dependence. Within the correlated Hubbard picture of a DM insulator, in the infrared frequency range we usually observe two main electronic contributions including interdimer excitation (Hubbard band) and intradimer excitation (dimer band);45−47 the interdimer band appears in the spectrum at lower frequency than the intradimer band, and its position gives an estimation for the effective on-dimer Coulomb interaction Ud. The overall shape of the spectrum strongly depends on the degree of dimerization. In the weak dimerization limit, both the Hubbard and dimer excitations are shifted to lower frequency, forming a single band component below about 2500 cm−1; while the dimer peak is not clearly seen in this case, it is usually present together with the Hubbard band.46 In the strong dimerization limit the energy of the dimer band is significantly higher than that of the Hubbard band and can be approximated by 2td, where td is the intradimer transfer integral.47,48 Let us consider the weakly dimerized molecular structure of (rac-DM-EDT-TTF)2PF6 as composed of dimer units, with t2/ t1 ≈ 0.8 in the stack direction (Figure 1b). In fact, in the lowtemperature optical conductivity spectra polarized in this direction we observe a single band component at 1100 cm−1, most probably including both the inter- and intradimer excitations. The narrow shape of the feature together with the significant temperature dependence (inset in Figure 2c) are characteristic for the interdimer Hubbard band in the 1D Mott insulator.47 The strong vibronic Fano-shaped dip at about 1300 cm−1,49 that usually appears in the spectra of low-dimensional organic conductors as a result of coupling of the central CC bond stretching mode of the donor molecule with the intradimer charge transfer, is a direct proof for the presence of the dimer mode at similar frequency. It also confirms that (rac-DM-EDT-TTF)2PF6 is dimerized in the whole temperature range,50 in agreement with structural data.30 The Hubbard band at 1100 cm−1 also appears below 110 K in the conductivity spectra polarized in the interstack direction (Figure 2d). At the same time, we assign a relatively strong absorption at 7000 cm−1 (inset in Figure 2d), that is present in the interstack direction in the whole temperature range, as the intradimer band in agreement with the dimer Mott picture. No EMV-related features are found in this polarization, which reflects the fact that the intramolecular vibrations of the DMEDT-TTF donor molecule are well separated in the spectra from the dimer band. The optical conductivity spectra of (rac-DM-EDT-TTF)2PF6 below 110 K validate the insulating DM phase proposed in this material.30 However, it is unclear if the response above 110 K is metallic or rather consistent with the dimer Mott state, as recently suggested in the case of the β-(meso-DMBEDT-

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RESULTS AND DISCUSSION Electronic Response. Figure 2 shows the reflectance and conductivity spectra of (rac-DM-EDT-TTF)2PF6 polarized along the stacking axis (a−b) and interstack axis (a + b) in the conducting plane, measured at several temperatures between 10 and 300 K. The large anisotropy of the reflectance (Figure 2a,b) is characteristic for a quasi-one-dimensional conductor. In general, the reflectance spectra of (rac-DM-EDTTTF)2PF6 along the stacking axis (Figure 2a) are similar to the response of Q1D TMTSF (tetramethyltetraselenafulvalene) salts,42,43 with a high reflectance level in the middle infrared range and a drop indicating plasma frequency at about 8000 cm−1. Reflectance polarized in the interstack direction (Figure 2b) is significantly lower, with a plasma drop at about 2000 cm−1. The optical conductivity spectra of (rac-DM-EDT-TTF)2PF6 calculated based on the measured reflectance are shown in Figure 2c,d. It can be noticed that the spectral intensity in the stack direction is about 10 times larger than that in the perpendicular direction, following the ratio between the respective transfer integrals.30 The room temperature spectrum 21977


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The Journal of Physical Chemistry C TTF)2PF6 organic conductor that is characterized by similar conductivity spectra in the interstack direction.23,51 Both materials display a transition from high-temperature conducting to low-temperature insulating phase at ambient pressure,40,52 but unlike (rac-DM-EDT-TTF)2PF6, the β-(meso-DMBEDTTTF)2PF6 material is two-dimensional and displays long-range charge ordering below Tc = 70 K.53 It was found that due to the very small band gap between the upper and lower bands, the β(meso-DMBEDT-TTF)2PF6 material cannot be regarded as fully dimerized.54 Therefore, from the point of view of the band structure we should probably consider both the (rac-DM-EDTTTF)2PF6 and β-(meso-DMBEDT-TTF)2PF6 salts as moderately dimerized, between 1/2-filled and 1/4-filled, with both U and V Coulomb parameters equally important. In the conductivity spectra of β-(meso-DMBEDT-TTF)2PF6 Okazaki et al. observe a dimer band centered at 4800 cm−1 together with the low-frequency band at 1600 cm−1 related with CO, and discuss their optical results in terms of the competition between the DM and CO insulating phases.23 In particular, they discuss a strong enhancement of the dimer band at 4800 cm−1 with lowering the temperature from 300 K to Tc, as a signature of the DM state.55 On the other hand, recent experimental46 and theoretical56 studies of κ-(BEDT-TTF)2Cu[N(CN)2]Cl suggest that both the frequency and oscillator strength of the dimer band remain basically unchanged on entering the Mott insulating phase. Unlike β-(meso-DMBEDTTTF)2PF6, the dimer band observed at 7000 cm−1 in (rac-DMEDT-TTF)2PF6 displays only minor changes with the temperature. In addition, the (rac-DM-EDT-TTF)2PF6 material displays substantially higher conductivity at room temperature, 250 S·cm−1 compared with 15 S·cm−1 in β-(meso-DMBEDTTTF)2PF6.30,40 Taking into account the lack of clear evidence for the DM insulator, we suggest that the high-temperature phase of (rac-DM-EDT-TTF)2PF6 should be regarded as ”bad metal”.46,51,55 It is known that DM insulator is unstable toward chargeordered states in the presence of weak dimerization,39,57,58 that is characteristic for (rac-DM-EDT-TTF)2PF6. We shall therefore discuss the possibility of charge fluctuations in the insulating phase below 110 K. Metal−Insulator Transition. In the resistivity measurement of (rac-DM-EDT-TTF)2PF6, a dramatic change in the slope is observed at 110 K, indicating the temperature of the metal−insulator phase transition.30 In our optical study, the conductivity in the low-frequency range is significantly enhanced below about 110 K (see Figure 2c,d). In order to examine changes of the Hubbard band centered at 1100 cm−1, we focus on the spectra polarized in the interstack direction, where it appears not disturbed by either the dimer band or EMV-related effects. The Hubbard band in this polarization is partly hidden in the far-infrared range above 110 K but shows a clear blue shift on lowering the temperature through TMI, from about 600 cm−1 up to 1100 cm−1; below 110 K the band’s position is almost constant (Figure 3a). Such a shift of the spectral weight from far-infrared to higher frequencies is likely related with the optical gap that develops at TMI. The values of reflectance compared for frequencies 900 and 1430 cm−1 (Figure 3b) also confirm gap opening. The sharp spectral change we observe in (rac-DM-EDT-TTF)2PF6 is therefore strongly correlated with the MI phase transition displayed in resistivity. We cannot directly observe the gap in our study. Most probably it is hidden in the far-infrared, in agreement with

Figure 3. Temperature dependence of the (a) Hubbard band frequency, (b) reflectance values at 900 and 1430 cm−1, in the interstack a + b direction; the Hubbard band position has been estimated based on the Lorentz fit. Here we demonstrate distinct changes of the electronic response between high-temperature metallic and low-temperature insulating phases.

the activation energy calculated based on the resistivity measurement, Ea ≈ 300 cm−1.30 Changes in electronic structure at 110 K can be recognized in the totally symmetric vibrational modes of DM-EDT-TTF donor molecule activated due to EMV-coupling. These socalled vibronic modes give a unique opportunity to study phase transitions related with the presence of a dimerized structure.50 The strongest vibronic feature observed in the infrared spectra of organic conductors based on BEDT-TTF donor molecule is usually the bridge CC stretching vibration labeled ν3 in the D2h point group symmetry, which has a large coupling constant.59 The pattern of the respective stretching CC mode of the chiral DM-EDT-TTF donor molecule assigned here as ν3 after BEDT-TTF is shown in Figure 4.

Figure 4. Schematic view of the three CC stretching modes of the neutral DM-EDT-TTF molecule, labeled here as ν2, ν27, and ν3 after similar modes of BEDT-TTF in D2h molecular symmetry (ref 30).

While the broad and rather weak ν3 mode clearly seen in (rac-DM-EDT-TTF)2PF6 at about 1300 cm−1 at room temperature is characteristic for a metallic response, it develops into a huge dip with the antiresonance Fano shape on lowering the temperature (Figure 5a). To disentangle the contributions from the electronic band centered at about 1300 cm−1 and the ν3 mode, we fitted optical conductivity spectra in the relevant frequency range using one Lorentz function for the overall 21978


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(BEDT-TTF)2Cu[N(CN)2]Cl.55 The ν3 feature becomes remarkably enhanced in the conductivity spectra of (rac-DMEDT-TTF)2PF6 with lowering the temperature, probably not due to dimerization because it is not changed at the phase transition.30 On the other hand, the ν3 mode is known to induce oscillations of charge within a dimer unit. Therefore, charge oscillations are most probably present in the insulating phase in (rac-DM-EDT-TTF)2PF6. In the infrared spectra of (rac-DM-EDT-TTF)2PF6 polarized in the interstack direction we also found a distinct temperature dependence of the antisymmetric PF stretching ν3(t1u) mode of the PF−6 anion (Figure 6a).60 The two mode components νFP 3a

Figure 5. Temperature dependence of the optical conductivity spectra of (rac-DM-EDT-TTF)2PF6 in the frequency range of vibrational modes. (a) A close-up view of DM-EDT-TTF modes in the stack direction activated due to coupling with the electronic background; the inset displays a weak ν3 overtone observed at low T. (b) Calculated Fano band shapes of the ν3 mode for selected temperatures, together with the values of the respective coupling q parameter. Panel (c) shows the temperature dependences of the normalized band intensities of both the ν3 band from Fano fits and the CH3 stretching mode at 1100 cm−1 that dramatically increases below 110 K.

Figure 6. (a) Stretching PF modes of the PF−6 anion observed in the interstack direction; arrows point to the νFP 3 mode components. Panel (b) displays softening of the stretching νFP 3 mode components below 110 K; the doublet structure reflects two different short H···F contacts in the structure. −1 and νFP 3b , centered at 800 and 830 cm , respectively, display a significant softening with lowering the temperature through TMI (Figure 6b). Also, the shape of these two features is changed in the insulating phase, from approximately symmetric and rather narrow into the asymmetric, suggesting a doublet structure. This significant change of the stretching modes of the PF6 anion reflects changes in the hydrogen-bonding type interaction between the DM-EDT-TTF layer and the PF6 anions. Charge Fluctuations. In order to clarify the origin of the MI phase transition in (rac-DM-EDT-TTF)2PF6, we now consider the possible charge-ordered states that are characteristic for weakly dimerized BEDT-TTF salts.6,61,62 Infrared and Raman spectroscopy is frequently used in investigations of charge disproportionation in these materials,59,63,64 with the focus on two charge-sensitive stretching CC vibrations: the in-phase ν2 mode observed in the Raman spectra and the outof-phase ν27 mode that is infrared-active. Both these modes are characterized by a linear relationship between frequency and charge, a large frequency shift on ionization, and a small time resolution that allows investigation of both localized and delocalized charge-ordered states.62,63 It is important to note here that vibrational spectroscopy is the local probe while the X-ray structural studies usually detect only the long-range order. The mode patterns of the three stretching CC vibrations of the DM-EDT-TTF donor molecule are shown in Figure 4. Due to low molecular symmetry, all these modes are Raman-active.30 Figure 7 displays the temperature dependence of the Raman spectra of (rac-DM-EDT-TTF)2PF6 in the frequency range of

electronic component and one Fano function for the ν3 mode, neglecting narrow vibrational features (Figure S1). Based on the phenomenological Fano model,49 the real part of the conductivity is expressed with the formula σ1Fano(ν) = σ0

γν[γν(q2 − 1) + 2q(ν 2 − ν02)] (ν 2 − ν02)2 + γ 2ν 2

(1)

with the phenomenological coupling parameter q, line width γ, resonance frequency ν0 = ω0/2πc, and spectral weight that describes intensity equal to ∫ |σ1(ν)|dν. Figure 5b displays the fitted Fano shapes for selected temperatures, together with the respective coupling parameter q. Our results indicate that the ν3 mode shifts to lower frequencies with lowering temperature, from about 1390 cm−1 at 240 K to 1310 cm−1 at 10 K. The q-values are close to zero, in agreement with the antiresonance shape characteristic for strong coupling. The two lowest temperatures are characterized by the positive q-values, which means that the maximum of the shape is located at higher frequencies, while the negative qvalues are obtained for T ≥ 100 K. Other vibrational modes most probably coupled with charge transfer are hardly visible at high temperatures but quickly increase their intensity below TMI = 110 K (marked by arrows in Figure 5a). Figure 5c shows the temperature evolution of the normalized intensity of both the calculated ν3 Fano band and the CH3 stretching mode, that quickly grows below 110 K, reflecting the localized nature of charge carriers in the insulating state. Similar behavior of vibronic modes was earlier observed in the Mott insulator κ21979


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64, we use the model to account for the ν2 mode broadening at low temperature in (rac-DM-EDT-TTF)2PF6. The band-shape function is assumed to be the real part of the complex function: 3(ω) =

-[(γ + 2υex ) − i(ω − ωw )] 2

9 − (ω − ω1)(ω − ω2) − 2i Γ(ω − ωav ) (2)

Here - = f1 + f 2, with f1 and f 2 being the oscillator strengths of the bands of the frequency ω1 and ω2 and halfwidth γ, υex is the charge fluctuation velocity, and Γ = γ + υex is the summarized width. The average and weighted frequency, ωav and ωw, are defined as ωav = (ω1 + ω2)/2 and ωw = (f 2ω1 + f1ω2)/( f1 + f 2), and 9 2 = 2γυex + γ2. In the case of slow charge fluctuations, we can expect two separate bands, that merge into one broaden shape for fast fluctuations. In our case we use formula (2) to fit the ν2 mode observed in the Raman spectra of (rac-DM-EDTTTF)2PF6 measured with λ = 488 nm at temperatures 10, 70, and 90 K (Figure 7a) (in the case of 50 K the fit failed due to excessive noise). The fitting results shown in Figure 8a for the Figure 7. Raman spectra of (rac-DM-EDT-TTF)2PF6 in the frequency range of the stretching CC modes of DM-EDT-TTF, polarized in the a + b direction, at selected temperatures between 300 and 10 K, measured with λ = 488 nm (a) and λ = 514.5 nm (b). The frequency difference of the two ν2 components marked on the figure as ν2R (charge-rich molecules) and ν2P (charge-poor molecules) was estimated using the model (see text) (a) or assuming splitting of the ν2 mode into two Lorentz components (b).

the stretching CC modes of the DM-EDT-TTF donor molecule, measured in two separate experiments with laser wavelengths λ = 488 and 514.5 nm. Similarly to many BEDTTTF salts, the spectra display two characteristic features. Based on density functional theory (DFT) calculations,30 and earlier work on BEDT-TTF salts,63,64 we assign the band at 1473 cm−1 as related with both the ν3 and ν27 mode components that are not sensitive to charge. Molecular charge can be determined based on the shape and position of the second band centered at about 1520 cm−1, that we assign as the ν2 mode of the DMEDT-TTF molecule with average charge +0.5.30 ν2 usually becomes narrower with lowering the temperature, unless charge disproportionation occurs.64 In (rac-DM-EDT-TTF)2PF6 it is characterized by a broadened shape already at room temperature and does not display a clear splitting down to 10 K, that would be characteristic for a typical charge-ordered state (Figure 7). We rather observe an increasing broadening of the ν2 mode when lowering the temperature in the insulating phase below 110 K. While weak, this effect becomes obvious if we compare Figures 7a and 7b. Since the frequency of the ν2 mode depends on the charge localized on the molecule, the broad line width suggests the presence of charge fluctuations. The charge order in organic conductors is often not complete but fractional D0.5+Δρ/2D0.5−Δρ/2, where D0.5+Δρ/2 (D0.5−Δρ/2) means a chargerich (charge-poor) donor molecule, and Δρ is the ionicity difference. Depending on Δρ and the time scale of charge fluctuations, we can observe a broadening or splitting of a mode. The asymmetric shape observed in (rac-DM-EDT-TTF)2PF6 in the case of ν2 (Figure 7) is related with different mode intensities of differently charged molecules. Such a band shape can be discussed using the ”two-states-jump model” introduced by Kubo that describes the charge hopping between two molecules.65 Following the procedure described in refs 21 and

Figure 8. Results of modeling selected Raman spectra of (rac-DMEDT-TTF)2PF6 for λ = 488 nm using the ”two-states-jump model” (see text). (a) ν2 mode observed at 10 K, approximated with the model. (b) Charge fluctuation velocity υex, and charge difference Δρ, as a function of temperature. The error bars were estimated based on points obtained with slightly different fitting conditions.

10 K Raman spectrum display a relatively broad asymmetric shape, which is characteristic for υex ≈ |ω1 − ω2|/2. As a result we obtain the frequencies of the two ν2 mode components ν2R and ν2P (Figure 7a). Above 90 K the ν2 mode while still relatively broad displays symmetrical shape and the model becomes unreliable. This effect may be partly related with the fact that the charge fluctuations are suppressed in the metallic phase.66 Therefore, the presence of charge fluctuations above TMI = 110 K is uncertain within the accuracy of our Raman experiment. While the lower frequency ν2R component in our calculations does not show any significant frequency shift between 10 and 90 K, the higher frequency ν2P component of the charge-poor 21980


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The Journal of Physical Chemistry C molecules shifts from 1527 cm−1 at 10 K to 1521 cm−1 at 90 K. Such a behavior is characteristic for dimerized BEDT-TTF salts, where, in the presence of the strong EMV coupling, only the higher frequency ν2 component is described by linear dependence of the frequency on charge.64 Therefore, to estimate the ionicity difference Δρ between the charge-rich and charge-poor molecule in (rac-DM-EDT-TTF)2PF6, we employ the formula: Δρ =

ν2P − 1516 cm−1 43 cm−1

e

The fluctuating charge order in (rac-DM-EDT-TTF)2PF6 is different than that observed in β-(meso-DMBEDT-TTF)2PF6. The latter material displays a clear band splitting of the counterparts of the ν27 and ν2 modes at low temperature in the long-range CO phase,23,51 that was confirmed by structural study.53 On the other hand, a similar broad and asymmetric shape of the ν2 mode as in (rac-DM-EDT-TTF)2PF6 below 110 K has been observed in the whole temperature range in the QSL candidate κ-(BEDT-TTF)2Ag2(CN)3 by Nakamura et al.,24 who discussed their data in terms of the dynamic charge fluctuation. This is in contrast with the results for (rac-DMEDT-TTF)2PF6, where the broadened shape of ν2 appears below 110 K, indicating that charge fluctuations can be closely related with the DM insulating state. To address the question whether CO fluctuations in (racDM-EDT-TTF)2PF6 are fully dynamic or related with some local symmetry lowering, we focus on the temperature dependence of the PF stretching ν3(t1u) mode of the PF−6 anion that displays both the softening and broadening below 110 K (Figure 6a). It is known that the ground state physical properties of organic conductors including charge ordering states can be influenced by disorder in the anion layer, through close contacts between the anion and the conducting donor layer.17,69,70 Most probably, such a mechanism is not relevant in the case of the (rac-DM-EDT-TTF)2PF6 material, as the octahedral PF6 anion is ordered.30 The behavior of the stretching PF mode components suggests, however, an increased disorder at low temperature with fluctuations between two possible local configurations. There is no evidence that the anion layer could drive the system into the insulating ground state itself. Close contacts between donor molecules and PF6 anions probably just follow changes in the conducting layer, in line with recent extensive investigations of (TMTTF)2X salts.71,72 The charge on dimers in the dimerized materials can locally fluctuate through the largest transfer integral that is equal to 0.36 eV in (rac-DM-EDT-TTF)2PF6.30 Considering the possible short-range CO order pattern we recall the earlier studies of β-(meso-DMBEDT-TTF)2PF6 that suggest shortrange order of the checkerboard CO phase in competition with the DM state and/or diagonal and horizontal CO fluctuations above the metal−insulator phase transition.51 More recently, Mori discussed the universality of the nonstripe charge order in dimerized dimer Mott systems.73 He suggests that the charge order pattern is strongly related with the Coulomb V parameters, that are quite uniform comparing transfer integrals among different materials. Following his approach, we estimate intermolecular Coulomb V parameters in (rac-DM-EDTTTF)2PF6 using the inverse of the R distance between molecular centers (Table 1). The relative parameters V/Vav

(3)

where 43 cm−1 is the frequency shift of the ν2 mode between 1559 cm−1 for the neutral DM-EDT-TTF molecule30 and 1516 cm−1 for DM-EDT-TTF in (rac-DM-EDT-TTF)2PF6 above 110 K (Figure 7), that we consider as related with the charge +0.5. Both the charge fluctuation velocities υex and ionicity difference Δρ are shown in Figure 8b. Our results suggest that increasing charge fluctuations develop with lowering the temperature in the insulating phase of (rac-DM-EDTTTF)2PF6, with the estimated values of Δρ and υex at 10 K equal ≈ +0.25 e and ≈0.8 cm−1, respectively. Most probably, no long-range CO is stabilized at low temperature based on our Raman experiment, in agreement with the structural data.30 Such a broadened shape of the ν2 mode as displayed in (racDM-EDT-TTF)2PF6 has been earlier observed in a number of nondimerized or weakly dimerized BEDT-TTF salts characterized by the so-called β″ packing in the vicinity of the insulator−superconductor transition temperature,62,64 and also in the more dimerized κ-phase spin-liquid candidates κ-(BEDTTTF)2Cu2(CN)3 and κ-(BEDT-TTF)2Ag2(CN)3.24,66 These data were discussed in terms of inhomogeneous charge distribution62 or charge fluctuations.24,64,66 Another feature, that confirms the presence of charge order fluctuations is a weak band that appears at 2750 cm−1 in the conductivity spectra polarized in the stack direction below 90 K (see the inset in Figure 5a). Its shape at 10 K closely follows the shape of the huge ν3 dip at the same temperature and emerges at the doubled frequency of this mode observed at 1370 cm−1; therefore, we assign the band as the ν3 overtone. It is known that such a feature develops as a result of anharmonicity in the presence of both the EMV-coupling and charge-ordered states within a dimer.67,68 That the 2750 cm−1 mode is very weak most probably reflects the two facts that we do not observe any static charge order in (rac-DM-EDT-TTF)2PF6 down to the lowest temperature and that Δρ is relatively small.67 Low-Temperature Insulating State. The analysis of the infrared and Raman spectra of (rac-DM-EDT-TTF)2PF6 provides a more complicated picture of the low-temperature insulating state than a simple dimer-Mott insulator. While the optical conductivity spectra (Figure 2) display characteristics of the DM state together with the relatively sharp change at TMI (Figures 3 and 5), the Raman spectra (Figure 7) demonstrate gradual broadening of the charge-sensitive ν2 mode below 110 K, suggesting that charge fluctuations develop with lowering the temperature in the insulating state. The temperature evolution of the Raman spectra below 110 K shows that no long-range CO is established down to the lowest temperature, in agreement with the X-ray analysis that did not find any charge disproportionation or symmetry breaking.30 This leads to the conclusion that the charge fluctuations exist within the DM insulating state regarded as the primary ground state.

Table 1. Transfer Integrals t at Room Temperature in (racDM-EDT-TTF)2PF6, together with Intermolecular Distances R and Coulomb Interactions V/Vav, Where Vi ∼ 1/Ri and Vav Are the Average of the Interstack Interactions

I II III IV V 21981

Interaction

t (eV)30

R (Å)

V/Vav

intradimer interdimer interstack interstack interstack

0.3600 0.3049 0.0200 0.0143 0.0346

4.082 4.368 6.204 6.377 6.666

1.59 1.48 1.04 1.02 0.97


Article

The Journal of Physical Chemistry C (last column), with Vav being the average of the interstack interactions, fit very well in Mori’s description.73 Similarly to β(meso-DMBEDT-TTF)2PF6 that is characterized by a checkeboard-type charge ordering at low temperature, the interstack interactions are uniform and only about 1.5 times smaller than the average relative Coulomb repulsion in the stack direction (compare Table 1 and Table 1 in ref 73). Thus, we suggest that the low-temperature insulating state in (rac-DM-EDTTTF)2PF6 can be related with the local fluctuations between equivalent configurations, including possibly the DM and checkerboard CO phases. Such a fluctuation state lowering the local symmetry can appear within a specific domain structure.17 In this regard, it is worth comparing present results for (racDM-EDT-TTF)2PF6 with those recently reported for the dimerized κ-(BEDT-TTF)2Hg(SCN)2 organic conductor that undergoes a similar MI transition at 80 K and is suggested to display charge fluctuations.74,75 The optical conductivity spectra of κ-(BEDT-TTF)2Hg(SCN)2 in the stack direction, similarly to (rac-DM-EDT-TTF)2PF6, display strong temperature dependence below 1500 cm−1.74 On the other hand, the charge-sensitive ν2 vibration of the BEDT-TTF molecule observed in the Raman study as a broad band, unlike (racDM-EDT-TTF)2PF6, does not show a clear change when lowering the temperature through the transition, although the authors notice some change in its width together with an appearance of a collective mode at 40 cm−1 that they relate to charge fluctuations within a dimer, possibly a signature of a quantum dipole liquid state at low temperature.75 Such a state is different than local fluctuations we propose for (rac-DMEDT-TTF)2PF6 that displays the broadening of the ν2 mode below TMI. We argue that the low-temperature insulating state in the (rac-DM-EDT-TTF)2PF6 material can be considered as the dimer-Mott state combined with the charge order fluctuations. An important ingredient here is likely the strong EMV coupling of the ν3 stretching CC mode that is known to induce charge oscillations within a dimer. We envision that the fluctuating CO appears in the insulating state of (rac-DM-EDT-TTF)2PF6 as a result of a subtle cooperative mechanism that stems from a specific configuration of the intermolecular Coulomb Vij parameters, EMV coupling, and structural details including hydrogen bonding between anions and a conducting layer. However, more investigations are needed to clarify the ground state physical properties of (rac-DM-EDT-TTF)2PF6. In particular, a magnetic study would be essential to discuss the spin configurations at low temperature.

temperature due to a specific configuration of intermolecular Coulomb repulsion parameters.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b08037. Selected optical conductivity spectra (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +48 618695271. Fax: +48 618684524. ORCID

Iwona Olejniczak: 0000-0002-7651-7204 Narcis Avarvari: 0000-0001-9970-4494 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in Poland by the Institute of Molecular Physics Polish Academy of Sciences. In France, the work was supported by the CNRS, the University of Angers and the National Agency for Research (ANR Inter, ANR-12IS07-0004-04, CREMM Project).

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REFERENCES

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CONCLUSIONS In summary, we have investigated the optical properties of the (rac-DM-EDT-TTF)2PF6 organic conductor, using infrared and Raman spectroscopy. Our results demonstrate a quasi-onedimensional response. The metal−insulator phase transition at 110 K is clearly seen in both the electronic bands and vibrational modes in the reflectance spectra, and the lowtemperature optical response is characteristic for the dimerMott insulator. Broadening of the charge-sensitive stretching CC mode in Raman spectra below 110 K is discussed in terms of charge fluctuations that develop in the insulating state with lowering the temperature. Based on the similarities with the optical response of the β-(meso-DMBEDT-TTF)2PF6 charge-ordered organic conductor, we propose that fluctuating charge order within the dimer-Mott insulating phase in the (rac-DM-EDT-TTF)2PF6 organic conductor is stabilized at low 21982


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Charge Fluctuations in the Dimer-Mott Insulating State of (rac-DM-EDT

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