Evidence for a quantum dipole liquid state in an organic quasi–two-dimensional material

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Science  08 Jun 2018:
Vol. 360, Issue 6393, pp. 1101-1104
DOI: 10.1126/science.aan6286

Quantum dipoles go liquid

Quantum spin liquids do not achieve an ordered magnetic state, even at the lowest temperatures. Hassan et al. studied an organic compound that may be both a spin liquid and a dipole liquid (see the Perspective by Powell). In the layered material κ-(BEDT-TTF)2Hg(SCN)2Br, molecules form charged dimers whose sites are arranged on a triangular lattice. The extra charge associated with each dimer can “live” on one of the two molecules in the dimer, resulting in a nonzero electric dipole moment for the dimer. Raman spectroscopy and heat capacity measurements revealed that, like spins in a quantum spin liquid, these dimers remained disordered down to the lowest temperatures.

Science, this issue p. 1101; see also p. 1073


Mott insulators are commonly pictured with electrons localized on lattice sites, with their low-energy degrees of freedom involving spins only. Here, we observe emergent charge degrees of freedom in a molecule-based Mott insulator κ-(BEDT-TTF)2Hg(SCN)2Br, resulting in a quantum dipole liquid state. Electrons localized on molecular dimer lattice sites form electric dipoles that do not order at low temperatures and fluctuate with frequency detected experimentally in our Raman spectroscopy experiments. The heat capacity and Raman scattering response are consistent with a scenario in which the composite spin and electric dipole degrees of freedom remain fluctuating down to the lowest measured temperatures.

Fluctuating dipolar degrees of freedom have been predicted to appear in molecular-based Mott insulators (1, 2) and optical lattices of dipolar molecules (3) and to lead to a spin-liquid state in the presence of charge-spin coupling. In quantum paraelectrics, fluctuations of electric dipoles are observed in the vicinity of a ferroelectric transition (4). A quantum dipole liquid in an antiferroelectric on a triangular lattice was recently reported for BaFe12O19 (5), but as a band insulator this compound is nonmagnetic. A quantum dipole liquid in a Mott insulator is a paradigm for quantum states of matter that brings together quantum paraelectrics and spin liquids. Here, we discuss experimental evidence for the quantum dipole liquid state in a layered organic Mott insulator κ-(BEDT-TTF)2Hg(SCN)2Br [here, BEDT-TTF stands for a molecule bis(ethylenedithio)tetrathiafulvalene]. In the presence of charge-spin coupling, it may result in a spin-liquid state.

Electronic and magnetic phenomena observed in this class of materials are determined by the properties of the molecular-based cation layers (Fig. 1A). In a Mott insulator of this kind, electrons are localized on the lattice sites of dimers Embedded Image with spin S = 1/2 per site. These dimer sites form layers (Fig. 1B) that can be represented by a two-dimensional anisotropic triangular lattice (Fig. 1C). In most such compounds, the dimers have an inversion center and thus zero electric dipole moment. Frustration of the lattice, competing electronic correlations, and magnetic interactions can lead to charges being distributed nonsymmetrically between the two molecules in a dimer (1, 6), producing a dipole. This can lead to a broken symmetry ground state, so called “paired electron crystal” (6) or “quantum dipole solid” (1), where the dipoles order forming a ferroelectric state (Fig. 1D) (6). In contrast to a displacive ferroelectric, a change in the underlying lattice is not necessary in this case. It was suggested (1) that the dipoles can fluctuate in a quantum dipole liquid (Fig. 1E), providing an explanation of the spin-liquid state observed in a triangular lattice κ-(BEDT-TTF)2Cu2(CN)3. However, the evidence for fluctuating quantum dipoles in this material remains elusive (7, 8).

Fig. 1 Crystal structure and phases of BEDT-TTF–based crystals.

(A) Schematic structure of a BEDT-TTF–based crystal; the molecule is highlighted in red. (B) Structure of a BEDT-TTF layer in the (bc) plane of the κ-Hg-Cl crystal as determined from x-ray diffraction (10). BEDT-TTF molecules are bound in dimers (circles). The dimer sites form an anisotropic triangular lattice. (C) Schematic structure of a BEDT-TTF layer in a dimer Mott insulator on an anisotropic triangular lattice formed by Embedded Image sites with S = 1/2 (spins depicted by green arrows) and magnetic exchange between sites JM and J′M. The model is relevant to the spin-liquid candidate κ-(BEDT-TTF)2Cu2(CN)3, with JM/J′M = 0.64 (37). (D) Schematic structure of a BEDT-TTF layer in the case of a dipole solid [paired electron crystal (6)]. Within Embedded Image dimer sites, charge-rich and charge-poor molecules are denoted by red and blue, respectively. The dimer sites thus possess a dipole moment. JDC is the magnetic interaction between spins (marked by green arrows) on neighboring charge-rich molecules. Spins of the nearest-neighbor charge-rich sites will form spin singlets (6). This situation is relevant to κ-Hg-Cl. (E) Schematic structure of a BEDT-TTF layer in a quantum dipole liquid. The charge is fluctuating between the molecules in Embedded Image dimers, as denoted by blurry red and blue ovals, leading to electric dipoles fluctuations. Associated spins also show fluctuations. This situation is relevant to κ-Hg-Br.

Here, we elucidate the properties of the quantum dipole liquid state in the triangular lattice Mott insulator (9, 10) κ-(BEDT-TTF)2Hg(SCN)2Br (κ-Hg-Br) [TMI = 80 K (11, 12)] by comparing them to those of an isostructural compound κ-(BEDT-TTF)2Hg(SCN)2Cl (κ-Hg-Cl), which shows signatures of a quantum dipole solid below 30 K (10, 11). We first use Raman molecular vibrational spectroscopy to follow the evolution of the distribution of charge on the lattice of these systems through the metal-insulator transition. The on-molecule charge is probed by measuring the frequency of the central C=C molecular bond vibration (v2) (Fig. 2E), which changes by about –140 cm–1 when the charge state changes from (BEDT-TTF)0 to (BEDT-TTF)1+ (13, 14). This is a result of a lengthening of the central C=C bond of the molecule when more charge occupies the highest occupied molecular orbital (HOMO). To exclude effects other than a change of charge distribution on the lattice, we compare the temperature dependence of the parameters of the charge-sensitive v2 band to that of the v3 mode at 1470 cm–1. The latter involves the stretch of the off-center C=C bonds (Fig. 2E) and is not sensitive to charge on the molecule but would be affected by structural disorder or symmetry breaking. The ν3 band stays a narrow single line throughout the measured temperature range for both materials. For κ-Hg-Cl, a single Embedded Image band at about 1490 cm–1 is observed in the high-temperature metallic state, whereas in the insulating state below TCO = 30 K, Embedded Image is split into two bands at 1475 and 1507 cm–1 (Fig. 2A). The difference in frequencies of the two modes is much higher than expected for a structural phase transition but corresponds to charges redistributed within the Embedded Image dimer as +0.4e on one molecule and +0.6e on the other (10, 14); this breaks the inversion symmetry in a Embedded Image dimer, creating an electric dipole. This result confirms that the ground state of κ-Hg-Cl is an order of electric dipoles localized on Embedded Image dimer sites (10), the so-called dipole solid (1).

Fig. 2 Raman spectra in the region of C=C vibrations of BEDT-TTF.

(A) Temperature dependence of the κ-Hg-Cl spectra in the region of v2 and v3 modes. Note the splitting of v2 mode in the dipole solid (charge ordered) state at 20 K with frequencies corresponding to BEDT-TTF0.4+ and BEDT-TTF0.6+. (B) Shape of v2 mode calculated from the two-sites jump model (see eq. S1). The upper spectrum is of a static system (ωEX = 0), with bands corresponding to BEDT-TTF0.4+ and BEDT-TTF0.6+ as in the dipole solid state of κ-Hg-Cl. On the increase of exchange frequency ωEX, the bands widen and move close to each other. The lower two spectra at ωEX = 30 and 40 cm–1 reproduce the v2 shape of κ-Hg-Br at 8 and 35 K correspondingly, taking into account the natural width Γ for the relevant temperature. (C) Temperature dependence of the κ-Hg-Br spectra in the region of v2 and v3 modes. The v2 band does not split but shows some widening at the lowest temperature. (D) Temperature dependence of center frequency (top) and line width (bottom) for v2 (triangles) and v3 (diamonds) modes for κ-Hg-Br. The line width of v2 for κ-Hg-Br goes through a minimum at around 80 K, whereas that of v3 decreases continuously. (E) Illustration of the movements of atoms associated with v2 and v3-mode vibrations in a BEDT-TTF molecule.

In contrast, for κ-Hg-Br, a single v2 mode observed in the whole studied temperature range (Fig. 2C) suggests a symmetric dimer with both molecules carrying half a hole (BEDT-TTF)0.5+ on average. However, the width of the v2 band shows abnormal behavior on cooling. Line widths of phonons are determined by decay mechanism (15), disorder, and dynamics of the lattice and charge systems. For example, the width of the v3 vibrational band of BEDT-TTF molecule is determined by decay processes into lower-frequency modes and decreases down to about 5 cm–1 at 10 K (see Fig. 2D). In contrast, the width of v2 goes through a minimum of 16 cm–1 at around 80 K and increases again up to 20 cm–1 at 10 K (Fig. 2, C and D). Abnormal temperature dependence of the width observed only for v2 rules out the possibility that structural changes or structural disorder are at its origin. Another possible reason for an increased line width is charge fluctuations (16, 17).

We estimate the effects of charge fluctuations on the shape of the v2 vibration using a “two-site jump” model (16, 17) (see eq. S1). In this model, we consider +0.6e and +0.4e charged molecules, where e is electron charge, observed in the ordered state of κ-Hg-Cl as two static species. They are characterized by frequencies of v2 vibrations v2[BEDT-TTF0.4+] = 1507 cm–1 and v2[BEDT-TTF0.6+] = 1475 cm–1. Their natural width Γ depends on temperature through the lifetime of the measured excited state and is expected to be the same as that of v3. The system can jump between these two states with a frequency of ωEX = 1/τ, where τ is the lifetime of each state defined by the exchange. As the exchange rate ωEX between these two states increases, the shape of the resulting spectra changes (Fig. 2B). The two original bands get wider and the difference in positions between them decreases, and at a high enough rate ωEX, they merge into a single band. The calculated spectrum at ωEX = 0 reproduces the doublet shape of v2 for κ-Hg-Cl in the dipole solid state (Fig. 2, A and B). The spectra calculated for ωEX = 40 and 30 cm–1 reproduce the shape of the v2 band in κ-Hg-Br spectra, where the width of v2 increases from 16 to 20 cm–1 on cooling below 80 K, and the band gains slight asymmetry (Fig. 2, B and C). These results suggest that in κ-Hg-Br charges fluctuate between two molecules in a dimer with frequency ωEX that slightly decreases on cooling. In other words, electric dipoles in κ-Hg-Br fluctuate with this frequency, forming a quantum dipole liquid state.

Apart from the difference in the v2 band behavior, the phonon Raman spectra of κ-Hg-Br and κ-Hg-Cl are very similar (Fig. 3, A, B, and S1 A, B) because the two compounds have very similar crystal structures. Whereas the spectral region below about 200 cm−1 for κ-Hg-Cl shows only phonon bands (Fig. 3 B), in the A1g scattering channel for κ-Hg-Br, the phonons are superimposed on a much wider feature with a maximum around 40 cm−1 (Fig. 3 A). In the B1g scattering channel, we also observe this feature, with phonon bands showing broad asymmetric shapes, apparently as a result of electron-phonon coupling (Fig. 3A, and fig. S2B). This asymmetric feature with a maximum around 40 cm–1 (see spectra with phonons subtracted in Fig. 3C) with the width at half maximum of about 40 cm–1 gains intensity below 100 K, when κ-Hg-Br enters the insulating state, and shows weak softening at the lowest temperature. Apparently, this wide feature observed only in κ-Hg-Br spectra originates from a different scattering channel than phonons. Other potential scattering channels are electronic or magnetic excitations on a triangular lattice of Embedded Image dimers. On a triangular lattice, polarizations of electronic or magnetic excitations cannot be completely disentangled to elucidate the origin of the excitations, in contrast to a square lattice (18).

Fig. 3 Temperature dependence of Raman spectra.

Shown are the spectra for (A) κ-Hg-Br and (B) κ-Hg-Cl in A1g symmetry in the frequency range between 0 and 300 cm−1. Phonons are found at similar frequencies for both compounds. In the spectra of κ-Hg-Br, a background develops at temperatures below 100 K. Spectra at 300 and 11 K for κ-Hg-Br for B1g symmetry are shown in the inset to (A). In the B1g scattering channel, the low-frequency background, interpreted as a collective mode, shows strong coupling to the phonons. (C) Temperature dependence of the collective mode in the A1g scattering channel for κ-Hg-Br, determined by subtracting phonons from the full Raman spectrum (see the supplementary materials for details of the procedure. (Inset) Temperature dependence of the normalized intensity of the collective mode. (D) Temperature dependence of the heat capacity Cp for κ-Hg-Cl (red line) and κ-Hg-Br (black line) below 40 K. The two curves deviate from each other below ~6 K. (Inset) Low-temperature data with linear behavior of heat capacity for κ-Hg-Br. (E) Raman spectra in B1g polarization at 20 K in the range between 800 and 1100 cm–1, with phonons and luminescence background subtracted for κ-(BEDT-TTF)2Cu2(CN)3 (top) and κ-Hg-Cl and κ-Hg-Br (bottom). See details on the subtraction procedure in the supplementary materials. Schematic pictures of the relevant models with different charge distribution are shown. The spectra of the dimer Mott insulator on the triangular lattice κ-(BEDT-TTF)2Cu2(CN)3 (top) demonstrate magnetic excitations below ~600 cm–1. This feature is absent in the spectra of both κ-Hg-Br (black) and κ-Hg-Cl (red). The increase of intensity in the spectra of κ-Hg-Br below 200 cm–1 is caused by the collective mode fully shown in (A).

Magnetic excitations are expected in the Raman response of a Mott insulator with ordered spins or even spins developing short-range correlations (1821). In Mott insulators based on Embedded Image dimers, magnetic excitations are observed both in Raman spectra of an antiferromagnetically ordered state on a square lattice (19) and in a spin-liquid candidate on triangular lattice κ-(BEDT-TTF)2Cu2(CN)3 (Fig. 3E). The spectra of the latter show a continuum of magnetic excitations below 600 cm–1. The position of the continuum is defined by the value of J and geometry of the lattice (18). For κ-(BEDT-TTF)2Cu2(CN)3, it is in agreement with Hubbard-model–based calculations for the magnetic response of S = 1/2 on an anisotropic triangular lattice with JM = 250 K (20).

It is clear at this point that magnetic interactions in a dipole solid, and possibly quantum dipole liquid, would be renormalized in comparison with a simple Embedded Image dimer Mott insulator with charge symmetrically distributed on a dimer. Hotta (1) proposes a renormalization and a decrease of J in a quantum dipole liquid compared with a simple dimer Mott insulator, however, without estimating J values. A simple argument suggests that, in a dipole solid, magnetic interactions occur between charge-rich molecules of the neighboring dimers, whereas in a simple Mott insulator the interactions occur between dimer lattice sites (illustrations in Fig. 3E). An estimate provided by a tight-binding approximation as Embedded Image, where t is a transfer integral and U is on-molecule Coulomb repulsion, yields the value of about JDS = 80 K for a dipole solid. This is considerably smaller than JM = 250 K (22) for a simple dimer Mott insulator, where the on-dimer U defines magnetic interactions. Here, the Coulomb repulsion parameters, as well as transfer integrals, are estimated from the optical conductivity spectra (23), and the difference is produced mainly by a variation between the values of U in these two models. A lower J would result in a lower ordering temperature and a spectrum of magnetic excitation shifting to lower frequencies. However, the maximum of the observed background is about ~40 cm–1 and is found below the expected JDS value, which is too low in frequency to be interpreted as purely magnetic excitations.

Another possibility is assigning this mode to a collective excitation associated with dipole fluctuations. Dipole fluctuations with a frequency of about ωEX = 40 cm–1 are detected through the line-shape analysis of charge-sensitive vibrations. If these fluctuations are a collective phenomenon, we would expect a collective mode at about 40 cm–1. The low-frequency mode observed in κ-Hg-Br thus is a good candidate for a collective response of dipole fluctuations. Optically detected collective modes associated with charge fluctuations are found in the metallic state close to a charge ordering metal-insulator transition in organic conductors (24, 25) and in under-doped high-temperature cuprate superconductors (26). In an insulating state, the closest analogy would be a soft mode close to the transition into the ferroelectric state in displacive ferroelectrics such as SrTiO3. A comparatively small width of the band, as well as its increase in intensity and its low-frequency shift below TMI = 80 K distinguishes it from a boson peak observed in glasses (27) and supports an interpretation in terms of a fluctuating system of dipoles versus charge glass. An absence of glassy behavior is also supported by the low-frequency dielectric response of κ-Hg-Br (12).

Fluctuations of electric dipoles coupled to S = 1/2 spins on a triangular lattice of Embedded Image dimers have been suggested as a mechanism for spin-liquid behavior (1, 2). Reference (2) discusses the coupling between the dipole and magnetic degrees of freedom within the Kugel-Khomskii model, showing an analogy between the fluctuating dipole liquid and orbital liquid (28, 29). This model suggests that for certain values of frustration J′/J and spin-charge coupling K, spin order is destabilized and would produce mixed spin-charge excitations. To understand whether the collective mode observed in κ-Hg-Br Raman spectra originates purely in dipole fluctuations or in mixed charge-spin excitations, theoretical calculations of the excitation spectrum for such a system would be of great importance.

Our heat capacity data are consistent with the presence of itinerant excitations in κ-Hg-Br but not in κ-Hg-Cl. The heat capacity Cp of κ-Hg-Br and κ-Hg-Cl was measured in the temperature range between 40 K and 100 mK. The temperature dependencies of heat capacity for these compounds overlap within the error of the measurements in the temperature range above 6 K (Fig. 3D), excluding the feature at 30 K in the κ-Hg-Cl data indicating a charge order transition. The low-temperature heat capacity Cp = βT3 + γT of both compounds shows basically the same bosonic contribution β = 19.0 ± 2.5 mJ K–4 mol–1. This is expected, as it is determined predominantly by phonons and vibrations of BEDT-TTF molecules, which are very similar for the studied compounds. The difference between the two materials appears below about 6 K, where for κ-Hg-Br, Cp shows a linear term γ = 13.8 ± 3.1 mJK–2 mol–1 (inset in Fig. 3D). Spinon excitations can produce a linear term in heat capacity (30, 31), suggesting a spin-liquid behavior of κ-Hg-Br. For κ-Hg-Cl, γ = 0 within the precision of our measurements.

An ordering of electric dipoles observed in κ-Hg-Cl does not necessarily imply magnetic order (1). However, a theoretical proposal for a dipole order in a “paired electron crystal” suggests magnetic interactions as a driving force for the charge order on a frustrated dimer lattice and a spin-singlet ground state (6). A single phase transition observed at 30 K can be evidence of simultaneous electric dipole ordering and singlet formation in κ-Hg-Cl. On the other hand, the temperature of spin ordering can be lower than that of the charge order, as is observed in one-dimensional materials and suggested by calculations (32). Because heat capacity is found to not be always sensitive to magnetic phase transitions in these two-dimensional materials (33), further studies, such as those with nuclear magnetic resonance (NMR), are necessary to identify the magnetic ground state of κ-Hg-Cl. Paired electron crystal proposed as a ground state of κ-Hg-Cl (6, 10) can be regarded as a variation of a valence bond solid (6, 29). In these terms, the quantum dipole liquid in κ-Hg-Br can be a realization of a resonant valence bond state (34).

The quantum dipole liquid was suggested as one possible explanation of the origin of the spin-liquid state in κ-(BEDT-TTF)2Cu2(CN)3 (1); however, our work shows that this material does not demonstrate the signatures of this state. Its spectrum of magnetic excitations is well understood within a model of S = 1/2 on a triangular lattice with J = 250 K (Fig. 3) ((20). There is a recent suggestion (35) that κ-(BEDT-TTF)2Cu2(CN)3 experiences a lowering of magnetic dimensionality owing to destructive interference of magnetic interactions in one of the directions. A necessary test would be a comparison of magnetic excitation spectra of this model to available experimental Raman scattering data on magnetic excitations in κ-(BEDT-TTF)2Cu2(CN)3 and antiferromagnetically ordered BEDT-TTF­–based material. At this point, it is clear that the spectrum of collective excitations in κ-Hg-Br is very different from that of κ-(BEDT-TTF)2Cu2(CN)3. Based on that, we can suggest that κ-(BEDT-TTF)2Cu2(CN)3 is a regular dimer Mott insulator with a homogeneous distribution of charge on Embedded Image dimer on relevant time scales. If the quantum dipole liquid model is relevant to κ-(BEDT-TTF)2Cu2(CN)3 at all, it puts this compound quite far from a quantum phase transition into a dipole solid state. According to the model in (1), tuning between a quantum dipole solid and a quantum dipole liquid can be accomplished by varying the tb/td ratio, where tb is an overlap integral between the dimers and td is an intradimer one. Indeed, td is found to be larger for κ-(BEDT-TTF)2Cu2(CN)3 than for κ-Hg-Cl (10). The existing experimental data do not provide straightforward evidence of tuning from a dipole liquid to a dipole solid by hydrostatic or chemical pressure for κ-Hg-Br and κ-Hg-Cl family of materials. Although a charge ordered state in κ-Hg-Cl is suppressed by an external pressure of about 1 kbar (36), the unit cell of κ-Hg-Br is somewhat larger than that of κ-Hg-Cl. Calculations of the electronic structure of these materials and its change with pressure, as well as further explorations of magnetic properties, are necessary for further understanding of the phase diagram.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 and S2

Tables S1 and S2

References (3840)

Data Files

References and Notes

Acknowledgments: Funding: The work at the Institute of Quantum Matter was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Material Sciences and Engineering under grant no. DE-FG02-08ER46544. The work in Chernogolovka was supported by FASO Russia, state registration number 0089-2014-0036. J.A.S acknowledges support from the Independent Research and Development program from the NSF while working at the Foundation and from the National High Magnetic Field Laboratory (NHMFL) User Collaboration Grants Program (UCGP). Work at ANL was supported by University of Chicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”) Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under contract no. DE-AC02-06CH11357. Author contributions: N.D. conceived and designed the experiments; N.H., S.C., and N. D. performed the experiments and data analysis; M.M. led heat capacity experiments; J.A.S. contributed characterized samples of κ-(BEDT-TTF)2Cu2(CN)3; S.T., E.I.Z., and R.N.L. contributed characterized samples of κ-(BEDT-TTF)2Hg(SCN)2Br and κ-(BEDT-TTF)2Hg(SCN)2Cl. Competing interests: The authors declare that they have no competing financial interests. Data availability: Tables of data presented in the paper are available in the supplementary materials.
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