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

Abstract

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) 2 Hg(SCN) 2 Br, 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

Full text

Observation of a quantum dipole liquid state in an organic quasi-two-dimensional
material
Nora Hassan,1Streit Cunningham,1Martin Mourigal,2Elena I. Zhilyaeva,3
Svetlana A. Torunova,3Rimma N. Lyubovskaya,3and Natalia Drichko1
1The Institute for Quantum Matter and the Department of Physics and Astronomy,
The Johns Hopkins University, Baltimore, Maryland 21218, USA
2School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
3Institue of Problems of Chemical Physics, Chernogolovka, Russia
(Dated: June 5, 2017)
A metal in which the repulsion between conduction electrons dominates over their ki-
netic energy becomes an insulator at low temperatures. Such Mott insulators are com-
monly pictured with electrons completely localized on lattice sites. Their low-energy
physics involves spins only. New degrees of freedom can emerge in molecule-based
Mott insulators as electrons occupy extended molecular orbitals. In this work we ex-
perimentally demonstrate an existence of a new emergent state quantum dipole liquid in a
triangular lattice molecular- based Mott insulator κ-(BEDT-TTF)2Hg(SCN)2Br. Here,
when in the Mott insulating state electrons localize on extend lattice sites, they form
electric dipoles which do not order at low temperatures and fluctuate with a frequency
we detect experimentally in Raman spectroscopy experiments. The heat capacity and
Raman scattering response of this quantum dipole liquid supports a scenario where
the composite spin and electric dipole degrees of freedom remain fluctuating down to
the lowest temperatures.
A class of materials which exhibit fluctuating electric
dipoles in a band insulating state are quantum para-
electrics, where fluctuations are observed in the vicinity
of a ferroelectric transition [5]. This example is related
to displacive ferroelectrics such as SrTiO3, where impor-
tant physics is defined by deformation of the lattice and
can be observed through the relevant lattice phonons,
so-called “soft modes”. An experimental observation of
fluctuations of dipoles in an antiferroelectric on a tri-
angular lattice, resulting in quantum dipole liquid was
recently reported for BaFe12 O19 [6]. Band insulators do
not posses unpaired electrons and thus are non-magnetic.
In contrast, quantum dipole liquid in a Mott insulator in
a presence of charge-spin coupling can also be an origin
of a spin liquid state [4, 7].
In this work we discuss a new experimental realization
of the quantum dipole liquid state in a layered organic
crystal κ-(BEDT-TTF)2Hg(SCN)2Br based on molecule
BEDT-TTF 1. Electronic and magnetic phenomena ob-
served in this class of materials are basically defined
by the properties of the molecular-based cation layers
(Fig 1 a). In the compounds studied here, lattice sites
of dimers of (BEDT-TTF)+1
2with one hole and S=1/2
per site form layers which can be approximated by two-
dimensional anisotropic triangular lattice. Many of these
class of materials are Mott insulators, where electrons are
localized on dimer sites (BEDT-TTF)+1
2(see Fig. 1 c).
In most of such compounds the dimers have an inver-
sion center and thus zero electric dipole moment. A
1bis(ethylenedithio)tetrathiafulvalene
loss of an inversion center in a molecular dimer due to
charge distributed non-symmetrically between the two
molecules in a dimer can be a results of frustration of
the lattice, competing electronic correlations and mag-
netic interactions [3, 4]. It would produce an electric
dipole. In contrast to a displacive ferroelectric this way
to form a dipole does not necessary need a change in the
underlying lattice. The dipoles can order leading to a
ferroelectric state (Fig. 1 d), or fluctuate in a quantum
dipole liquid (Fig. 1 e). In fact, a fluctuating quantum
dipole state was suggested as an explanation of a spin
liquid state on a triangular lattice observed in κ-(BEDT-
TTF)2Cu2(CN)3. However, the evidence for fluctuating
quantum dipoles in this material remains elusive [8, 9].
In this work, properties of quantum dipole liquid
state in κ-(BEDT-TTF)2Hg(SCN)2Br (κ-Hg-Br) are elu-
cidated by a comparison to an isostructural compound
κ-(BEDT-TTF)2Hg(SCN)2Cl (κ-Hg-Cl) which shows or-
dered dipoles state, so-called quantum dipole solid as
ground state. These materials have organic BEDT-TTF
molecules as building which allows us to use ideas of
molecular spectroscopy to characterize the distribution of
charge on the lattice and its fluctuations. Electronic and
magnetic Raman response which was previously observed
predominantly in strongly correlated inorganic materials
provides further information on the electronic and mag-
netic ground state. The physical phenomena observed
in these molecular materials extend our knowledge on
states of matter produced in solids by strong electronic
correlations, both of inorganic and organic origin.
The crystal structure of the two studied materials is
very similar (see details of the structure in the Supple-
arXiv:1704.04482v2 [cond-mat.str-el] 2 Jun 2017

2
ment information), with dimers of (BEDT-TTF)+1
2form-
ing weakly anisotropic triangular lattice [1, 10] (Fig. 1 b).
κ-Hg-Cl shows metallic behaviour of resistivity and un-
dergoes a charge order metal-insulator transition at
30 K[1, 11]. Resistivity of κ-Hg-Br decreases slower on
cooling in the high-temperature state. This compound
undergoes an insulating transition at around 100 K,
which was suggested to be a Mott insulator [11].
We first use Raman molecular vibrational spectroscopy
to receive information on the distribution of charge on the
lattice of these systems through the metal-insulator tran-
sition. The on-molecule charge is probed by following the
frequency of the central C=C molecular bond vibration
(ν2) (Fig. 2 e ), which changes by ∼-140 cm−1when
the charge of the molecule changes from (BEDT-TTF)0
to (BEDT-TTF)+1 [12, 13]. This is a result of a length-
ening of the central C=C bond of the molecule when
more charge occupy the highest occupied molecular or-
bital (HOMO). To demonstrate a contrast between the
temperature behaviour of charge sensitive and standard
modes we also follow the temperature dependence of the
ν3mode. (Fig. 2) which is known not to be coupled to
HOMO. It also involves C=C deformations and is found
at a close frequencies of about 1470 cm−1but stays single
and narrow through the measured temperature range for
both materials. Both modes have large intensity in A1g
and B1gsymmetries.
A single ν2found at about 1490 cm−1is observed in
the high temperature metallic state for κ-Hg-Cl while in
the insulating state below TCO =30 K ν2is split into two
bands at 1475 and 1507 cm−1(see Fig. 2 a). The dif-
ference in frequencies of the two modes is much higher
than expected on a structural phase transition, but cor-
responds to charges redistributed within the (BEDT-
TTF)+1
2dimer as +0.4eon one molecule, and +0.6eon
the other [1, 13] which breaks the inversion symmetry
in a (BEDT-TTF)+1
2dimer creating an electric dipole.
The ground state of κ-Hg-Cl thus can be described as
an order of electric dipoles localized on (BEDT-TTF)+1
2
dimer sites, so-called dipole solid, following [4].
A single ν2mode observed in the whole studied
temperature range for κ-Hg-Br suggests a symmetric
dimer with both molecules carrying half a hole (BEDT-
TTF)+0.5on average. However, the width of ν2band
shows abnormal behaviour on cooling, going through a
minimum of 16 cm−1at around 80 K, and increasing
again up to 20 cm−1at 10 K (see Fig. 2 c,d). Line width
of phonons are generally defined by decay mechanism,
disorder and dynamics of the lattice and charge system.
A typical width of vibrations of BEDT-TTF molecule
defined by a decay processes into lower-frequency modes
is exemplified by the behaviour of ν3mode (see Fig.2 d)
which decreases down to about 5 cm−1at 10 K. The
singular abnormally wide charge-sensitive ν2band ex-
cludes a possibility of structural changes or structural
disorder as its origin. Another possible reason for an in-
creased line width which we will consider is charge fluc-
tuations. [14, 15].
We estimate the effects of charge fluctuations on
the shape of the ν2vibration using ”two- sites jump”
model [14, 15] presented by Eq. 1. In this model, we
consider +0.6eand +0.4echarged molecules observed
in the ordered state of k-Hg-Cl as two static species.
They are characterized with frequencies of ν2vibra-
tions ν2[BEDT-TTF+0.4] = 1475 cm−1and ν2[BEDT-
TTF+0.6])= 1507 cm−1and natural width Γ. The system
can jump between these two states with a frequency of
ωEX =1/τ , where τis a life time of each state, or in other
words a correlations time. As an exchange rate ωEX be-
tween these two states will increase, the shape of the re-
sulting spectra will change as shown in Fig. 2 c. The two
original bands will get wider, move together and at high
enough rate will become a single band. The calculated
spectrum in a static state ωEX = 0 consists of two bands
and reproduces the ν2part of the spectrum for κ-Hg-Cl
(Fig. 2 a,b). The spectra calculated for ωEX = 40 and
30 cm−1reproduce the shape of the ν2band in κ-Hg-
Br spectra, where the width of ν2increases from 16 to
20 cm−1on cooling below 80 K, as well as the slight asym-
metry the band gains(Fig. 2 b,c). The calculation took
into account the decrease of natural width Γ on cooling.
Thus the abnormal increase of the width of ν2on cooling
in the insulating state of κ-Hg-Br can be explained in
terms of charges fluctuating between two molecules in a
dimer with frequency ωEX , the latter slightly decreases
on cooling. This suggests that the electric dipoles in κ-
Hg-Br fluctuate with this frequency, forming a quantum
dipole liquid state.
Apart from the discussed difference in the ν2band
behaviour, the molecular vibrations-related and phonon
Raman spectra of κ-Hg-Br and κ-Hg-Cl are very sim-
ilar (Fig. 3 a,b,e). It is natural, since the compounds
are basically iso-structural. On cooling all the vibra-
tional bands narrow down to 5-7 cm−1, including the low
frequency lattice phonons, which are well distinguished
in low temperature spectra in Fig. 3 a,b below approx-
imately 100 cm−1. In the spectra of κ-Hg-Br (see A1g
symmetry spectra in Fig. 3) the somewhat widened by
few wavenumbers phonons, some of them demonstrating
so-called Fano shape, are superimposed on a much wider
background band. As can be followed from the spectra
with the phonons extracted shown in Fig. 3 c, this asym-
metric feature becomes intense below 100 K, when κ-Hg-
Br enters insulating state. Its maximum around 40 cm−1
shows weak softening at the lowest temperature.
Apparently, this wide feature observed only in κ-Hg-
Br spectra originates from a different scattering chan-
nel than phonons. The frequency of the maximum of
this mode corresponds to the frequency of dipole fluctu-
ations received from vibrational spectroscopy data for κ-
Hg-Bras discussed above. This suggests the assignment
of this mode as a collective excitation associated with

3
on-site dipole fluctuations. The presence of a collective
mode is essential to the understanding of the material.
It is an evidence of a distinct difference between dipole
liquid and charge glass, where charge-sensitive vibrations
can experience broadening, but no collective excitations
are expected.
While polarization dependence of collective modes can
be a helpful information for understanding their origin,
the clear separation of the response by polarization is ob-
served in D4hsymmetry only [16]. The dimer-based lat-
tice of κ-Hg-Br is approximated by anisotropic triangular
lattice, where polarizations cannot be completely disen-
tangled. Indeed, the collective mode feature is observed
in A1g, B1g(for B1gsee inset in Fig. 3 a and Supplement
information). The phonons in B1gpolarization are signif-
icantly more widened and have asymmetric Fano shapes,
evidencing the interaction with the collective mode, for
details see Supplemental information.
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 [17, 18] and in under-doped high tempera-
ture cuprate superconductors [19]. To the best of our
knowledge a collective mode due to fluctuations of elec-
tric dipoles or any other configuration of charge in a Mott
insulator is observed by ground state spectroscopy for
the first time. In an insulating state, the closest analogy
would be a soft mode in ferroelectrics. However, in con-
trast to displacive ferroelectrics, the dipoles in κ-Hg-Br
are induced by charge inequilibrium on (BEDT-TTF)+1
2
dimer which does not necessary depend on the lattice
deformation.
Fluctuations of electric dipoles on sites with S=1/2 on
a triangular lattice was suggested as a mechanism for a
spin-liquid behaviour [4, 7]. An order of electric dipoles
does not necessary imply magnetic order [4]. However,
an approach of Ref. [3] which includes antiferromagnetic
interactions as a driving force for the charge order on
a frustrated dimer lattice suggests a spin singlet ground
state. This so-called paired electron crystal proposed as
a ground state of κ-Hg-Cl [1] can be regarded as a varia-
tion of valence bond solid. In these terms, the quantum
dipole liquid in κ-Hg-Br can be a realization of a resonant
valence bond (RVB) state.
Our data on heat capacity of both materials is the
first step to the understanding of their magnetism. Heat
capacity Cpof κ-Hg-Br and κ-Hg-Cl was measured in
the temperature range between 40 K and 100 µK. The
temperature dependence of heat capacity for these com-
pounds is overlapping within the error of the measure-
ments in the temperature range above 6 K (Fig. 3 d), but
for the feature at 30 K in the temperature dependence for
the Cpof κ-Hg-Cl indicating the charge order transition.
The heat capacity Cp=βT 3+γT of both compounds
shows basically same bosonic contribution β= 19.0 ±2.5
mJ K−4mol−1. This is natural, since it is defined pre-
dominantly by phonons and vibrations of BEDT-TTF
molecules which are very similar for the studied com-
pounds. The difference between the two materials starts
to appear below about 6 K, where for κ-Hg-Br Cpshows
a linear term γ= 13.8±3.1mJK−2mol−1, while Cpof κ-
Hg-Cl goes down to zero on lowering temperature (inset
in Fig.3 d). A linear term in the low temperature heat
capacity of a Mott insulator κ-Hg-Br suggests a presence
of spinon excitations. On the other hand, for κ-Hg-Cl γ=
0 within the precision of our measurements, suggesting
an ordered ground state in accord with the theoretical
proposal of a singlet ground state. A single phase transi-
tion observed at 30 K can be an evidence of simultaneous
electric dipole ordering and singlet formation in κ-Hg-Cl.
The temperature of spin ordering can be lower than that
of the charge order, as is observed in one-dimensional ma-
terials, and suggested by calculations [21]. However, heat
capacity is found not to be sensitive to an antiferromag-
netic transition, see for example [22], thus further studies
such as NMR are necessary to identify the temperature
of magnetic transition in κ-Hg-Cl. On the other hand,
to clarify magnetic low-temperature state of the studied
materials much information can be received from mag-
netic Raman scattering
Raman scattering was previously successfully used to
study spinon excitations in both inorganic kagome-lattice
[23] and BEDT-TTF-based triangular lattice [24, 25]
spin liquid candidates. Continuum of magnetic excita-
tions appears in Raman spectra at frequencies close to
the value of few J, the exact spectra and polarization de-
pendence defined by the dimensionality of the system, the
ordering, and frustration parameters. It is clear at this
point, that magnetic interactions in a dipole solid, and
possibly quantum dipole liquid would be re-normalized in
comparison to a simple (BEDT-TTF)+1
2dimer Mott in-
sulator with charge symmetrically distributed on a dimer.
In a dipole solid, magnetic interactions occur between
charge-rich molecules of the neighboring dimers, while
in a simple Mott insulator the interactions are between
dimer lattice sites, as is schematically shown in Fig. 3 e.
An estimate provided by a tight-binding approximation
as J=4t2
U, where tis a transfer integral, and Uis on-
molecule Coulumb repulsion, yields the value of about
JDS = 80 Kfor a dipole solid, considerably smaller com-
pared to JM= 250 K[26] for a simple dimer Mott
insulator, where on-dimer Udefines magnetic interac-
tions. The Coulomb repulsion parameters, as well as
transfer integrals are estimated from the optical conduc-
tivity spectra [27], and the difference is produced mainly
by a variation between the values of Uin these two mod-
els. More complex approach of Ref. [4] proposes both
a re-normalization of Jand a decrease of effective mag-
netic frustration in a quantum dipole liquid compared to
a simple dimer Mott insulator. Lower Jwould result in
a lower ordering temperature, and a spectrum of mag-
netic excitation shifting to lower frequencies as well as a

4
respective decrease in intensity of the Raman response of
the excitations as ω4.
Indeed, we find a difference in the Raman spectrum
of magnetic excitations between compounds represent-
ing the two models. Fig. 3 e compares low-temperature
Raman spectra of a dimer-based spin liquid candidate
on triangular lattice κ-(BEDT-TTF)2Cu2(CN)3(upper
panel), and the spectra of κ-Hg-Br and κ-Hg-Cl (lower
panel, black and red curves) in the same frequency range.
A simple case of κ-(BEDT-TTF)2Cu2(CN)3, a Mott in-
sulator with dimers (BEDT-TTF)+1
2forming anisotropic
triangular lattice shows a continuum of magnetic ex-
citations below 600 cm−1, as marked in the spectra
by a shaded area. The spectrum is well-reproduced
by Hubbard-model-based calculations for magnetic re-
sponse of S=1/2 on anisotropic triangular lattice with
JM=250 K [24]. This background is absent from the
spectra of κ-Hg-Cl and κ-Hg-Br, the latter showing an
increase of intensity below 200 cm−1which is a part
of the collective excitations band discussed above. The
maximum of the collective excitations response is around
50 cm−1which is below the expectant JDS value, thus
found at too low frequencies to interpret them as purely
magnetic. Here it is worth to mention an approach of
Ref. [7] to the dipole liquid state, where the system
is discussed within Kugel-Khomskii model, showing the
analogy between the fluctuating dipole liquid and orbital
liquid[28, 29]. This model suggests that at a certain frus-
tration J‘/J and spin-charge coupling Kvalues, spin or-
der in a system is destabilized, and would produce mixed
spin-charge excitations. To understand if the collective
mode observed by us has its origin purely in dipole fluc-
tuations or in mixed charge-spin excitations theoretical
calculations of the excitation spectrum for such a system
would be of great importance. In κ-Hg-Cl spectra no
additional background is distinguishable, in accord with
absence of itinerant excitations in heat capacity.
By now we showed the presence of quantum dipole liq-
uid state in κ-Hg-Br and the relevant excitations. Now
we would like to discuss how this state fits into our knowl-
edge on spin liquid candidates on triangular lattice lat-
tice, in particular BEDT-TTF based organic conductors,
and what parameters could control the state. Theoretical
approach of Ref. [4] suggest that the tuning of quantum
dipole solid into quantum dipole liquid can be done by a
change of tb/tdratio, where tbis an overlap integral be-
tween the dimers, and tdan intra-dimer one, which can be
tuned by application of pressure. The unit cell of κ-Hg-
Br is somewhat larger than that of κ-Hg-Cl. On the other
hand, it was shown that dipole order in κ-Hg-Cl can be
suppressed by external pressure of about 1 kbar, while
insulating state is suppressed at higher pressures [30].
A calculation of electronic structure of these materials
and their change with pressure, as well as further explo-
rations of magnetic properties are necessary for further
understanding of the phase diagram.
A phase transition between dipole solid and quantum
dipole liquid state is a playground for studies of quan-
tum criticality. An absence of order in κ-Hg-Br close to
the quantum dipole solids suggest a presence of quantum
phase transition in the region of phase diagram between
κ-Hg-Cl and κ-Hg-Br, and puts κ-Hg-Br in a quantum
critical regime, characterized by the frequency of dipole
and spin fluctuations studied in this work. A soften-
ing of the collective mode which we observe at 11 K
is the realization of the temperature/frequency scaling
which is characteristic of quantum critical regime. While
our present work is aimed on understanding of quantum
dipole solid and liquid states, the next step would be to
investigate in detail a presence of quantum critical regime
and critical scaling.
Quantum dipole liquid was suggested as one of possible
models for the origin of spin liquid state in κ-(BEDT-
TTF)2Cu2(CN)3[4], however our work shows that it
does not demonstrate all the fingerprints of this state.
Its spectrum of magnetic excitations is well understood
within a model of spin 1/2 on triangular lattice with
J=250 K (Fig. 3, Ref. [24]), and is quite different from
the spectrum of κ-Hg-Br. Charge fluctuations are faster
and do not slow down at low temperatures, as demon-
strated by molecular spectroscopy in Ref. [8]. If the
quantum dipole liquid model is relevant to κ-(BEDT-
TTF)2Cu2(CN)3at all, it puts this compound quite far
from a quantum phase transition into a dipole solid state.
An increased intra-dimer overlap integral tdis the best
candidate for a tuning parameter between dimer Mott
insulator and quantum dipole liquid, and indeed is found
to be larger in κ-(BEDT-TTF)2Cu2(CN)3than in κ-Hg-
Cl [1].
In conclusion, we demonstrated a quantum dipole liq-
uid state in κ-Hg-Br, and found the frequency of dipole
fluctuations at around 40 cm−1both using vibrational
spectroscopy and observing a collective mode associated
with the fluctuations. While the frequency of the collec-
tive mode is similar to that of dipole fluctuations, a mixed
charge-spin excitations are also a possible explanation. A
presence of a linear term in heat capacity down to 100 µK
suggests a presence of spinon excitations. Magnetic Ra-
man scattering points on re-normalization of magnetic
interactions Jand a different energy scale for these exci-
tations compared to dimer Mott insulator-based organic
spin liquid candidates.
Methods
Single crystals of κ-(BEDT-TTF)2Hg(SCN)2Cl (κ-Hg-
Cl) and κ-(BEDT-TTF)2Hg(SCN)2Br (κ-Hg-Br) were
prepared by electrochemical oxidation of the BEDT-
TTF solution in 1,1,2-trichloroethane (TCE) at a tem-
perature of 40◦C and a constant current of 0.5 µA.
A solution of Hg(SCN)2, [Me4N]SCNKCl, and dibenzo-
18-crown-6 in 1:0.7:1 molar ratio in ethanol/TCE was
used as supporting electrolyte for the κ-Hg-Cl prepa-
ration. For the κ-Hg-Br preparation, a supporting

5
electrolyte Hg(SCN)2/[Me4N]SCN1.5KBr/ dibenzo-18-
crown-6 in 1:0.4:1 molar ratio was used. The composition
of the crystal was verified by electron probe microanalysis
and X-ray diffraction.
Raman scattering was measured in pseudo-Brewster
angle geometry using T64000 triple monochromator spec-
trometer equipped with the liquid N2cooled CCD de-
tector. For the measurements in the 5-400 cm−1range
T64000 in triple monochromator configuration was used,
for the measurements in the range 80-2000 cm−1single
monochrmonator configuration with the edge filter op-
tion was used. Spectral resolution was 2 cm−1. Lines
of Ar+-Kr+Coherent laser at 514.nm and 647 nm where
used for excitation. Laser power was kept at 2 mW for
the laser probe size of approximately 50 by 100 µm. This
ensured that laser heating of the sample was kept below
2 K, as was proved by observing the temperature of order-
ing transition in κ-Hg-Cl. Measurements at temperatures
down to 10 K were performed using Janis ST500 cold
finger cryostat. Cooling rates used were between 0.2 and
0.5 K/min. The samples were glued on the cold finger
of the cryostat using GE varnish. The experiments were
performed on at least 6 samples to ensure reproducibility
of the results. A few wavenumbers spread in the width
of ν2band at low temperatures for κ-Hg-Br was asso-
ciated with a weak strain originating from GE varnish,
all the other parameters of the spectra were reproducible
within the error bar of the measurements. The crystals
were oriented using polarization-dependent Raman scat-
tering measurements. For the measurements, electrical
vector of excitation eLand scattered eSlight were polar-
ized along band caxes. Our notations of polarizations
refer to the structure and symmetry of the BEDT-TTF
layer, to make an easy comparison to the calculations
which refer to D4h[16] without loosing the information
about the symmetry of the real crystal. Thus A1gsym-
metry corresponds to the were measurement in (b, b) and
(c, c) geometries, and B1gcorresponds to (b, c) and (c, b)
geometries (xy). All spectra were corrected by the Bose-
Einstein thermal factor.
Intensity of the collective mode was calculated as
I(T) = R200 cm−1
0χ00(ω)dω
The calculations of the shape of the ν2band depend-
ing on ωEX jump rate between sites are done using Eq. 1.
Here a shift of the bands from the averaged band param-
eter ∆ = 16 cm−1is received using the spectra in the
ordered phase of κ-Hg-Cl, as well as the position of the
original bands. Γ is the natural width of the vibrational
bands experimentally followed by the width of ν3.ωEX
is the frequency of the jumps between to states, which
was varied on the calculations.
I(ω)∝Re[aR, aPi(ω−(ω1/2−∆)) + ωEX /2+Γ/2−ωEX /2
−ωEX /2i(ω−(ω1/2−∆)) + ωE X /2+Γ/2−1aR
aP]
(1)
Heat capacity was measured using Quantum Design
PPMS system equipped with the DR option.
Acknowledgements The work at IQM was sup-
ported by the U.S. Department of Energy, Office of Basic
Energy Sciences, Division of Material Sciences and En-
gineering under Grant No. DE-FG02-08ER46544. The
work in Chernogolovka was supported by FASO Russia,
state task #0089-2014-0036.
Correspondence and requests for materials should be
addressed to Natalia Drichko (email: drichko@jhu.edu).

6
dipole solid quantum dipole liquid
pressure
dimer Mott insulator
spin liquid candidate
k-(BEDT-TTF)2Hg(SCN)2Br
(k-Hg-Br)
k-(BEDT-TTF)2Cu2(CN)3
JDS
k-(BEDT-TTF)2Hg(SCN)2Cl
(k-Hg-Cl)
c
b J’M
anion layer
cation
layer
anion layer
(a) (b) (c) (d) (e)
b
c
FIG. 1. (a) Schematic structure of BEDT-TTF based crystal, in the BEDT-TTF-based cation layer the molecule is highlighted
in red; (b) Structure of BEDT-TTF layer in (bc) plane of κ-Hg-Cl crystal as received from X-ray diffraction [1]. BEDT-TTF
molecules are bound in dimers as highlighted by circles. These dimer sites form anisotropic triangular lattice. (c) Schematic
structure of BEDT-TTF layer in a dimer Mott insulator on an anisotropic triangular lattice formed by (BEDT-TTF)+1
2sites
with S=1/2 (spins depicted by green arrows) and magnetic exchange between sites JMand J0
M. The model is relevant to a
spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3with JM/J0
M=0.64 [2]. (d) Schematic structure of BEDT-TTF layer in case of
dipole solid (paired electron crystal [3] ). The molecules within (BEDT-TTF)+1
2dimer sites carry different charge, charge-rich
and charge-poor are denoted by red and blue correspondingly. The dimer sites thus possess dipole moment. JDC is a magnetic
interaction between spins (marked by green arrows) on neighboring charge-rich molecules. According to Ref. [3] spins of the
nearest neighbor charge-rich sites will form spin-singlets, while Ref. [4] suggest spin fluctuations. This model is related to
κ-Hg-Cl. (e) Schematic structure of BEDT-TTF layer in case of quantum dipole liquid. The charge on the (BEDT-TTF)+1
2
dimers is distributed non-equally between the molecules, but is fluctuating within dimers, as denoted by blurry red and blue
ovals, leading to electric dipoles fluctuation. Relevant spins also show fluctuations. This model is related to κ-Hg-Br.
k-(BEDT-TTF)2Hg(SCN)2Cl
dipole solid below T=30 K
dipole
solid
1440 1460 1480 1500 1520
''(a.u.)
Raman shift (cm-1)
1440 1460 1480 1500 1520
''(a.u.)
Raman shift (cm-1)
1440 1460 1480 1500 1520
''(a.u.)
Raman shift (cm-1)
quantum
dipole
liquid
3
2(A)
(a)
Calculated line
shapes for 2
wEX
2
200 K
150 K
100 K
40 K
35 K
8.5 K
30 cm-1
40 cm-1
15 cm-1
5 cm-1
1 cm-1
0 cm-1
(c) (d)
charge-sensitive 2
dipole
solid
TCO
2
2(B)
T 2(A)
2(B)
k-(BEDT-TTF)2Hg(SCN)2Br quantum dipole liquid
3
200 K
150 K
100 K
40 K
35 K
8 K
(b)
2
T
050 100 150 200 250 300
0
5
10
15
20
25
30
Line width (cm-1)
Temperature (K)
050 100 150 200 250 300
1460
1470
1480
1490
1500
Raman shift (cm-1)
3
3
2
2
3
(e)
quantum
dipole
liquid
FIG. 2. (a)-(c) 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 ν2and ν3modes. Note the splitting of ν2mode in the dipole solid (charge ordered) state at 8 K with
frequencies corresponding to BEDT-TTF+0.4and BEDT-TTF+0.6. (b) Shape of ν2mode calculated by two-sites jump model,
see Eq. 1. The upper spectrum is of a static system (ωex ) with bands corresponding to BEDT-TTF+0.4and BEDT-TTF+0.6
as in dipole solid state of κ-Hg-Cl. Note that 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−1reproduce the ν2shape 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 ν2and ν3modes. Note that the ν2band is always single and shows some widening at lowest temperature. (d)
Temperature dependence of position (upper panel) and line width (lower panel) for ν2(triangulares) and ν3(diamonds) modes
for κ-Hg-Br. Note that line width of ν2for κ-Hg-Br goes through a minimum at around 75 K, while it decreases continuously
for ν3. (e) BEDT-TTF molecule with marked movements of atoms on ν2and ν3vibration.

7
050 100 150 200 250
0.0 6.2 12.4 18.6 24.8 31.0
Raman shift (meV)
Raman shift (cm-1)
'' (a.u.)
11 K
40 K
120 K
200 K
300 K
050 100 150 200 250 300
0.0 6.2 12.4 18.6 24.8 31.0 37.2
Raman shift (meV)
11 K
40 K
120 K
200 K
300 K
'' (a.u.)
Raman shift (cm-1)
210 40
5x101
102
103
Cp(mJK-1mol-1T-1)
Temperature (K)
050 100 150 200 250 300
0.0 6.2 12.4 18.6 24.8 31.0 37.2
Raman shift (meV)
7 K
40 K
300 K
 (a.u.)
Raman shift (cm-1)
(a)
(b)
(c) k-Hg-Br A1g
phonons extracted
k-Hg-Cl
A1g
k-Hg-Br
A1g
50 100 150
''(a.u.)
Raman shift (cm-1)
80 200 400 600 800 1000
Raman shift (meV)
'' (a.u.)
Raman shift (cm-1)
24.8 49.6 74.4 99.2 124.0
'' (a.u.)
k-Hg-Br
k-Hg-Cl
k-(ET)2Cu2(CN)3
B1g T=20 K
B1g T=20 K
JDC
JM
J’M
dipole
solid
quantum
dipole
liquid
triangular lattice
S=1/2
dimer Mott insulator
dipole
solid
quantum
dipole
liquid
0 1 2 3 4 5 6 7 8 9 10
0
25
50
75
100
125
150
175
CpT-1(mJ K-2mol-1)
T2(K2)
k-Hg-Br (dipole liquid)
k-Hg-Cl (dipole solid)
(d)
(e)
Tco
B1g
050 100 150 200 250 300
I (T)/I(11 K)
Temperatures (K)
FIG. 3. (a)-(b) Temperature dependence of low-frequency Raman spectra of (a) κ-Hg-Br and (b) κ-Hg-Cl in A1gsymmetry.
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 B1gsymmetry are shown in the inset in (a). The collective mode is observed
in B1gwith more prominent coupling to the phonons. (c) Temperature dependence of the collective mode in A1gsymmetry
for κ-Hg-Br received by extracting phonons from the full Raman spectrum. The inset shows a temperature dependence of the
normalized intensity of the collective mode. (d) Temperature dependence of heat capacity for κ-Hg-Cl (red line) and κ-Hg-Br
(black line) below 40 K. But for a feature due to the phase transition at T=30 K for κ-Hg-Cl Cpis similar for these materials
in the hight-temperature regime. The difference in the behaviour is observed below approximately 6 K. The inset shows low
temperature data with linear behaviour of heat capacity for κ-Hg-Br. (e) Raman spectra in B1gpolarization at 20 K in the
range between 800 and 1100 cm−1for κ-(BEDT-TTF)2Cu2(CN)3(upper panel) and κ-Hg-Cl and κ-Hg-Br (lower panel) which
represent three different models for charge and spin states discussed in this paper. All the spectra show narrow bands of
phonons, superimposed on a background, the part of background similar in this materials and coming from luminescence [20].
Spectra of dimer Mott insulator on triangular lattice κ-(BEDT-TTF)2Cu2(CN)3(upper panel) demonstrate a background due
to magnetic excitations on triangular lattice below approx. 600 cm−1, marked in the figure. 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−1is due
to the collective mode fully shown in (a) panel.

8
SUPPLEMENT INFORMATION
Crystal structure
Crystal structures of the studied materials κ-Hg-Br
and κ-Hg-Cl were published in Ref. [10] and [1]. In the
Table 1 we present basic information about both struc-
tures. It shows that the volume of the unit cell for κ-
Hg-Br compound is somewhat larger than κ-Hg-Cl. Cal-
culations of the electronic structure are necessary to un-
derstand how exactly this change of geometry between
two compounds will affect parameters which define the
ground state.
Raman scattering data
Raman scattering data: temperature dependence of
vibrational modes for κ-Hg-Cl
In Fig. 4a Supplement information we present tem-
perature dependence of parameters of ν3and charge-
sensitive ν2vibrations for κ-Hg-Cl. ν3band shows nor-
mal hardening on cooling and a decrease of the width,
with the temperature dependence coinciding with that
for κ-Hg-Br. The width of the charge-sensitive ν2de-
creases below that of κ-Hg-Br on cooling down to 50 K,
and then increases till the compound reaches the ordering
transition at 30 K, and decreases again below the tran-
sition as expected in the ordered state. This increase
suggest charge fluctuations above the transition and out-
side of the scope of this paper.
Raman scattering data: Low-frequency spectra of κ-Hg-Br
and κ-Hg-Cl in B1gsymmetry
In Fig. 4b Supplement information we present temper-
ature dependence of the Raman scattering spectra for
κ-Hg-Br and κ-Hg-Cl compounds for B1gsymmetry in
the spectral region between 25 and 400 cm−1. It shows
that (i) Similar to A1gfor κ-Hg-Br, the background fea-
ture due to the collective mode at about 50 cm−1appears
also in spectra of κ-Hg-Br in B1gsymmetry as an increase
of the intensity in the range below 150 cm−1. (ii) The
low frequency phonons in κ-Hg-Br B1gspectra remain
broad, which can be explained by an interaction of these
phonons with the collective mode. This is in contrast
with spectra of κ-Hg-Cl and κ-Hg-Br in A1gpolariza-
tion, where at low frequencies narrow phonon modes are
superimposed on the collective mode background. (iii)
Some drop of intensity in κ-Hg-Cl spectra between 35
and 7 K is due to an opening of a gap due to an ordering
transition.
Polarization dependence is an important way to char-
acterize excitations observed in Raman scattering [16].
For D4hsymmetry a clear separation of A1g(x2+y2),
B1g(x2−y2), and B2g(xy) polarization is expected for
electronic and magnetic excitations. Spectra of some ma-
terials can be mapped on D4hsymmetry and understood
within it even if the symmetry of the unit cell is lower.
A good example is the antiferromagnetically ordered or-
ganic compound κ-(BEDT-TTF)2Cu[N(CN)2]Cl, where
in a monoclinic unit cell (BEDT-TTF)+1
2dimers form a
weakly frustrated square lattice, and two-magnon Raman
excitations in that material follow the symmetry selection
rules expected for D4h.
In the materials studied in this work, the symmetry
of the unit cell is monoclinic as well, however it was
shown [1] that the (BEDT-TTF)+1
2dimers in (bc) plane
form slightly anisotropic triangular lattice. For D3hpoint
group Raman-active symmetries cannot be fully sepa-
rated by selecting polarizations. It was shown by nu-
merical calculations, too, that magnetic excitations on a
triangular lattice loose their anisotropy between A1gand
B1g[31, 32], a similar charge is expected for electronic
excitations. This explains the presence of the collective
mode in spectra of κ-Hg-Br in A1g, B1g(xy), and x2−y2
which would exist as B2gonly in D4h.
On the other hand, polarization dependence of
phonons follows the full symmetry of the lattice. Our
experimental data suggest that the coupling to the col-
lective mode is larger for B1gphonons than for A1g. This
fact can be a realization of the expected anisotropy of the
electronic excitation.
Heat capacity
In Fig. 4c Supplement information we compare our re-
sults on temperature dependence of heat capacity for
κ-Hg-Br and κ-Hg-Cl with that received by us for κ-
(BEDT-TTF)2Cu2(CN)3. This plot demonstrates the
high quality of the data obtained by us, where the κ-
(BEDT-TTF)2Cu2(CN)3data coincide with the litera-
ture. Within the precision of the measurements we per-
formed, βof κ-(BEDT-TTF)2Cu2(CN)3is similar to the
published, and to that of κ-Hg-Br, which can be ex-
plained by a similar structure and thus phonon DOS
of the compounds. Interestingly through, values of γ
coefficient in heat capacity of κ-Hg-Br and κ-(BEDT-
TTF)2Cu2(CN)3are similar, too. [33].

9
050 100 150 200 250
'' (a.u.)
Raman shift (cm-1)
4 K
50 K
80 K
175 K
200 K
280 K
050 100 150 200 250
7 K
35 K
300 K
'' (a.u.)
Raman shift (cm-1)
k-(BEDT-TTF)2Hg(SCN)2Cl
dipole solid below T=30 K
050 100 150 200 250 300
0
5
10
15
20
25
30
Line width (cm-1)
Temperature (K)
050 100 150 200 250 300
1460
1470
1480
1490
1500
1510
Raman shift (cm-1)
3
2
2
3
2(B)
2(A)
k-Hg-Br
B1g
quantum
dipole
liquid
k-Hg-Cl
B1g
dipole
solid
210 40
0.1
1
Temperature (K)
Cp/T(JK-2mol-1T-1)
k-Hg-Br
k-Hg-Cl
k-(BEDT-TTF)2Cu2(CN)3
(a) (b)
(c)
FIG. 4. Temperature dependence of (bc) spectra for (a) κ-Hg-
Br and (b) κ-Hg-Cl. Note a collective mode which appears
at low frequencies in the spectra of κ-Hg-Br, similar to bb po-
larization. The phonons are widened by the interaction with
the collective mode. (c) Comparison of temperature depen-
dance of heat capacity of κ-Hg-Br and κ-Hg-Cl with that of
κ-(BEDT-TTF)2Cu2(CN)3.
TABLE I. Crystal structure data for κ-Hg-Br and κ-Hg-Cl
Formula κ-(ET)2Hg(SCN)2Br (κ-Hg-Br) [10] κ-(ET)2Hg(SCN)2Cl (κ-Hg-Cl) [1]
Space group C2/c C2/c
a(˚
A) 37.09(1) 36.9564
b(˚
A) 8.338(3) 8.2887(2)
c(˚
A) 11.738(5) 11.7503(3)
α(deg) 90 90
β(deg) 89.71 90.067
γ(deg) 90 90
V(A3) 3570.2(8) 3564.29
Z 4 4

10
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