Quantum ferroelectricity in charge-transfer complex crystals

Quantum phase transition achieved by fine tuning the continuous phase transition down to zero kelvin is a challenge for solid state science. Critical phenomena distinct from the effects of thermal fluctuations can materialize when the electronic, structural or magnetic long-range order is perturbed by quantum fluctuations between degenerate ground states. Here we have developed chemically pure tetrahalo-p-benzoquinones of n iodine and 4–n bromine substituents (QBr4–nIn, n=0–4) to search for ferroelectric charge-transfer complexes with tetrathiafulvalene (TTF). Among them, TTF–QBr2I2 exhibits a ferroelectric neutral–ionic phase transition, which is continuously controlled over a wide temperature range from near-zero kelvin to room temperature under hydrostatic pressure. Quantum critical behaviour is accompanied by a much larger permittivity than those of other neutral–ionic transition compounds, such as well-known ferroelectric complex of TTF–QCl4 and quantum antiferroelectric of dimethyl–TTF–QBr4. By contrast, TTF–QBr3I complex, another member of this compound family, shows complete suppression of the ferroelectric spin-Peierls-type phase transition.

L attice instability coupled with charge and/or spin degrees of freedom has become an interesting area of research in solid state science as the electric, magnetic and optical properties exhibit high susceptibility to external stimuli. One intriguing characteristic is ferroelectricity susceptible to changes in temperature, pressure and external electric field. Typical examples among p-conjugated molecular solids are charge-transfer (CT) complexes 1-8 that have one-dimensional stacks of alternating p-electron donor (D) and acceptor (A) molecules, as in a series of complexes of p-benzoquinones with tetrathiafulvalene (TTF) or its 4,4 0 -dimethyl-substituted version (DMTTF). The bistable polarity along the molecular stack can be constructed by a pairwise molecular displacement (dimerization denoted by underlines such as DA DA.. or AD AD y).
There are at least two different classes of ferroelectrics in TTF complexes. The emergence of ferroelectricity in TTF-QCl 4 (ref. 9; QCl 4 or CA ¼ p-chloranil) and antiferroelectricity in DMTTF-QCl 4 (ref. 10) accompanies a phase transition from a neutral to ionic state under a temperature or pressure change. The charge degree of freedom is thus closely relevant to the mechanism of the neutral-ionic phase transition (NIT). The crystal volume is an effective parameter to characterize the NIT, because it can change the energy balance between the electrostatic Madelung gain and the cost of ionization during increasing the degree of CT r (ionicity defined by D þ r A -r ) 9 . The recent discovery of large spontaneous polarization on TTF-QCl 4 has highlighted a new mechanism of ferroelectric induction, 'electronic ferroelectricity', that is governed by the electronic overlap integral over the intermolecular space rather than the static molecular charge 3,[11][12][13] . Note that the recent studies on organic CT compounds also demonstrated gigantic permittivity from the charge-order mechanism as the similar class of electronic ferroelectricity 14 .
The contrastive ferroelectric, the bromine-substituted analogue, TTF-QBr 4 (QBr 4 ¼ p-bromanil) 15 exhibits a similar DA dimerization but preserves the monovalent ionic state during the ferroelectric transition. The antiferromagnetically coupled S ¼ 1/2 spins residing on D þ and Aradical ions turn to spin-singlet D þ Apairs on cooling, changing the chains from paramagnetic to nonmangetic. This ferroelectricity, thus, has a magnetic origin corresponding to the spin-Peierls (SP)-type phase transition that is manifested by the magnetoelectric phenomena such as magnetic control of electric polarization 16 .
For both NIT and SP systems, one challenging issue is the quantum phase transition 17 achieved by fine tuning the continuous phase transition down to zero kelvin. New states of matter may materialize when the electronic, structural and/or magnetic long-range order is perturbed by quantum fluctuations such as the 'zero-point motion' between the degenerate ground states as opposed to thermal fluctuations. The 'quantum ferroelectric' and 'quantum paraelectric' states represent those in proximity to the zero-kelvin transition point, that is, the quantum critical point (QCP) [18][19][20][21][22] . For instance, in the typical quantum paraelectric SrTiO 3 , the temperature-dependent dielectric permittivity exhibits a saturation behaviour at a gigantic value (B20,000) as the manifestation of the proximity to the QCP, and quantum ferroelectricity can be induced with subtle structural perturbations such as oxygen isotope exchange 21 . Although a quantum critical behaviour has been found in the NIT system by pressurizing DMTTF-QBr 4 crystals, the inter-stack antiferroelectric coupling, which leads to the antiferroelectrically ordered state, is responsible for the much smaller permittivity (B180) at the QCP.
To search for the QCP accompanied by quantum ferroelectricity, tetrahalo-p-benzoquinones of variable molecular volume are ideal for inducing structural changes with least perturbations to the electron affinities. In fact, the NIT has been demonstrated through optical spectra of two neutral TTF-QI 4 complexes of different stoichiometries (1:1 and 2:1) under a modest pressure of B2-3 GPa [23][24][25] . In this study, we prepared tetrahalo-pbenzoquinones with n iodine and 4-n bromine substituents (QBr 4-n I n , n ¼ 0-4; Fig. 1a) to examine the stepwise change in the lattice volume and to modify the NIT of TTF-QI 4 and the ferroelectric SP of TTF-QBr 4 . In this family, we have realized the ideal NIT type quantum ferroelectricity (TTF-QBr 2 I 2 ) by tuning the applied hydrostatic pressure

Results
Materials preparation. Considering that even small chemical inhomogeneity will mask the genuine properties around the QCP, we pursued QBr 4-n I n molecules with sufficient chemical purity for fine and systematic chemical tuning. However, previous synthetic protocols did not include the regioselective iodination step. This work established an effective purification method using gel permeation chromatography and regioselective iodination procedures, the details of which are described in the Supplementary Fig. 1. Gel permeation chromatography isolated 2-iodo-3,5,6-tribromo-p-benzoquinone (QBr 3 I) and 2-bromo-3,5,6-triiodo-p-benzoquinone (QBrI 3 ) as well as pure QI 4 , but the dibromodiiodo-p-benzoquinones could not be separated into three isomers. The symmetrically diiodo-substituted quinone (QBr 2 I 2 ) was synthesized through the new regioselective iodination process using symmetric dibromodimethoxybenzene.
CT complex formation. Without seeding specific crystal forms, the mixed acetonitrile solution of each QBr 4-n I n and TTF afforded neutral CT complexes of a 2:1 stoichiometry as the main products. The crystal structures of (TTF) 2 (QBr 4-n I n ) are isomorphous and belong to the monoclinic system with a centric space group of P2 1 /n. The molecules assemble into a DAD trimer with inversion symmetry, as shown in Fig. 1b. Previous spectroscopic studies of the pressure-induced NIT of (TTF) 2 (QI 4 ) suggested an inhomogeneous charge distribution in the ionic phase at high pressures beyond 3.1 GPa 26 . High-pressure structural studies, albeit beyond the focus of this study, would be interesting to confirm the asymmetric charge distribution suggested as a polar D þ A -D 0 and to examine the possible emergence of electronic ferroelectricity.
The 1:1 TTF complexes of QBr 4-n I n with an infinitely alternating DA sequence are usually obtained as minor products. They crystallized as either fully ionic or neutral CT complex depending on the degrees of bromine substitution between the neutral TTF-QI 4 and ionic TTF-QBr 4 . The overall CT complexes of TTF are listed in terms of the isomorphous crystal forms in Supplementary Table 1.
Ionic 1:1 TTF complexes. The 1:1 complex of 2-iodo-3,5,6-tribromo-p-benzoquinone (QBr 3 I) crystallizes as an isomorphous form of the fully ionic TTF-QBr 4 (ref. 15), the SP-type ferroelectric. Crystal structural analysis determined an analogous triclinic lattice with a space group of P-1 and two formula units (Z ¼ 2; Fig. 1c). The D and A molecules, occupying their respective inversion centres, are alternately stacked with a regular separation. The lattice constants of the a and b axes, which are both parallel to the DA stack, are elongated by 1.2% and 1.1%, respectively, compared with those of the TTF-QBr 4 crystal. Figure 2a,b depicts the temperature-dependent magnetic susceptibility and dielectric constant of these two isomorphous compounds. The magnetic susceptibility in the high-temperature region indicates the analogous paramagnetism arising from the spin-1/2 residing on each D þ and A À radical, but its monotonous increase on cooling in the case of TTF-QBr 3 I represents the absence of the SP transition. In accord with this, the dielectric permittivity has no peak anomaly characteristic of the ferroelectric transition down to the lowest temperature. Nevertheless, the gradual increase in the permittivity with decreasing temperature may reflect the quantum fluctuations of the polar dimerization.
Neutral 1:1 TTF complexes. The 1:1 TTF complexes of QBr 2 I 2 and QBrI 3 with rB0.11 at ambient pressure (as estimated from the C ¼ O stretch mode frequency; see Supplementary Discussion) are isomorphous to TTF-QI 4 (ref. 24) in crystal structure. According to previous studies of high-pressure optical spectra at room temperature, the ionicity of TTF-QI 4 steeply increases from B0.3 to 0.5 and the DA stack starts to dimerize at pressures beyond 1.9 GPa 23 . Because previous studies of TTF-QI 4 were not accompanied by a full report of the atomic coordinates, we have repeated the structural analysis. The triclinic lattice with a space group of P-1 comprises simply one formula unit (Z ¼ 1). The D and A molecules, occupying their respective inversion centres, are alternately stacked with a regular separation along the crystal b direction (Fig. 1d,e). The molecular arrangement is very similar to that of DMTTF-QCl 4 (ref. 10) in the triclinic cell (Z ¼ 1) and distinct from that of TTF-QCl 4 in the monoclinic cell (Z ¼ 2) 27 .
Bromine substitution of TTF-QI 4 shortens the D-A distance along the stack, namely, the half of b axis lattice constant, and would stabilize the ionic state by chemical pressure effect, or equivalently by increasing the attractive Coulomb interaction between D and A. We have examined the compressibility of the lattice parameters to relate the lattice shrinkage to the effective pressure Dp eff that would contribute to promotion of NIT. Using the volume compressibility of TTF-QBr 2 I 2 crystal (DV ¼ -28 Å 3 at Dp ¼ 1 GPa), the volume change from that of TTF-QI 4 corresponds to the application of Dp eff ¼ 0.29 GPa for TTF-QBrI 3 (DV ¼ -8.2 Å 3 ) and 0.60 GPa for TTF-QBr 2 I 2 (DV ¼ -16.7 Å 3 ). From the b axis compressibility (Db ¼ -0.23 Å at Dp ¼ 1 GPa), we obtained similar pressures of 0.29 GPa (Db ¼ -0.067 Å) and 0.68 GPa (Db ¼ -0.157 Å), respectively.
Dielectric properties of neutral 1:1 TTF complexes. Figure 2c depicts the temperature T dependence of relative permittivity e r measured at 300 kHz along the DA stacking direction of neutral 1:1 compounds. In the displayed temperature range, the permittivity exhibited no frequency dispersion, at least up to 1 MHz. The increase in permittivity with lowering temperature starts to deviate from the Curie-Weiss law for ferroelectrics, e r ¼ C/(T-y), where y is the Weiss temperature and C is the Curie constant. The temperature dependence including the saturation behaviour around the lowest temperature has been often fitted with the theoretical (Barrett) formula for quantum paraelectricity 28 : Here T 0 represents the Curie-Weiss temperature in the classical (high T) limit, and T 1 is the characteristic crossover temperature dividing the quantum-mechanical and classical regions. The fitting parameters for To140 K are T 0 ¼ þ 3(1) K and T 1 ¼ 71(1) K; and C ¼ 6.3(2) Â 10 3 K for TTF-QBr 2 I 2 ; and T 0 ¼ -62(10) K, T 1 ¼ 70(4) K and C ¼ 5.4(7) Â 10 3 K for TTF-QBrI 3 . In the case of TTF-QI 4 , the values are T 0 ¼ -165(12) K, T 1 ¼ 86(2) K and C ¼ 8.0(7) Â 10 3 K (see the Supplementary Fig. 4 for the fittings).
It should be noted that the saturated value of the permittivity as well as T 0 increase with the effective (chemical) pressure noted above, whereas C is almost unchanged. This behaviour is quite analogous to the case of the antiferroelectric NIT of DMTTF-QBr n Cl 4-n (ref. 29). Lattice compression under chlorine substitution or hydrostatic pressure increases the low-temperature permittivity until the temperature-induced phase transition appears together with a peak anomaly of the permittivity. The temperature-pressure phase diagram marks the zero-kelvin transition point, that is, the QCP. One may think that decreasing the D-A separation with further bromine substitution beyond TTF-QBr 2 I 2 would surpass the QCP and realize the temperature-induced ferroelectric NIT at ambient pressure. Unfortunately, this expectation has not yet materialized solely by the chemical modifications because of formation of the ionic CT complexes as noted above. To search for the QCP, we applied the hydrostatic pressure on the TTF-QBr 2 I 2 crystal.   ARTICLE TTF-QBr 2 I 2 under hydrostatic pressure. At ambient and low pressures, the relative permittivity around the lowest temperature (4 K) exhibits saturation behaviour and increases from 200 to 700 with pressure (Fig. 3a). According to the fit with the Barrett formula, T 0 increases to þ 18.2(6) K at 0.23 GPa with T 1 ¼ 68.7(7) K and C ¼ 1.22(2) Â 10 5 K. Although the phase transition is expected near this positive T 0 in the classical picture, it is suppressed by the quantum fluctuations. Beyond the critical pressure of p c ¼ 0.25 GPa, a sharp peak indicative of the phase transition appears and shifts towards a higher temperature with further increasing pressure. The phase transition is accompanied by a small peak anomaly in the temperature dependence of dielectric loss (that is, imaginary part of dielectric constant). The Barrett formula has a drawback in its theoretical accuracy, although it is a prevailingfitting equation for quantum paraelectricity and convenient for estimating Curie-Weiss temperature in the classical limit as above: it cannot describe the behaviour around the QCP 22 . One of the reasons is that the fluctuation spectrum is assumed to be independent of wave vector and temperature, in contradiction to the observed softening of optical phonon mode in the displacive ferroelectrics. The mode softening has been observed near the ferro-and antiferroelectric transitions also in the family of electronic ferroelectric TTF-CA 3,4,30 . The fluctuating and softening polar mode in the latter ferroelectric is considered to be the so-called Peierls mode, which is accompanied by the intermolecular electron transfer oscillation coupled with the dimeric molecular displacement. According to the theory of quantum criticality 22 , the inverse dielectric susceptibility should be proportional to the square of temperature near the QCP for the typical displacive ferroelectrics such as SrTiO 3 and KTaO 3 . In fact, this critical behaviour is clearly seen in the linear T 2 -1/e r relation (Fig. 3c) at temperatures below 50 K and pressures near the QCP for the TTF-QBr 2 I 2 crystal. Figure 3b shows the pressure-temperature phase diagram obtained from this permittivity measurement. Here the hydrostatic pressure values at the phase transition temperatures are corrected considering the effect of the thermal contraction of the pressure-transmitting oil in the clamp-type high-pressure cell (see Methods). The NIT critical temperature (T c ) tends to increase linearly with pressure in the high-pressure region. Its extrapolation to 1.63 GPa at room temperature (295 K) agrees well with the pressure of 1. roughly explained by the effective pressure of Dp eff ¼ 0.60 GPa noted above. The large slope (dT c /dp ¼ 0.166 K MPa -1 ), which is half that of TTF-QCl 4 (0.32 K MPa -1 ) 31 , also reflects the pressure-sensitive nature of the NIT. In contrast, the phase boundary (Fig. 3b) in the low-pressure region exhibits a critical drop, which can be approximated as T c p(p À p c ) 1/2 . The QCP is well defined at p c ¼ 0.246 GPa through the linear p-T c 2 relation (see inset in Fig. 3b). The permittivity at the lowest temperature e r (T ¼ 5 K) as a function of pressure reveals a divergent-like sharp maximum at p c (Fig. 4a). There are some similarities and dissimilarities in the quantum critical behaviour near the QCP between the present case and the pressure-induced antiferroelectric NIT of DMTTF-QBr 4 (ref. 29). Despite the very similar crystal structures in the paraelectric state, the inverse-e r versus p plot (inset to Fig. 4a) indicates the different behaviour between the two crystals around the QCP; in TTF-QBr 2 I 2 , the permittivity increases much more rapidly, obeying a simple power law of e r (T ¼ 5 K)p|p-p c | -1 . Because the maximum e r (T ¼ 5 K) of TTF-QBr 2 I 2 (B800) is four times as large as that of DMTTF-QBr 4 (o200), these observations reflect the different nature, that is, ferroelectric versus antiferroelectric, of the pressure-induced ordered phases. This difference manifests itself in structural changes. Figure 4b presents the electric polarization (P) versus electric field (E) diagram measured along the DA stacking direction at 4 K. The linear P-E relation at ambient pressure is characteristic of the paraelectric state. The expected pressure-induced ferroelectric state is clearly demonstrated by the P-E hysteresis loop at p ¼ 0.34 GPa. The magnitude of P r (1.7 mC cm -2 at p ¼ 0.34 GPa) is 410 times as large as that of the ionic ferroelectric TTF-QBr 4 (0.15 mC cm -2 ) 16 but rather close to that of TTF-QCl 4 (6.3 mC cm -2 ) 12 . This fact suggests that the microscopic origin of ferroelectricity, in particular its electronic nature as mentioned above, is similar in TTF-QCl 4 and TTF-QBr 2 I 2 .
According to the X-ray diffraction experiments with TTF-QBr 2 I 2 at 7 K under several different pressures (0.61, 0.67, 1.40, 1.80 and 2.27 GPa), the low-temperature, high-pressure phase is not accompanied by the appearance of any satellite reflections arising from superlattice. Because the triclinic unit cell involves simply one formula unit (Z ¼ 1), the symmetry-breaking DA dimerization therein confirms its ferroelectric nature. This structural change is in sharp contrast to the antiferroelectric change of unit-cell doubling in the DMTTF complexes 29 . The full structural analysis of the high-pressure phase is under examination and will be reported elsewhere.

Discussion
QBr 4 has been successfully substituted with iodine in a stepwise and regioselective manner. The TTF-QBr 2 I 2 complex has enabled us to continuously control the ferroelectric NIT over a wide temperature range from zero kelvin to room temperature. In past studies, the TTF-QCl 4 complex was partially replaced with tetraselenafulvalene (TSF), which has a larger molecular volume, to reduce the ferroelectric NIT temperature 32 . Quantum fluctuations are generally fragile against the inhomogeneity of the system, which cannot be removed in terms of the ionization energy in ternary compounds such as TTF 1-x TSF x -QCl 4 . The binary compound DMTTF-QBr 4 overcame this problem, and clear quantum critical behaviour of the NIT was exhibited, although the ionic DA lattice is dimerized into an antiferroelectric structure, cancelling out the polarization between neighbouring chains 29 . Renewed interest in the NIT system has also originated from the large electric polarization of TTF-QCl 4 arising from the intermolecular CT process, namely, 'electronic ferroelectricity'. The TTF-QBr 2 I 2 complex is free from inhomogeneities such as the site energy variations and disordered molecular dipoles. TTF-QBr 2 I 2 exhibits quantum critical behaviours relevant to the ferroelectric order, and hence can be considered as the first clean example of a 'quantum electronic ferroelectric'.
While the temperature-induced NIT would be expected for a lattice-contracted isomorph of TTF-QBr 2 I 2 , the TTF-QBr 3 I complex forms a different type of crystal structure as another interesting class of quantum ferroelectrics. The monoiodination of the paramagnetic TTF-QBr 4 salt is accompanied by a complete suppression of the ferroelectric SP transition. The lattice expansion and/or random orientation with dipolar QBr 3 I molecules may be plausible origins of the modified ground state. The ferroelectric SP state of TTF-QBr 4 is suppressed under a strong magnetic field, exemplifying the 'organic multiferroelectric'. Further chemical modifications or high-pressure studies of the TTF-QBr 3 I single crystal would provide promising phase controls for magnetoelectric phenomena.

Methods
Crystallization of TTF CT complexes. Neutral CT complexes of 2:1 stoichiometry, (TTF) 2 (QBr 4-n I n ) (n ¼ 0-4), were obtained by slow evaporation or cooling ARTICLE (B0°C) of mixed acetonitrile solution of QBr 4-n I n and TTF as the main products. Occasionally, the 1:1 neutral complexes of TTF-QBr 2 I 2 and TTF-QBrI 3 crystallized as dark brown elongated plates, while the 1:1 ionic complexes of TTF-QBr 3 I and TTF-QBr 4 crystallized as black rectangular plates. These minor crystal forms could be selectively crystallized with a size sufficient for electric measurements by prior seeding of several small single crystals. The 1:1 form of the TTF-QI 4 complex was crystallized as elongated plates by slow evaporation or cooling of the toluene solution of the stoichiometric mixture of components.
Electric, magnetic and optical measurements. Infrared absorption spectra of the samples dispersed in KBr disks ( Supplementary Figs 2 and 3) were recorded at room temperature with a Fourier transform infrared spectrometer (JASCO FTIR-200) in a frequency range of 4,000 À 400 cm À 1 at a resolution of 4 cm À 1 . The magnetization of the polycrystalline TTF-QBr 3 I powder wrapped in a thin aluminium foil was measured at a constant magnetic field of 0.2 T by a superconducting quantum interference device magnetometer (MPMS XL, Quantum Design). The spin susceptibility data were obtained with correction for the magnetization of a blank foil and the core diamagnetism using the compilation of Pascal's constant (2.2 Â 10 À 4 e.m.u. mol À 1 ). The temperature-dependent dielectric constant was measured with an LCR metre (HP 4284A) and at a cooling/ heating rate of 1 À 2 K min À 1 . Hydrostatic pressure in the pressure-transmitting oil (Daphne 7,373, Idemitsu Kosan) was generated using a clamp-type highpressure cell. The applied pressure at each transition point or T ¼ 5 K (Figs 2b and  3) was obtained by correcting the thermal change of the pressure (dp/dT ¼ 0.76 MPa K À 1 for T490 K and constant p for To90 K) owing to the contraction of the medium 33 . The P-E hysteresis curves were measured at 1 kHz with a commercial ferroelectric tester (Precision Premier II, Radiant Technologies) equipped with a voltage amplifier (Precision 4 kV HVI, Radiant Technologies).
Crystallographic studies. For the TTF-QBrI 3 and (TTF) 2 (QBr 2 I 2 ) crystals, both the X-ray diffraction data collection at room temperature and the assignment of the crystallographic axes of the bulk single crystals were completed using a four-circle diffractometer (Rigaku AFC7R; graphite-monochromated MoKa radiation) equipped with a charge-coupled device area detector. For the TTF-QBr 2 I 2 , TTF-QBrI 3 and TTF-QI 4 crystals, the X-ray diffraction experiments at room temperature were carried using a Rigaku DSC imaging plate diffractometer and synchrotron radiation (l ¼ 0.6889 Å) at beamline BL-8A or BL-8B of the photon factory, High-Energy Accelerator Research Organization. The X-ray beam was monochromatized by a Si double-crystal monochromator and focused by a bent cylindrical mirror made of a Si crystal coated with Rh. The reflection intensity data were collected with the use of the Rapid-AUTO software package (Rigaku Corp.) and analysed with the Crystal Structure crystallographic software packages (Molecular Structure Corp. and Rigaku Corp.). The final refinements were done with anisotropic atomic displacement parameters for the non-hydrogen atoms and with calculated positions (with a fixed C-H distance of 0.95 Å) for the hydrogen atoms. Crystallographic data and experimental details of the CT complexes of TTF and QBr 4-n I n are summarized in Supplementary Table 2 and Supplementary Data 1-5.
The change in the lattice parameters under hydrostatic pressure was examined at room temperature for a TTF-QBr 2 I 2 single crystal using synchrotron radiation and a clamp-type Be-cylinder high-pressure cell filled with Daphne 7373 oil as the pressure-transmitting medium 34 . The diffraction study of a TTF-QBr 2 I 2 single crystal under hydrostatic pressure was performed using synchrotron radiation and a diamond anvil cell filled with a 4:1 methanol-ethanol mixture. Diffraction spots were recorded on the imaging plate using a diffractometer equipped with a closedcycle He-gas refrigerator, and the diamond anvil cell was mounted on the cold head of the refrigerator. The pressure was evaluated from the lattice constant of a NaCl internal pressure marker.