LETTERS PUBLISHED ONLINE: 12 AUGUST 2012 | DOI: 10.1038/NMAT3400
Multiferroicity in an organic charge-transfer salt that is suggestive of electric-dipoledriven magnetism Peter Lunkenheimer1 *, Jens Müller2 , Stephan Krohns1 , Florian Schrettle1 , Alois Loidl1 , Benedikt Hartmann2 , Robert Rommel2 , Mariano de Souza2† , Chisa Hotta3 , John A. Schlueter4 and Michael Lang2 101 E⊥b 10¬1 E ll b σ dc (Ω¬1 cm¬1)
Multiferroics, showing simultaneous ordering of electrical and magnetic degrees of freedom, are remarkable materials as seen from both the academic and technological points of view1,2 . A prominent mechanism of multiferroicity is the spin-driven ferroelectricity, often found in frustrated antiferromagnets with helical spin order1,3–5 . There, as for conventional ferroelectrics, the electrical dipoles arise from an off-centre displacement of ions. However, recently a different mechanism, namely purely electronic ferroelectricity, where charge order breaks inversion symmetry, has attracted considerable interest6 . Here we provide evidence for ferroelectricity, accompanied by antiferromagnetic spin order, in a two-dimensional organic chargetransfer salt, thus representing a new class of multiferroics. We propose a charge-order-driven mechanism leading to electronic ferroelectricity in this material. Quite unexpectedly for electronic ferroelectrics, dipolar and spin order arise nearly simultaneously. This can be ascribed to the loss of spin frustration induced by the ferroelectric ordering. Hence, here the spin order is driven by the ferroelectricity, in marked contrast to the spin-driven ferroelectricity in helical magnets. Here, we have investigated single-crystalline κ-(BEDT-TTF)2 Cu[N(CN)2 ]Cl (κ-Cl), where BEDT-TTF stands for bis(ethylenedithio)-tetrathiafulvalene (often abbreviated as ET). Three crystals with different geometries and contact materials were investigated (see Methods). In these compounds, dimers of ET molecules form an anisotropic triangular lattice with a half-filled dimer band, where the strong on-dimer Coulomb interaction U drives the system to a Mott insulating state7,8 . In addition, the importance of intra-dimer degrees of freedom and inter-site interactions V has been pointed out9–11 . κ-Cl consists of alternating conducting ET layers and insulating anion sheets (see Supplementary Fig. S1). Within the ET layers, adjacent molecules form dimers on which a single hole is located. Below TN ≈ 27 K, intralayer antiferromagnetic and interlayer ferromagnetic ordering of hole spins occur, followed by weak ferromagnetic canting below 23 K (refs 12,13). κ-Cl becomes superconducting below 12.8 K, when applying pressures of 300 bar (ref. 14). Figure 1 shows the temperature-dependent conductivity σ 0 for field directions E ⊥ b and E k b, measured at low frequencies, providing a good estimate of the d.c. conductivity σd.c. (see
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Figure 1 | Temperature dependence of conductivity of κ-(ET)2 Cu[N(CN)2 ]Cl. Conductivity of sample 1 at 2.1 Hz for E k b (b denotes the interlayer direction) and of sample 3 at 1 Hz for E ⊥ b, representing a reasonable estimate of the d.c. conductivity. The arrow indicates the Néel temperature reported in ref. 12; see Supplementary Information for sample-to-sample variations. The insets show schematic drawings of the ac planes for temperatures below and above TFE . Thick grey lines: ET molecules; red spheres: holes (the red shaded areas for T > TFE indicate their delocalization); orange arrows: dipolar moments arising at T < TFE .
Supplementary Information). Besides the known overall semiconducting characteristics of σd.c. (T ) (refs 14–16), including the abrupt increase of the charge gap below about 50 K (refs 15,16), some interesting and hitherto unreported behaviour is observed: whereas at elevated temperatures (T > 50 K) the conductivity within the planes exceeds the out-of-plane conductivity by a constant factor of more than 200, the anisotropy becomes significantly reduced on cooling to 4.2 K, with an overall reduction of the conductivity by about 6 (E k b), respectively 9 (E ⊥ b) orders of magnitude. Of particular interest here is the jump-like drop in the conductivity by two decades at around 27 K, about the same temperature where long-range antiferromagnetic ordering is reported7,8 , which is most clearly pronounced for E k b.
1 Experimental
Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany, 2 Institute of Physics, Goethe-University Frankfurt, Max-von-Laue-Str. 1, 60438 Frankfurt(M), Germany, 3 Department of Physics, Faculty of Science, Kyoto Sangyo University, Kyoto 603-8555, Japan, 4 Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA. † Present address: IGCE, Unesp—Univ Estadual Paulista, Departamento de Física, Cx. Postal 178, CEP 13506-900 Rio Claro (SP), Brazil. *e-mail:
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NATURE MATERIALS DOI: 10.1038/NMAT3400
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An anomaly, although less clearly pronounced, is visible also for the field directed parallel to the ET planes (E ⊥ b) in the data for crystal 3 in Fig. 1. A less clear signature is not surprising given the strong overall reduction of σd.c. (E ⊥ b) below 50 K being much stronger than for E || b. A corresponding jump in the out-of-plane conductivity was also found in sample 2 (see Supplementary Information). A distinct drop in σd.c. has not been observed in most a.c. and d.c. studies reported so far (except in ref. 16), which may be ascribed to the higher precision of dielectric measurements at high resistances, compared with standard d.c. set-ups. This abrupt reduction of the conductivity within the Mott insulating state is a first hint to a charge-order transition, that is, a collective localization of charge carriers. Figure 2 shows the dielectric constant ε 0 (T ) of sample 1 for various frequencies. Pronounced peaks reaching absolute values of up to several hundred are revealed. Whereas the peak positions are nearly frequency independent, their amplitudes become strongly suppressed with increasing frequency. The overall behaviour is typical for order–disorder-type ferroelectrics, where the electric dipoles that are disordered at high temperatures order with net overall polarization below a phase-transition temperature TFE (ref. 17). Identifying the dipoles with the holes fluctuating within the dimers at T > TFE and cooperatively locking in to one of the two ET molecules at T < TFE provides a plausible scenario for the present material (see Fig. 1 insets). Similar behaviour as observed in Fig. 2 was also found for other ferroelectric charge-transfer salts18,19 . The peaks are superposed to a rather high background contribution εb of about 120, partly arising from stray-capacitance contributions due to the small sample dimensions. The dashed line in Fig. 2 demonstrates that the high-temperature flanks of ε0 (T ) at low frequencies (that is, the static dielectric constant εs (T )) are consistent with a Curie– Weiss behaviour, εs = C/(T − TCW ) + εb , with a Curie–Weiss temperature TCW = 25 K ≈ TFE and a background term εb . This temperature agrees reasonably with the Néel temperatures between about 25 and 30 K reported in the literature (see Supplementary Information for a detailed discussion) and with TN ≈ 27 K deduced from thermal expansion measurements (Supplementary Fig. S7). Sample 2 showed a similar dielectric response to that seen in Fig. 2 (see Supplementary Information), despite having a significantly different geometry and a different contact material—clear evidence for the intrinsic nature of the observed behaviour. In a previous dielectric investigation of κ-Cl (ref. 20), relaxational behaviour was deduced from frequency-dependent dielectric measurements below 30 K, consistent with the notion of order–disorder ferroelectricity17 . Owing to the restricted temperature range in that work, no ε0 (T ) peaks were detected20 . Further evidence for ferroelectric ordering in κ-Cl is provided by so-called positive-up-negative-down (PUND) measurements, where a sequence of trapezoid pulses (Fig. 3a) is applied to the sample. The resulting current response (Fig. 3b) shows strong peak-like features occurring when the electric field |E| exceeds about 10 kV cm−1 for the first and third pulse. Obviously, here the macroscopic polarization of the sample is switched, that is, the dipoles within the ferroelectric domains reorient along the field, implying a motion of charges and, thus, a peak in I (t ). As expected for ferroelectrics, at the second and forth pulse, no corresponding features show up because the polarization was already switched by the preceding pulse. (The horizontal sections in I (t ) represent the trivial charging and discharging currents of the sample capacitor.) The typical PUND response was clearest for low frequencies, ν < 100 Hz. Stimulated by these results, we have also performed fielddependent polarization measurements, P(E). Typical results are shown in Fig. 3c. Above TFE , elliptical curves are observed (crosses), typical for linear polarization response (paraelectricity) with
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Figure 2 | Temperature dependence of the dielectric constant. ε 0 (T) for sample 1, for selected frequencies and E k b. The solid lines are guides for the eyes. The dashed line demonstrates Curie–Weiss behaviour with TCW = 25 K.
loss contributions from charge transport17 . However, at lower temperatures, a clear onset of nonlinearity above about 8.5 kV cm−1 occurs and saturation at the highest fields is observed (circles), as expected for ferroelectrics. The saturation polarization of several tenths of a microcoulomb per square centimetre compares well to that of the ferroelectric charge-transfer salt tetrathiafulvalenep-bromanil (0.2 µC cm−2 ; ref. 21) and the electronic ferroelectric and multiferroic magnetite (0.5 µC cm−2 ; ref. 22). In the electronic ferroelectric Pr1x Cax MnO3 (44 µC cm−2 ; ref. 23), higher values are found. Interestingly, at higher fields, |E| > 12 kV cm−1 , breakdown effects were observed. This may indicate that the sample resistance has become too low and that interplane charge transport sets in. Thus, there is a rather restricted range of roughly 9–12 kV cm−1 for nonlinear polarization response in κ-Cl. Overall, the results presented in Figs 2 and 3 provide strong evidence for ferroelectricity in κ-Cl, coinciding with the occurrence of magnetic ordering. The appearance of simultaneous electrical and magnetic order is a well-understood phenomenon in multiferroic systems with spiral spin order1–3 . There the onset of helical spin order breaks inversion symmetry and, owing to the Dzyaloshinskii–Moriya interaction, triggers the formation of displacive ferroelectric order through the electro-magnetic coupling P ∝ e × Q. Here Q denotes the propagation vector of spin order and e = Si × Sj , a cross product between adjacent spins Si and Sj , gives the spiral axis2,4 . Thus, these systems are regarded as spin-driven ferroelectrics. Could this be the mechanism generating multiferroicity in κ-Cl? Indeed, it has been pointed out that a finite Dzyaloshinskii–Moriya interaction is present in κ-Cl (refs 8,13). However, to our knowledge no experimental evidence for a helical magnetic structure in this material has been found until now. To check for a spin-driven mechanism, we have performed magnetic field-dependent dielectric measurements. Usually, spindriven multiferroics show a strong dependence of the dielectric properties on externally applied magnetic fields (so-called magnetocapacitive effects)1,2,24 . Moreover, in κ-Cl a spin-flop transition at 0.25 T into a direction perpendicular to the field has been found below 23 K (refs 12,13). In the spin-driven scenario, the spin-flop transition would affect the dielectric properties through P ∝ Q×(Si ×Sj ). Remarkably, no variation of the dielectric properties in fields up to 9 T was found (see Supplementary Information), ruling out a spin-driven mechanism for multiferroicity in κ-Cl. This suggests that for κ-Cl a purely electronic, charge-orderdriven ferroelectric state, as also considered for other ferroelectric charge-transfer salts6,9,18,25,26 , is realized. In fact, in a review article on this mechanism6 , charge-transfer salts were considered as good candidates for multiferroics with a ferroelectric state driven by NATURE MATERIALS | VOL 11 | SEPTEMBER 2012 | www.nature.com/naturematerials
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NATURE MATERIALS DOI: 10.1038/NMAT3400 a
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Figure 4 | Temperature-dependence of the dielectric constant. ε0 (T) for sample 3, for selected frequencies and E ⊥ b. The lines are guides for the eyes.
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Figure 3 | Electric polarization switching. a, Time-dependent excitation signal E k b of the PUND measurements performed at 25 K with waiting time δ and pulse width p. b, Resulting time-dependent current of sample 2. The spikes in response to pulses I and III provide evidence for polarization switching. c, Polarization-field hysteresis curves at temperatures below and above the ferroelectric phase transition.
charge order. The mechanism discussed in that work is based on a combination of bond- and site-centred charge order leading to the breaking of inversion symmetry. This provides a plausible scenario for κ-Cl: just as in the structurally related κ-(ET)2 Cu2 (CN)3 , at high temperatures each hole can be assumed to be delocalized on an ET dimer9–11 . This corresponds to pure bond centring (see Fig. 1c of ref. 6). Below TFE , the holes lock in to one of the two molecules of the dimers, additionally establishing site centring (Fig. 1d in ref. 6). This will primarily lead to a polarization parallel to the planes, but, owing to the inclined spatial orientation of the ET molecules8 , a polarization along b is also induced. The results presented so far were obtained with E k b to exclude problems arising from the high in-plane conductivity of κ-Cl, which considerably exceeds the out-of plane conductivity, at least at elevated temperatures (Fig. 1). Below TN , which coincides with the charge-order transition, the conductivities come rather close to each other and the out-of-plane conductivity exceeds the in-plane behaviour only by about one order of magnitude. This indicates that dielectric experiments, aiming at a detection of the polar ground state, should be possible. In general, measurements of the dielectric properties of highly conducting samples are difficult to perform owing to dominant charge-transport and inductance contributions as well as Maxwell–Wagner relaxations27 , making the interpretation of those results difficult. However, in light of the distinct anomalies seen for E k b, some signatures of the ferroelectric polarization parallel to the planes (E ⊥ b) can be expected. Figure 4 shows such results for sample 3. At T > 30 K, a peak shows up that strongly shifts
with frequency, thus showing the typical signature of a relaxation process. Most likely it is of Maxwell–Wagner type and can be ascribed to electrode polarization arising from the formation of the depletion layers of Schottky diodes that form at the electrode– sample interfaces27 . However, at lower temperatures and partly superimposed by this non-intrinsic contribution, another peak is revealed. It occurs close to TN and its position does not, or only weakly, depend on frequency (the apparent weak shift at frequencies beyond several kilohertz can be ascribed to the contribution of the Maxwell–Wagner peak, which dominates at high frequencies). Just as for E k b, the maximum becomes strongly suppressed for high frequencies. The observation of a peak in ε’ for E ⊥ b, despite its significant rounding, which is probably due to partial shielding by mobile charge carriers, is a clear indication for an in-plane component of the ferroelectric polarization. The measurements of the in-plane dielectric properties of κ-Cl reported in ref. 28, which were restricted to temperatures below 25 K and a narrow frequency range, showed similar behaviour as in Fig. 4. Interestingly, close to the upper temperature limit of 25 K of this investigation, just the onset of a peak was observed, in good agreement with the present results. Owing to the high conductivity for E ⊥ b, meaningful P(E) results could not be obtained. PUND experiments for E ⊥ b also suffer from the high conductivity, which, moreover, is revealed to be highly nonlinear28 . Nevertheless, the obtained results (see Supplementary Information) are consistent with a ferroelectric polarization for E ⊥ b. In contrast to the spin-driven systems, for charge-order multiferroics the ferroelectric and magnetic transition temperatures can differ significantly6,22 . How can the nearly identical transition temperatures in κ-Cl be explained within the above framework? The magnetism in κ-Cl arises from the spins of the holes, which, at T > TN , are already located on a single dimer. As the holes fluctuate within the dimers, their spins—on average—sit at the centres of the dimers, forming an anisotropic triangular lattice within the ac planes (indicated by lines in the schematic drawing in the right inset of Fig. 1), giving rise to geometrical frustration. Indeed, in κ-(ET)2 Cu2 (CN)3 , where frustration is even stronger, a spin-liquid state is formed29 . There, dielectric measurements9 have revealed relaxor ferroelectricity, that is, short-range clusterlike ferroelectric order. However, in κ-Cl, we find long-range ferroelectricity, which we assume to be caused by charge order, which implies the collective off-centre positioning of holes within
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NATURE MATERIALS DOI: 10.1038/NMAT3400
LETTERS the dimers below TFE . Consequently, the spins no longer reside on a highly frustrated triangular lattice (left inset of Fig. 1). The frustration should therefore be reduced and magnetic order sets in (see Supplementary Information). The observed conductivity, dielectric and polarization properties of κ-Cl provide evidence for ferroelectricity, making this material the first example of a multiferroic charge-transfer salt. We propose charge-order-driven electronic ferroelectricity as the most plausible scenario at present to explain the observed polar order in this material. Our measurements indicate that ferroelectric order drives the magnetic order, in marked contrast to the well-known spindriven mechanism in the helical magnets. Thus, κ-Cl not only stands for a new class of multiferroics but also represents a candidate for the realization of a new coupling mechanism of magnetic and ferroelectric ordering.
Methods Crystal growth. Crystals of κ-(BEDT-TTF)2 Cu[N(CN)2 ]Cl were grown according to literature methods15,30 . Sample 2 was grown on the surface of a platinum electrode, as is typical for growth by electrocrystallization. It was roughly plate-like (b axis vertical to the surface) with an area of about 0.3 × 0.5 mm2 and a thickness of 0.2 mm. Occasionally during the electrocrystallization process, crystals grow on the bottom of the electrochemical cell, removed from the electric field at the electrode surface, and have a rod-like morphology. X-ray diffraction measurements show both morphologies are the same crystalline phase. Samples 1 and 3 were grown by this method. The long crystal axis of sample 1 (parallel to the b crystallographic axis) was about 0.4 mm and it had a cross-section of about 0.07 mm2 . Sample 3 had a nearly cubic shape with an edge length of about 0.5 mm. The block-like morphology of this sample enabled the dielectric measurements to be performed for E ⊥ b. Dielectric measurements. For the dielectric measurements, contacts of graphite paste (samples 1 and 3) or evaporated gold (sample 2) were applied at opposite sides of the crystals, ensuring an electrical field direction parallel (samples 1 and 2) or perpendicular to b (sample 3); that is, for samples 1 and 2 the electrical field was directed perpendicular and for sample 3 parallel to the ET planes. The dielectric constant and conductivity were determined using a frequency-response analyser (Novocontrol α-Analyzer) and an autobalance bridge (Hewlett-Packard HP4284). For sample cooling at zero magnetic field, a 4 He-bath cryostat (Cryovac) was used. Magnetic-field-dependent dielectric measurements of sample 2 with H k b up to 9 T were performed in a Quantum Design physical properties measurement system. Further measurements of sample 2 up to 1.5 T, with the external magnetic field directed parallel to the ac plane, were performed using a conventional electromagnet. In this case, sample cooling was achieved by a closed-cycle refrigerator. For the nonlinear measurements, a ferroelectric analyser (aixACCT TF2000) was used, where cooling was also provided by a closed-cycle refrigerator.
Received 8 December 2011; accepted 13 July 2012; published online 12 August 2012
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Acknowledgements We thank H-A. Krug von Nidda and H. Jeschke for helpful discussions. This work was supported by the Deutsche Forschungsgemeinschaft through the Transregional Collaborative Research Centers TRR 80 and TRR 49. Work at Argonne was supported by the US Department of Energy Office of Science, operated under contract no. DE-AC02-06CH11357.
Author contributions M.L., A.L., P.L. and J.M. conceived and supervised the project. J.A.S. grew the high-quality single crystals. B.H., J.M. and R.R. prepared the samples for the experiments. S.K., P.L. and F.S. performed the dielectric measurements and analysed the data. P.L. together with M.L. and J.M., wrote the paper with contributions from C.H., A.L., J.A.S. and M.d.S. All authors discussed the results and commented on the manuscript.
Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to P.L.
Competing financial interests The authors declare no competing financial interests.
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