Main

A straightforward guideline for designing spin-driven ferroelectricity might be to use the symmetric interaction, simply because it is more dominant in ubiquitous magnets, rather than the antisymmetric exchange interaction (that is, the Dzyaloshinskii–Moriya interaction). In this context, the up-up-down-down (↑↑↓↓) magnetic order on the alternating (ABAB) atom sites was proposed as a promising candidate for symmetric-exchange-driven ferroelectricity9; this prediction has actually been confirmed in the frustrated Ising chain system, Ca3Co2−xMnxO6 (A=Co and B=Mn)10, and the f–d spin-coupled state of GdFeO3 (A=Gd and B=Fe)11. Moreover, there is a theoretical argument that symmetric-exchange-driven ferroelectricity can host potentially large polarization12. This recent progress is prompting a pursuit of not only materials showing the ↑↑↓↓ order but also other clear-cut examples of symmetric-exchange-driven ferroelectricity.

In the same way as one-dimensional (1D) metals with inherent lattice instability (Peierls instability)13, 1D Heisenberg spin-1/2 quantum magnets possess an instability to form a dimer-singlet state because of the energy gain of symmetric exchange14,15. This is known as the spin–Peierls instability, a textbook example of spin–lattice coupling. Therefore, the spin–Peierls instability with alternating ABAB spin sites can host a polar singlet-dimer and hence is expected to provide a new mechanism for magnetically controllable ferroelectrics of symmetric-exchange origin. The organic charge-transfer salt TTF–BA (tetrathiafulvalene-p-bromanil) has been proposed as a possible candidate of this new class16 of material, namely a ferroelectric spin–Peierls material; nevertheless, direct observations of ferroelectricity, that is, electric-field reversal of polarization, have yet to be accomplished in TTF–BA. Furthermore, the prominent magnetoelectric effect is anticipated in the possible ferroelectric spin–Peierls phase because of the magnetic-field effect on the spin–Peierls transition, yet this is also unexplored. In this work, using successfully synthesized large crystals of TTF–BA (see the Methods section), we demonstrate both the ferroelectric properties and their magnetic-field modification and argue a new feature of the ferroelectric spin–Peierls transition.

According to the structural analysis of TTF–BA (ref. 17), the space group changes from (nonpolar) to P1 (polar) below Tc (≈53 K), and a 1D polar stack is realized through the dimer-singlet formation of the ionic TTF donor (D+) and BA acceptor (A−) molecules, as schematically shown in Fig. 1a. The real crystal structure (Fig. 1b) consists of two D+A−D+A−… mixed stacks (‘α stack’ and ‘β stack’ along the a and b axes, respectively), and the dimerization occurs in both stacks17,18. Note that unlike the prototypical neutral–ionic transition system TTF-p-chloranil (ref. 19), TTF and BA molecules in TTF–BA are almost ionic in a whole temperature region (the ionicity is ∼0.95; ref. 18); thus, the D+A− stack can be regarded as a 1D Heisenberg chain with spin-1/2. In fact, TTF–BA undergoes a paramagnetic-to-non-magnetic transition at Tc≈53 K (Fig. 1c)18, being consistent with the singlet formation in the 1D Heisenberg chain involving the spin–Peierls instability. The D+A−-dimerized stack is also manifested by the steep increase below Tc in the spectral weight of ag mode activity at 1,422 cm−1 probing the local D+A− dimerization18 (Fig. 1d). From the temperature dependence of spin susceptibility, the magnitude of the spin gap in the dimerized phase is estimated to be ∼230 K (Fig. 1c and Supplementary Fig. S1), which is clearly larger than Tc. This means that the condensation energy of the dimerized phase originates mainly from the singlet formation. Therefore, the magnetism–lattice coupled phase transition at 53 K can be regarded as the spin–Peierls transition.

Figure 1: Ferroelectric spin–Peierls transition in TTF–BA.
figure 1

a, Schematic structure of ionic donor (D+) and acceptor (A−) mixed stacks in high- and low-temperature phases of TTF–BA. The arrow, underline and ellipsoid represent spin-1/2, a dimer and a singlet state, respectively. P denotes electric polarization. b, Crystal structure of TTF–BA. c–f, Temperature dependence of spin susceptibility (c), normalized spectral weight of the ag mode at 1,422 cm−1 as a measure of local D+A− dimerization (d), dielectric constant at 10 kHz (e) and spontaneous polarization (f) along the b axis. In c, the spin susceptibility at 1 T is presented after subtracting both the estimated core diamagnetism (∼−2.2×10−4 e.m.u./mol f.u.) and the Curie contribution discernible below 20 K. The blue curve in c is the activation-type fitting (Supplementary Fig. S1), χspin∼exp(−Δs/kBT), with the spin gap Δs (≈230 K). The temperature dependence of the ag mode spectra is shown in the inset of d; see also Supplementary Fig. S2.

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The actual dimerization is not necessarily face-to-face17, and thus the local polarization induced by each dimerized stack may deviate from the original stacking direction. To estimate the polarization direction, we calculated local polarizations by using a classical point-charge model, which is the first approximation in the case of an ionic crystal such as TTF–BA, and found that the dimerization pattern may result in total polarization P approximately along the b axis (slightly inclined towards the a axis, see Supplementary Fig. S3 and Table S1). In fact, a sharp enhancement of the dielectric constant (ɛ1≈210) is observed at ∼53 K along the b axis (Fig. 1e). In contrast with the blurred anomaly reported for the polycrystalline sample20, this clear feature is indicative of a ferroelectric transition. We also observed a ɛ1 peak of ∼24 along the a axis, with no enhancement along the c axis (Supplementary Fig. S4). This overall dielectric behaviour including the dielectric anisotropy is at least qualitatively consistent with our expectation. Below 53 K, the spontaneous polarization P was actually observed along the b axis by pyroelectric current measurements (Fig. 1f). More directly, a clear P–E hysteresis loop is also obtained (Fig. 2). The magnitudes of P agree well except for around 43 K (Fig. 2, inset), demonstrating unambiguously that the low-temperature phase is not only composed of polar singlet-dimers but is also ferroelectric with reversible spontaneous polarization. The polarization at the lowest temperature is ∼0.15 μC cm−2, which is larger than the representative cycloidal-spin-based multiferroics, TbMnO3 (∼0.08 μC cm−2; ref. 1).

Figure 2: P–E hysteresis loop along the b axis.
figure 2

The measurement was done at 0.1 Hz. Inset: Comparison between the temperature dependence of remnant polarization obtained in the P–E hysteresis loop and that obtained in the pyroelectric measurement (Fig. 1f).

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Next, we investigate the potential magnetoelectric coupling in the ferroelectric dimer-singlet phase. If the D+A−-dimerized ferroelectricity results from the spin–Peierls instability as postulated, the polarization should vanish when the singlet state is suppressed by a magnetic field. The M–H curves at various temperatures are shown in Fig. 3a. Below Tc (≈53 K) the characteristic nonlinearity is observed, whereas it is absent above Tc; moreover, the susceptibility (that is, the slope of M–H curve) is larger in the high-field phase than that in the low-field phase. These characteristics indicate a breakdown of the singlet state at some critical field, Hc(T). More importantly, this singlet suppression is accompanied simultaneously by the disappearance of D+A−-dimerized ferroelectricity: as shown in Fig. 3b, the polarization at 50 and 52 K is almost extinguished around Hc(T), indicating that the paraelectric uniform stack is restored. At lower temperatures, P does not vanish up to ∼56 T; yet the partial suppression is still obvious at 40 K. Therefore, we conclude that the D+A−-dimerized ferroelectric transition is primarily due to the magnetic energy gain, that is, spin–Peierls instability; nevertheless, it is possible that other mechanisms (for example, long-range Coulomb interaction) assist the ferroelectric spin–Peierls state. As far as we know, TTF–BA is the first material in which the ferroelectric spin–Peierls state and its prominent magnetoelectric coupling have been experimentally identified. Note that in other prototypical spin–Peierls systems such as TTF–CuS4C4(CF3)4 (ref. 21) and CuGeO3 (ref. 22), the 1D Heisenberg chain consists of a single-component spin site and thus a polar dimer cannot be realized.

Figure 3: Magnetic-field-induced transition from the ferroelectric nonmagnetic phase to the paraelectric paramagnetic phase.
figure 3

a, M–H curves of TTF–BA (assembly of randomly oriented small crystals) at various temperatures. The triangles indicate the critical field where dM/dH becomes a maximum. The error bars represent the numerical ambiguity of the dM/dH maximum. b, Magnetic-field dependence of electric polarization (∥b) under at various temperatures in TTF–BA.

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For a better understanding of the newly identified ferroelectric spin–Peierls state, it is interesting to compare this with other conventional (non-ferroelectric) spin–Peierls systems. The H–T phase diagrams of spin–Peierls systems are known to be reduced to the universal one when plotted on a plane of reduced temperature versus reduced magnetic field14,23,24,25. In this universal phase diagram, the phase boundary in a low-field regime obeys the following form:

where TSP, g, μB and kB are the spin–Peierls transition temperature, g value, Bohr magneton and Boltzmann constant, respectively. According to Cross’s theory23, the value of α is ∼0.38, which is actually in good agreement with the experiments in conventional spin–Peierls systems24,25. We plotted Tc(H) of TTF–BA in the form of equation (1) with g=2. The result (Fig. 4) demonstrates that in the low-field regime, equation (1) holds even in the ferroelectric spin–Peierls material. However, the value of α turns out to be ∼0.18, significantly smaller than 0.38. This means that the ferroelectric spin–Peierls state is more robust against a magnetic field.

Figure 4: Magnetic-field dependence of the transition temperature.
figure 4

The transition temperatures are plotted in the form of 1−Tc(H)/Tc(0) versus {μBH/kBTc(0)}2. The squares were obtained from the M–H curves shown in Fig. 3a, and the open circles were determined from the peak temperature of ɛ1(T) at 10 kHz under various magnetic fields shown in the inset. The dashed line represents the theoretical prediction (α=0.38) for the spin–Peierls system23, where α≡{1−Tc(H)/Tc(0)}/{μBH/kBTc(0)}2 in a low-H region. The error bars correspond to those shown in Fig. 3a.

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Why does the spin–Peierls transition in TTF–BA deviate from the conventional framework of spin–Peierls systems? The following two experimental results may provide clues. One is the temperature dependence of the ag mode intensity probing the local D+A− dimerization; in Fig. 1d, the ag intensity persists clearly up to 100 K (∼2Tc), indicating the dimerization fluctuation well above Tc. Note that such fluctuation is not expected far above Tc within the framework of Cross’s theory, which is based on the mean-field treatment of spin–phonon coupling. The other clue is the magnitude of the spin gap Δs (≈230 K). Note that Δs/kBTc≈4.3 in TTF–BA, whereas typically Δs(0)/kBTc≈2.5 (ref. 26). Such a large value of Δs/kBTc indicates that Tc in TTF–BA is substantially suppressed compared with the mean-field Tc expected from Δs. Curiously, unlike the conventional Peierls picture13, Δs(T) seems temperature-insensitive in the range 25–53 K (Supplementary Fig. S1); this peculiarity is readily understood, given that the enhanced dimerization fluctuations would lead to a pseudo-spin-gap well above Tc in analogy with the pseudo-charge-gap in some charge–Peierls systems27. In the light of the strong electron–phonon coupling discussed in the charge–Peierls transition28, the two distinct results described above are attributable to strong spin–phonon coupling, which may be characteristic of organic donor–acceptor-type ferroelectric spin–Peierls system such as TTF–BA.

A key factor for the emergence of magnetically controllable ferroelectricity in TTF–BA is now realized as the spin–Peierls instability. This mechanism is clearly different from the case of hitherto known multiferroics, where the emergence of ferroelectricity relies on the specific magnetic order in spin-frustrated magnets. From the present results, we propose a new guideline for designing symmetric-exchange-driven ferroelectrics, that is, the ferroelectricity induced by low-dimensional instability in quantum spin magnets. The spin-1/2 1D Heisenberg chain composed of binary spin sites is the most clear-cut example. Organic donor–acceptor charge-transfer complexes ubiquitously possess the spin–Peierls instability because of the low dimensionality in the stacking of the building blocks29, and therefore they may provide a new field of this kind of spin-driven ferroelectricity.

Methods

Crystal growth.

Commercially available TTF and BA were purified by repeated recrystallization and sublimation in a vacuum. An acetonitrile solution of the stoichiometric mixture in a Teflon beaker was slowly evaporated under a stream of argon gas at −5 to 0 ∘C. The single crystals obtained have a typical dimension of 1.5×1×0.5 mm3.

Pyroelectric and displacement current measurements.

The pyroelectric current (or polarization current with sweeping magnetic field) along the b axis was measured under zero electric field after carrying out a poling procedure with a cooling field of ∼4.8 kV cm−1. Along the a axis, we could not obtain a reproducible pyroelectric current even though the crystal was cooled under ∼8 kV cm−1. The magnetic-field (H) dependence of P(∥b) was measured up to 56 T in a pulsed magnetic field with a duration of 37 ms, at the International MegaGauss Science Laboratory of the Institute for Solid State Physics, University of Tokyo. The P–H curves were obtained by integrating the displacement current dP/dt as a function of time t.

Magnetization measurements.

The M–H curve was measured up to 56 T in a pulsed magnetic field with a duration of 37 ms. The experimental set-up is described, for example, in ref. 30. To attain a good signal-to-noise ratio, we needed a large sample volume and therefore used an assembly of many randomly oriented small crystals of TTF–BA (total weight: ∼57.5 mg).

Infrared reflectivity measurements.

To deduce ɛ2 spectra of the TTF-agν3 mode at 1,422 cm−1, the infrared reflectivity data, measured with a Fourier-transform type spectrometer, were fitted with the Lorentz oscillator function (Supplementary Fig. S2). The spectral weight was deduced by the ω-integral of the optical conductivity ω ɛ2(ω) spectrum.