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1 doi: 1.138/nature8731 Here we supplement the results of the X-ray crystallographic analysis at room temperature and detail procedures for evaluation of spontaneous polarization of the croconic acid crystal. 1. Crystallography. The croconic acid purchased from Tokyo Chemical Industry was purified by repeated recrystallization from 1N hydrochloric acid solution and transparent yellow platelet crystals were grown in slow evaporation of the solution under stream of inert gas. The plates are typically elongated along the crystallographic a-axis and develop well a (1) crystal plane (Fig. S1). The crystal structure of croconic acid was reexamined by the X-ray diffraction experiments in order to confirm its polar nature and also to scrutinize its hidden pseudo-centricity. The satisfactory outcome of analysis (R = 3. %) 1 mm b a Figure S1 Photograph of croconic acid crystals. reproduced the acentric space group Pca2 1 of orthorhombic system, which has a uniaxial polarity parallel to the c axis. Crystallographic data at room temperature: C 5 H 2 O 5, F w = 142.7, orthorhombic space group Pca2 1 (#29), a = 8.711(13), b = 5.169(2), c = 1.962(3), V = 493.6(3), Z = 4, ρ calc = g cm 3, R int =.15, R =.3, wr =.43, GOF =.987 for 1 parameters on 15 (I >2σ(I) for 2θ < 55 ) reflections. The intensity data collection using MoKα radiation (λ =.717 Å) was performed on a Rigaku four-circle diffractometer equipped with the Mercury CCD detector. After the direct methods with Sir92, the refinements of non-hydrogen atoms were done with anisotropic thermal factors using the CrystalStructure crystallographic software packages (MSC Corporation). The hydrogen atoms obtained from the differential Fourier map were included in the final least-square refinements. The hidden pseudo-centricity was examined by assuming some plausible centric super-groups of Pca2 1 applied for the analysis of the same diffraction data. The direct method could not solve the structure with the super-group symmetry Pbca (#61), which is originally reported by the Braga et al. This is due to the absence of adequate symmetry elements applicable to the molecules. Rather, when protons are ignored, additional mirror plane can survive perpendicularly to the pentagon (parallel to (1) in Fig. 1a). The least-squares refinement of parameters has reduced R to some extent by employing the corresponding space group, Pbcm (#57) with crystallographic a and b axes 1

2 doi: 1.138/nature8731 interchanged: R =.66, wr =.169, GOF = 1. for 5 parameters on 575 (I >2σ(I) for 2θ < 55 ) independent reflections. It should be noted that the choice of acentric Pca2 1 or centric Pbcm space group does not affect the extinction rules on X-ray reflections. The parameters of non-hydrogen atoms could be reasonably refined without showing significant anomalous thermal parameters. The hydrogen atoms were found to be disordered over two sites according to the differential Fourier analysis (see Fig. S2). These results validated the presence of hidden pseudo-centricity as expected. These structural data re-examined with space group Pca2 1 and Pbcm are deposited to the Cambridge Structural Database (CCDC ). a b O c O c Figure S2 Comparison of true acentric (space Gr. Pca2 1 ) (left) and possible centric (space Gr. Pbcm) crystal structures (right) of croconic acid. The vertical lines represent the mirror plane (normal to this figure) symmetry originally hidden in the acentric form. 2. Optimization of spontaneous polarization. All the electric measurements as described were made on the single crystals (typical size of (1-1.5) (.6-.8).2 mm 3 ) with gold paste painted as the electrodes. The silver paint also works well just after its painting, but the crystal surface was found to degrade gradually probably due to formation of some coordination compounds with silver. In all the hysteresis and poling procedures, the maximum field was set to less than 4 kvcm -1. With the higher voltage, the crystals, especially those of optimized polarization, become fragile against the electric breakdown. The remanent polarization P r ranges from 3 to 21 μc cm -2 depending on the quality of single crystals and also the history of thermal and/or electric treatments as below. On a repeatedly purified fresh sample, the currently optimized P r of 21 μc cm -2 with the coercive field E c of about 14 kv cm -1 at f = 1 Hz (shown in Fig. 4a) was achieved by applying 15 cycles of 1 Hz triangular waves (E max = 37 kv cm -1 ). 2

3 doi: 1.138/nature8731 Polarization P (μccm -2 ) f = 1 Hz 4) 3) 2) 1) Remanent polarization P r (μc cm -2 ) V t Pulse number Coercive field E c (kvcm -1 ) Figure S3 Hysteresis loops of electric polarization measured with ac electric field of triangular waveform (f = 1 Hz). The spontaneous polarization develops from the initial run (curve 1), by applying 6 cycles of 1 Hz triangle waves (2), subsequent 12 hr annealing at T = 4 K (3), and applying additional 4 cycles of.1 Hz triangle waves (4). Figure S4 Fatigue behaviour of polarization. A continuous pulse voltage (f = 1 Hz, E max = 23 kvcm -1 > E c ) and the triangular waveform voltage (f = 1 Hz, E max = 25 kvcm -1 ) for the P-E hysteresis measurements were applied. See the inset for the schematic waveform. The hysteresis measurements were repeated with constant interval in a logarithmic time scale. The other crystal specimen with optimized P r of 2 μc cm -2 and the coercive field E c of about 13 kv cm -1 at f = 1 Hz was obtained by both repeating the hysteresis measurements and annealing at T = 4 K for 12 hours, as shown in Fig. S3. For optimization of the ferroelectric properties, we also examined the ferroelectric fatigue properties as follows. As depicted by the waveform in the inset to Fig. S4, we applied a continuous pulse voltage (f = 1 Hz, E max = 23 kvcm -1 > E c ) and repeated the P-E hysteresis measurements applying the triangular waveform voltage (f = 1 Hz, E max = 25 kvcm -1 ) with constant interval in a logarithmic time scale. Figure S4 depicts the change of remanent polarization P r and coercive field E c, both of which first increase gradually with cycle number N. This specimen, being different from that of other figures, exhibited the optimum P r = 12 μc cm -2 at N = 5x1 3. Then the P r suddenly started to decrease because the gradually increasing coercive field finally approaches the maximum field applied. During initial 1 4 cycles, the electric oscillation would possibly release some domains originally pinned around impurities or defects, and then increases the P r. The fatigue of this ferroelectric usually appears as hardening in polarization reversal beyond N = 1 4 cycles. This might 3

4 doi: 1.138/nature8731 originate from the degradation near the interface with electrodes; the impurity injection, charge trapping, and/or diffusion lost of protons. As shown in Fig. S3, thermal annealing at K was found to further improve the polarization effectively, especially after the subsequent application of repeating ac electric field. After the polarization is optimized, the ferroelectric properties get similarly fatigued: the repeating hysteresis measurements rapidly increase the coercive field and diminish the polarization. Significant hardening of polarization reversal also occurs only by simply leaving the polarization-optimized sample as poled after the final hysteresis for a few days. This can be related to the so-called imprint of ferroelectricity into one polar state. Indeed, the centre of hysteresis loop was found to shift toward the preferred polarity even after thermal annealing of poled sample with prolonged time. This is perceived in Fig. S3, and also might be responsible for the somewhat asymmetric nature of pyroelectricity (Fig. 4b). 3. Verification of optimized spontaneous polarization and pyroelectricity. The raw P-E hysteresis and pyroelectricity may include the non-ferroelectric contribution such as leakage current. To estimate and discriminate this component quantitatively, the polarization hysteresis was also scrutinized by the following technique called positive-up-negative-down (PUND). Here, the crystal specimen used is identical to that of Figure 4 but different from those of Figs. S3 and S4. Instead of conventional use of pulse voltage, we applied ac voltage of triangular waveform as shown in Fig. S5a. In this experiment, the polarization reversal occurs during the positive and negative processes, whereas the up and down processes retain the polarity and then can extract the non-hysteresis contributions. The non-hysteresis components are negligibly small compared with the total polarization at frequencies of 1 Hz (Fig. S5b) or more. Whereas the small open loop (green dotted curve in Fig. S5c) represents the typical effect of leakage current at the lower-frequency (contribution of several percentages of P r at f =.1 Hz), non-ferroelectric contributions is still small in the J-E relationship during the up and down processes in the room-temperature PUND measurements (Fig. S5d). These non-ferroelectric contributions were easily eliminated by subtracting the up and down hysteresis data from the positive and negative ones, respectively. The resulted loop shown by the red curves represents the intrinsic ferroelectric P E hysteresis, from which we obtained the intrinsically large remanent polarization of μccm -2 (Fig. S5b, c). 4

5 doi: 1.138/nature8731 a c V Pre-treatment b Polarization P (μccm -2 ) Positive Up Negative Down t P U N D 3 P r =21μCcm -2 f =1 Hz positive 2 1 up down -1-2 negative Polarizarion P (μccm -2 ) d Current density J (Am -2 ) P r = 22.4 μccm -2 3 f =.1Hz positive 2 1 up down -1-2 negative f =.1Hz positive.5 up down -.5 negative Figure S5 Correction of polarization hysteresis using positive-up-negative-down (PUND) procedure. a, Applied voltage waveform with ac electric field of triangular waveform of various frequency f. b, Raw PUND hysteresis data (dotted lines) at f = 1 Hz and intrinsic ferroelectric contributions obtained by the subtracting correction (solid curve). c, Raw PUND and intrinsic hysteresis data at f =.1 Hz. d, J-E relationship in the PUND measurements. The current density (J) curves in the positive and negative processes (red curves) include insignificant contribution from leakage effect as shown by those of the up and down processes (green curves). The measurements of the steady (leakage) current under dc electric field of 5.3 kvcm -1 using an electrometer (Keithley 6517A) confirmed a sufficiently high resistivity (>1 12 Ωcm at room temperature, Fig. S6) on the same crystal. At higher temperature, the resistivity decreases to some extent. If the leakage contribution were significant, the polarization ΔP s obtained by integrating the current would depend on the thermal treatments. The observed ΔP s data were 5

6 doi: 1.138/nature8731 almost independent of the cooling/heating directions (Fig. S7) and also the rate of temperature changes (for 2.5~1 Kmin -1, not shown), confirming the intrinsic nature of observed pyroelectricity. Resistivity (Ωcm) E = 5.3 kvcm -1 ΔP s (μc/cm 2 ) P(warming) +P(cooling) -P(warming) -P(cooling) Temperature (K) -2 dt/dt = 5 K min Temperature(K) Figure S6 Temperature dependence of electric resistivity. Figure S7 Temperature dependence of ΔP s, the change of P s from that at T = 5 K obtained by the pyroelectric current measurements in the cooling/heating runs (dotted/solid curve). 6