Introduction

Ferroelectrics with switchable spontaneous electrical polarizations in response to electric fields, having demonstrated great scientific and application values in data storage, sensors, optoelectronics, and versatile micro-electro-mechanical systems (MEMSs)1,2,3,4,5,6,7. As the most important properties of ferroelectricity: spontaneous polarization (Ps), coercive electric field (Ec), and Curie temperature (TC), vitally determine the comprehensive performances of ferroelectric materials and their commercial value for applications8,9,10,11. Inorganic oxide ferroelectrics, e.g., perovskite BaTiO3 and Pb(Zr, Ti)O3, have long been the successful mainstream of commercial applications, thanks to their high TC, large Ps, small Ec, as well as chemical stability12,13,14,15. However, their rigid structures, non-passive surfaces, and incompatibility with silicon industry, becomes more and more challenging for next-generation devices, such as nanoscale MEMSs and flexible electronics.

With the requirements from flexible applications, organic-inorganic hybrid perovskite (OIHP) ferroelectrics have emerged as a promising branch, by taking the advantage of low-cost manufacture, environmentally friendly, ease of fabrication, and excellent film formation16,17,18,19,20,21. OIHP ferroelectrics own rich structural diversity22,23,24,25,26,27,28, including three-dimensional (3D) ABX3-type (pseudo-)cubic structures29,30, two-dimensional (2D) layered structures31,32, and even quasi-one-dimensional (1D) ABX3-type hexagonal structures33. Different with 3D and 2D OIHPs whose structures are limited by many issues such as tolerance factor, 1D OIHPs do not have strict selections on metal halide anions and organic cations regarding their sizes, shapes, or valences. Thus 1D OIHPs are endowed with great structural freedom to engineer high-performance ferroelectrics with intriguing functionalities. Indeed, some 1D OIHP ferroelectrics have been synthesized and exhibit interesting properties such as large piezoelectric response34, multi-step nonlinear optical switches35, photoluminescence, magnetism36, and circularly polarized luminescence37. In particular, two 1D OIHP ferroelectrics [Me3NCH2Cl]MCl3 (M = Mn and Cd) have been reported to show large piezoelectric response on par with BaTiO338. Even though, the comprehensive performances of available OIHP ferroelectrics remain incompetent when competing with conventional ferroelectric oxides. The most serious problems are their small Ps (typically <10 μC/cm2) and relatively high Ec (~100 kV/cm). For comparison, the Ps of BaTiO3 reaches 26 μC/cm2 and its typical Ec is ~10 kV/cm39.

Screening and modifying organic cations (imidazole, pyrrolidine, quinuclidine, etc.) are efficient strategies to improve the material performance40. Because the polarization switching of OIHPs is generally related to the ordering reorientation of organic cations, it appears that small organic cations may be beneficial in reducing the coercive field. Besides, the inorganic framework of BX6 octahedra is also with remarkably compositional diversity. But their contributions to polarization have mostly been omitted since those octahedra formed by common transition metals (i.e., Cd, Cr, Mn, Cu) are generally inactive to ferroelectricity.

Inspired by the aforementioned ideas (Supplementary Fig. 1), we used the small DMA+ cation and germanium halide to synthesize a series of OIHP DMAGeX3 (X = Cl, Br, I) (Supplementary Note 1). Remarkably, OIHP DMAGeI3 exhibits excellent ferroelectricity with TC = 363 K, a high Ps = 24.14 μC/cm2, and a low Ec = 0.8-2.2 kV/cm at room temperature. To our best knowledge, such an experimental Ps is higher than those of most reported pure-organic and inorganic-organic hybrid ferroelectrics, and rivals the popular ferroelectric oxide BaTiO3. And equally importantly, its Ec value is one order of magnitude lower than that of recently reported inorganic perovskite CsGeI3 (∼40 kV/cm)41, and two orders of magnitude lower than those of PVDF (∼500 kV/cm) and its copolymers39. Moreover, it owns a large SHG response, whose intensity is more than ten times stronger than that of KH2PO4 (KDP, a commonly used standard system). Our finding brings the comprehensive performances of OHIP ferroelectrics to a comparable level with typical inorganic ferroelectric perovskites.

Results

Structural analysis of crystal

Yellow and transparent rod-shaped single crystals of DMAGeI3 in size of 2 × 2 × 16 mm3 (Fig. 1a) were prepared by hydrothermal method (Supplementary Note 1). The phase purity and thermal stabilities of grown crystals were identified by powder X-ray diffraction (XRD) and thermogravimetric analysis (TGA), which shows good environmental and thermal stability (Supplementary Figs. 2 and 3). Phase transition of DMAGeI3 was characterized using differential scanning calorimetry (DSC) measurements. As shown in Supplementary Fig. 4, the DSC curves show a pair of thermal anomalies peaked at 359 K and 363 K in cooling/heating runs, respectively. For convenience, we defined the phase above TC of 363 K as the high-temperature phase (HTP) and the phase below TC as the low-temperature phase (LTP). Crystal structures in LTP and HTP were determined by variable-temperature single-crystal X-ray diffraction in the range of 223-373 K (Supplementary Note 2 & Table 1).

Fig. 1: Structural information of DMAGeI3.
figure 1

a The image and simulated crystal growth morphology of single crystal. b, c Packing view of the unit cell in HTP and LTP along the b-axis. Hydrogen ions are omitted for clarity. The red dashed lines indicate the 2-fold crystallographic rotation axes and the polarization direction are indicated by yellow arrows.

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The structural analysis discloses that DMAGeI3 crystallizes in a centrosymmetric space group Pnan in HTP, while in LTP it transforms into a polar space group Pna21. Figure 1b, c show that the two phases are similar except for the DMA orientation and GeI3 distortion. DMAGeI3 adopts the hexagonal perovskite structure containing 1D inorganic framework, where the GeI3 units are linked via the face-sharing GeI6 octahedra. The cavities between GeI3 columns are filled by organic DMA cations, which are loosely connected with the inorganic framework via N-H···I and C-H···I hydrogen bonding interactions. In HTP, the organic DMA cations locate at the 2-fold crystallographic rotation axes of lattice and exhibit orientational disorder toward two equivalent directions, making their dipole moments cancel each other (Fig. 1b). In LTP, the DMA cations become ordered with an aligned manner along the c-axis (Fig. 1c and Supplementary Fig. 5), and also their positions move significantly (0.38 Å) along the c-axis direction compared with those in HTP (Supplementary Fig. 6), both of which induce a net dipole moment in this direction (Fig. 1c). Concomitantly, the Ge-I bond lengths and I-Ge-I angles in LTP also changed obviously (Supplementary Fig. 7 and Supplementary Table 2), although the GeI6 octahedra are already distorted in HTP. The value of the octahedron distortion parameter Δ and angle variance σoct rise from 0.0096/60.6 (HTP) to 0.0121/69.3 (LTP) respectively, which reflect a more distorted state of GeI6 octahedra in LTP (Supplementary Table 3).

These structural characteristics, including the orientation ordering of DMA cation, the structural distortion of GeI3 framework, and the relative moving between these two parts, will contribute to a ferroelectric polarization along the c-axis, which will be further analyzed later.

Characterization of ferroelectricity

According to the above structural analysis, the symmetry breaking occurs with the change of space group from Pnan to Pna21, and the symmetry elements halved from eight (E, C2, 2C2, i, σh, and 2σv) to four (E, C2, and 2σv), which means the DMAGeI3 is a mmmFmm2-type ferroelectric with two equivalent polarization directions42.

Second harmonic generation (SHG) experiment on powder sample was used to characterize its paraelectric-ferroelectric phase transition (Supplementary Note 2). As shown in Fig. 2a, DMAGeI3 shows a strong SHG response at room temperature, which confirms its non-centrosymmetric LTP. With increasing temperature, the SHG signal intensity gradually decreases to zero above TC, indicating that the HTP structure is transformed into a centrosymmetric one. Moreover, the SHG measurement on a single crystal surface of DMAGeI3 can further reveal the direction vector of ferroelectric polarization (Supplementary Note 2 & Supplementary Fig. 9)43,44. As shown in Fig. 2b, the angle-dependent SHG intensity shows a clear bipolar behavior, namely its intensity reaches the maximum (minimum) when the polarization direction of incident light is parallel (perpendicular) to the spontaneous polarization direction (i.e., c-axis) of DMAGeI3 crystal. It is worth to mention that the SHG strength of DMAGeI3 (of power sample) is more than ten times that of KDP (Fig. 2a), comparable to that of previous reported hybrid halide antiperovskite Cs3Cl(HC3N3S3) (11.4 \(\times {{\mbox{}}}\) KDP)45, and better than many other reported ferroelectrics (Fig. 2c and Supplementary Table 4). Thus, a direct application of DMAGeI3 crystal is the nonlinear optical converter, which can omit bright green light via photoluminescence, as demonstrated in Supplementary Fig. 10.

Fig. 2: Ferroelectric properties of DMAGeI3.
figure 2

a The SHG intensity of DMAGeI3 as a function of temperature on powder samples. Inset: the comparison of SHG signals between DMAGeI3 and KDP powder samples (in the same range of particle diameter 300–450 μm) at room temperature. More comparisons with various particle sizes can be found in Supplementary Fig. 8, which leads the same conclusion. b The SHG anisotropic polar plot of DMAGeI3 crystal, where the φ is the angle between the b-axis and the polarization of incident light. c Comparison of SHG intensity between DMAGeI3 and other ferroelectrics. d The temperature-dependent dielectric real part (ε′) of DMAGeI3 measured on single crystals along the a, b, and c-axis at 1 kHz. e The temperature-dependent dielectric real part (ε′) of DMAGeI3 measured on single crystals along the c-axis at various frequencies. f Comparison of the maximum value of ε′ of DMAGeI3 and other ferroelectrics. g, h The typical polarization-electric field (P-E) hysteresis loops measured along the c-aixs at various temperatures and at different frequencies. i Comparison of polarization values between DMAGeI3 and other ferroelectrics.

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Paraelectric-ferroelectric phase transition is generally accompanied by an obvious dielectric anomaly. The temperature-dependent dielectric real part (ε′) of DMAGeI3 was measured on single crystals along three crystallographic axes at various frequencies. As shown in Fig. 2d, e, the dielectric constant along the c-axis (ε′c) is much larger than those along the other two axes, especially in the region around TC. This dielectric anisotropy can be ascribed to this mmmFmm2-type phase transition that only allows spontaneous polarization along the c-axis. It is noteworthy that the value of ε′c reveals an obvious frequency-dependence. Specifically, as the frequency decreases from 1 MHz to 1 kHz, the peak value of ε′c at TC increases from 4679 to 102988 which is about 3269 times of its dielectric constant (~31.5) at room temperature (Fig. 2e). To our knowledge, this is the largest dielectric response in the reported hybrid perovskite materials to date (Fig. 2f & Supplementary Table 5). Additionally, according to the Curie–Weiss law, the Cpara and Cferro are calculated to be 9664 and 17469 K at 1 kHz, respectively. The ratio of Cferro /Cpara is 1.8 (smaller than 4), which discloses the characteristics of second-order ferroelectric phase transition (Supplementary Fig. 11).

The polarization-electric field (P-E) hysteresis loop is the most direct evidence of ferroelectricity. Figure 2g shows the P-E loops at various temperatures. Above TC (e.g., 373 K), the polarization response to the applied field presents almost linear behavior with a very narrow loop, while the well-defined P-E hysteresis loops were observed in the range of 343–303 K (below TC), as expected for the paraelectricity and ferroelectricity of the HTP and LTP. As the temperature decreases in the LTP, both the saturation polarization (Ps) and remnant polarization (Pr) increase gradually, and reach up to 24.14 μC/cm2 and 20.26 μC/cm2 at 303 K, respectively. Remarkably, the Ps of DMAGeI3 is larger than those of most reported famous organic and OIHP ferroelectrics such as [Me3NCH2CH2OH]CdCl3 (17.1 μC/cm2)28, [MeHdabco]RbI3 (6.8 μC/cm2)29, [Me3NCH2Cl]MnCl3 (4.0 μC/cm2)38, and very close to that of BaTiO3 (Fig. 2i & Supplementary Table 6).

Another notable feature of DMAGeI3 ferroelectricity is its small coercive field (Ec) values (0.8–2.2 kV/cm), which are one order of magnitude lower than that of the recently reported all-inorganic perovskite CsGeI3 (∼40 kV/cm)41, and two orders of magnitude lower than those of PVDF (∼500 kV/cm) and its copolymers39. More comparisons with other hybrid ferroelectrics can be found in Supplementary Table 7. Such a small Ec is advantageous for energy-saving operations in devices. Furthermore, the polarization switching speed is also a key property for ferroelectric applications, thus the frequency dependence of P-E hysteresis loops is investigated, as shown in Fig. 2h. With rising frequency, the values of Ps and Pr slightly decrease, while the coercive voltage increases. Its ferroelectric polarization can be switched at a frequency up to 100 kHz, which shows excellent high-frequency performance for macroscopic crystals with large scale domains. Given the large Ps value in combination with the small Ec and the high-frequency performance, DMAGeI3 represents promising hybrid ferroelectric materials for device applications. Moreover, the piezoelectric response has also been measured by using the quasi-static method. At room temperature, the d33 of the DMAGeI3 crystal reaches 3 pC/N, along the polar axis [001] under a testing frequency of 110 Hz (Supplementary Fig. 13).

For ferroelectrics, the microscale domain structure is another essential property of polarity, which can be characterized by using the piezoresponse force microscopy (PFM) technology46. By adjusting the lateral (in-plane) or vertical (out-of-plane) mode in PFM, the relative strength of piezoelectric response and polarization directions from different components can be harvested. Figure 3a, b display a schematic diagram of PFM in-plane testing on DMAGeI3 crystal along the c-axis (polarization direction), and the obtained topography of the crystal surface is shown in Fig. 3c. In the lateral mode, the observed obvious stripy domain walls parallel to the c-axis eliminate the interference of topography and confirm the existence of ferroelectric polarization (Fig. 3d). Combined with amplitude, the two sides of the domain wall show the response to different polarization directions, displaying obvious phase difference (Fig. 3e). In contrast, the piezoelectric signals do not give a component in the vertical direction (Supplementary Fig. 14), verifying the results of crystal structure determination (mmmFmm2-type ferroelectric).

Fig. 3: Ferroelectric domain structures and polarization switching of DMAGeI3.
figure 3

a, b Three-dimensional and overhead schematic diagram of lateral mode of PFM for DMAGeI3. c–e Topography, lateral amplitude, and phase images. f Lateral PFM amplitude (blue) and phase (red) signals as functions of the tip voltage, showing local PFM hysteresis loops. g Initial phase image with 30 × 30 μm2. h Phase image after applying positive bias of +50 V for 0.5 s in the center of the area. i Succeeding phase image after applying negative bias of −50 V for 0.5 s at the same location.

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To further illustrate the ferroelectricity of DMAGeI3, the ferroelectric domain is switched using PFM. As shown in Fig. 3f, the butterfly-shaped amplitude (blue) and phase hysteresis loops (red) provide evidence for ferroelectric switching. A single domain state region with 30 × 30 μm2 is selected to demonstrate the domain inversion of DMAGeI3 (Fig. 3g). After applying positive bias of +50 V for 0.5 s, in the sectional area parallel to the c-axis on the right side of the point where the bias was applied, the polarization direction is switched (Fig. 3h). On the contrary, when giving a bias of −50 V for 0.5 s, the domain in the left area is reversed, resulting in the appearance of the stripy domain (Fig. 3i). Subsequently, a higher bias is applied to the center point, and the left area turns to the same phase, which is obviously different from the reverse polarization direction on the right (Supplementary Fig. 15). Our PFM measurement results strongly prove that DMAGeI3 possesses stable and switchable polarization.

Discussion

To further understand the prominent ferroelectricity of DMAGeI3, we performed density-functional-theory (DFT) calculations to reveal underlying mechanisms. Our DFT calculation leads to lattice constants close to the experimental LTP one (Supplementary Fig. 17). And its electronic structure is shown in Supplementary Fig. 18, suggesting a good insulator with a band gap 2.79 eV. The valance band maximum is contributed by Ge and I. The theoretical value of polarization is estimated as 29.09 μC/cm2 at the ground state (i.e., T = 0 K), which agrees well with (and slightly higher than) the experimental value at room temperature.

Then the ferroelectric origin of DMAGeI3 is analyzed. First, the 4s2 lone pair of Ge2+ ion is a strong driving force of ferroelectricity, as appeared in the all-inorganic 3D perovskite CsGeI341. As illustrated in Fig. 4a, the 4s2 lone pairs form a zigzag pattern along the inorganic chain, leading to an uncompensated dipole along the c-axis in the LTP. In contrast, in the HTP structure, the local dipoles from 4s2 lone pairs are fully compensated, as compared in Fig. 4b. Second, besides the contribution from Ge2+’s 4s2 lone pair, the effect of DMA cation is also non-negligible. Both the bodily movement of this +1 charged group and stereo orientation of this asymmetric structure will generate a local dipole. A simple estimation of their individual contributions are 16.18 μC/cm2 (from the DMA cations) and 13.62 μC/cm2 (from the GeI3 framework) respectively (see Supplementary Note 3 and Supplementary Fig. 19). In other words, the large polarization of DMAGeI3 is due to the synergistic effect of inorganic and organic parts, with almost half-half weights.

Fig. 4: Ferroelectricity revealed by ab initio calculations.
figure 4

a The schematic of polarization of the GeI3 framework (upper) and DMA cations (lower). The yellow arrows correspond to the local dipoles’ directions. The lone pairs of Ge’s 4s2 electron clouds can be clearly visualized as a driving force of dipoles. And the dipoles of DMA cations can be flipped by rotation. b The calculated energy barriers and evolution of polarization of ferroelectric switching. The barrier depends on the switching process, namely how many DMA cations (1, 2, or 4) rotate synchronously in a unit cell. The one-by-one rotation of DMA rotation leads to a lower barrier. Note that the theoretical barrier only defines the upper limit, while the real barrier can be even lower, especially at room temperature. c The comparison of calculated SHG plots of DMAGeI3 and KDP crystals (both on the bc plane). The 0o (90o) is along the b-axis (c-axis).

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The ferroelectric switching process of DMAGeI3 can be also simulated by rotating the DMA cations, as depicted in Fig. 4a. If the four DMA cations in one unit cell rotate synchronously, the switching barrier energy is 292.9 meV, which is not as low as expected. However, this barrier can be significantly reduced by rotating the DMA cations one by one, as compared in Fig. 4b, where the first and second barriers of the rotating steps are 109.6 meV and 115.6 meV, respectively. For comparison, the DFT switching barrier for a BaTiO3 unit cell is ~8.3 meV and its experimental coercive field Ec is <10 kV/cm12. But it should be noted that the unit-cell volume of DMAGeI3 is ~16.5 times of BaTiO3. Thus, the two one-by-one barriers are only ~6.6 meV and ~7.0 meV for DMAGeI3 when normalized to the volume of BaTiO3. Compared with BaTiO3, the proximate Ps and lower barrier of DMAGeI3 suggest an even smaller Ec, as observed in our experiments.

Furthermore, its prominent SHG signal can be also well reproduced theoretically. The nonlinear optical susceptibility tensors (dij’s) of LTP of DMAGeI3 are calculated, which determine the intensity and anisotropy of SHG signals. For DMAGeI3 with space group Pna21, its SHG intensity on the bc crystalline plane can be expressed as47: \({I}_{DMAGe{I}_{3}}\propto {(2{d}_{24}\sin 2\varphi )}^{2}+{(2{d}_{32}{\cos }^{2}\varphi+2{d}_{33}{\sin }^{2}\varphi )}^{2}\), where φ is the angle between the polarization direction of incident light and b-axis (more details can be found in Supplementary Note 4). As shown in Fig. 4c, the calculated SHG plot of DMAGeI3 shows a bipolar behavior, and the strongest signal appears when the polarization direction of incident light is along the c-axis of crystal, consistent with the experimental observation.

For comparison, the dij’s of KDP room temperature phase (space group \(I\overline{4}2d\)) is also calculated, which agrees well with the experimental values (Supplementary Fig. 20). As expected, these values are systematically smaller than those of DMAGeI3. Thus the SHG signal of KDP is much smaller than that of DMAGeI3, since generally the SHG response is proportional to the square of dij’s, as compared in Fig. 4c.

Our study unambiguously demonstrated the excellent comprehensive ferroelectric properties of DMAGeI3 with quasi-one-dimensional structure, which is a breakthrough of organic-inorganic hybrid ferroelectrics as well as low-dimensional ferroelectrics. Its remarkable ferroelectricity originates from the synergistic overlap of two robust mechanisms: ordering of polar cations and soft mode of 4s2 lone pairs, which doubles its net polarization and keeps its coercivity at a low level. This successful example provides a reliable and simple route to pursue more superior ferroelectrics or even multiferroics in organic–inorganic hybrid systems, to finally reach the aim of commercial applications. The opportunities are vast for emerging hybrid germanium halide perovskites, and the ones equipped with multipolar characteristics and outstanding piezoelectric performance may be available in the near future.

Methods

DSC, SHG, and XRD measurements

Differential scanning calorimetry (DSC) measurements were carried out by using a NETZSCH DSC 200F3 instrument under the nitrogen atmosphere, where the dry powder of DMAGeI3 (28.9 mg) were heated and cooled with a rate of 10 K/min in the temperature ranges of 293–390 K. SHG switching experiments were measured with powder samples by pulsed Nd: YAG (1064 nm, Vibrant 355 II, OPOTEK), and the temperature varies from 300 K to 380 K. The powdered KH2PO4 (KDP) was used as the reference. The SHG phase matching tests were performed with a particle size range of 62–375 μm at room temperature. Furthermore, the SHG intensity anisotropy was investigated by using Witec alpha 300 on single-crystal surfaces. Variable-temperature single-crystal X-ray diffraction data were collected on a Rigaku VarimaxTM DW diffractometer with Mo Kα radiation (λ = 0.71073 Å). Data processing with empirical absorption correction was conducted by using the CrysAlisPro 1.171.40.14e (Rigaku OD, 2018). The crystal structures were confirmed by direct methods and refined by full-matrix least-squares methods based on F2 through the OLEX2 and SHELXTL (version 2018) software package. All non-hydrogen atoms were refined anisotropically and all hydrogen atoms were generated geometrically in suitable positions.

Dielectric and ferroelectric measurements

For the dielectric measurements, the sample of DMAGeI3 was made with single-crystals cut perpendicular to the a-, b-, and c-axis respectively. Silver conduction paste deposited on the plate surfaces was used as the electrodes. The temperature-dependent dielectric constants were performed on the Tonghui TH2828A instrument under the frequency range from 1 kHz to 1 MHz with an applied electric field of 1 V. The single crystal electrodes of DMAGeI3 were prepared for the P-E hysteresis loop measurements by Sawyer-Tower method. The ferroelectric polarization imaging and local switching studies on the bulk crystal surface were carried out by using a resonant-enhanced PFM (MFP-3D, Asylum Research).

PXRD and TGA measurements

Powder XRD data were measured using a Rigaku D/MAX 2000 PC X-ray diffraction system with Cu Kα radiation in the 2θ range of 5°–50° with a step size of 0.02°. The thermogravimetric analysis (TGA) were performed on the NETZSCH TG 209F3 instrument in the range of 298–1000 K with a heating rate of 20 K/min.

DFT Calculations

The electronic structure calculations were performed based on projector augmented wave pseudopotentials, as implemented in Vienna ab initio Simulation Package (VASP)48. Plane-wave cutoff energy of 500 eV and 3 × 4 × 4 k-point meshes were used. The lattice constants and the atomic positions were fully relaxed with the convergence criteria of 10−5 eV and 0.01 V/Å for energy and force, respectively. The exchange-correlation potential was approximated in the form of Perdew–Burke–Ernzerhof (PBE) functional and the van der Waals (vdW) interaction was considered by adding D3 Grimme correction49,50. Other choices of functional and vdW correction were also tested (Supplementary Fig. 17). The climbing nudged elastic band method was used to determine the paths and energy barrier of ferroelectric switching51. Ferroelectric polarization was calculated by using the Berry phase method52. The second-harmonic nonlinear optical susceptibility tensors for SHG were calculated using the exciting package53.