Construction of ferroelectric topological domains in freestanding epitaxial BiFeO₃ nanostructures

Abstract

Topological center domains in ferroelectric nanostructures have garnered considerable attention owing to their novel functionalities and potential applications in next-generation electronic devices. In this study, we demonstrate the stabilization of room-temperature topological center domains in freestanding epitaxial BiFeO₃ nanoislands grown on a SrRuO₃ bottom layer. Notably, we demonstrate electrically reversible control of highly conductive channels localized at center domain core regions through applied electric fields, establishing critical functionality for non-volatile memory applications. The realization of these switchable conductive states in transferable architectures further establishes a materials platform for integrating functional topological domains with flexible electronics.

---

1. Introduction

Recent advances have uncovered rich topological polarization configurations in low-dimensional ferroelectrics, such as flux-closure domains,^1–3 vortices,^4–7 center domains,^8–10 skyrmions,^11–15 and merons,¹⁶ among others.^17–21 These exotic textures, stemming from polarization discontinuity and charge redistribution, exhibit emergent functionalities distinct from bulk ferroelectrics, such as enhanced conductivity,^22–24 negative capacitance,²⁵ magnetism,^26–28 enhanced optoelectronic/electromechanical responses,^29,30etc. Such field-tunable topological states position them as promising building blocks for next-generation nanoelectronics and energy-efficient devices.^23,31 However, the implementation of these topological structures has been largely confined to substrate-constrained epitaxial films or superlattices, which restricts their compatibility with semiconductor processes and hinders their application in flexible electronics.

In recent years, the advent of freestanding ferroelectric films and 2D layered ferroelectrics have revolutionized domain engineering paradigms, enabling atomic-scale polarization control in flexible architectures.^32,33 In particular, freestanding thin films have the remarkable capability to endure substantial large curvature and strain, leading to the development of a voltage-free control strategy known as flexoelectricity.^34–37 This also allows for the mechanical tuning of polar polarization and the creation of artificial domains.^38–43 While normal domain structures, such as stripe and bubble domains, have been extensively studied in such systems, topological domains remain underexplored despite their theoretical potential, which hinders their progress in the development of flexible and wearable electronic devices.⁴⁴ Recent theoretical calculations have predicted stable meron-like textures in wrinkled SrTiO₃ membranes,⁴⁵ yet experimental realization and dynamic control of these states persist as critical challenges. The development of flexible electronics further requires methods to read and erase polar topological domains in freestanding thin films. A promising strategy is to exploit the domain wall conductance of these structures for signal readout; however, research in this area remains limited and requires deeper exploration.

It is well established that dimensional reduction to the nanoscale serves as an effective strategy for manipulating topological defects,^{3,5,6,8,9,23,32,33,46–52} attributed to the size-confinement effects and enhanced surface contributions in nanostructures, particularly within isolated ferroelectric nanoisland systems. In this study, we integrate dimensional confinement engineering with freestanding film technology to fabricate a freestanding BiFeO₃ nanoisland array supported on a SrRuO₃ layer. This method creates center-type topological domains that exhibit enhanced conductive channels for memory readout and show good operational stability during static and cyclic bending, underscoring their potential for flexible electronics.

2. Experimental details

In the previous work, we demonstrated that ordered BFO nanoisland arrays with tunable dimensions can be fabricated through Ar⁺ ion beams etching a monolayer polystyrene sphere (PS) mask array deposited on high-quality epitaxial thin films.^6,9,53 Building upon this foundation, we further refined and advanced this method to fabricate large areas of freestanding BFO nanoisland arrays on the SRO layer. To achieve high-quality freestanding BFO nanoisland arrays, the epitaxial growth of superior sacrificial layer and thin films via pulsed laser deposition (PLD) in the initial stages is of paramount importance.

The fabrication schematic is presented in the Methods section and Fig. 1(a). It initiates with the deposition of a 20-nm-thick epitaxial SRO bottom electrode layer on a water-soluble sacrificial layer (∼10 nm thickness), followed by growth of a high-quality 30-nm-thick BFO epitaxial film. A monolayer of PS spheres (initial diameters ∼500 nm) is then transferred onto the BFO surface to form a dense masking array. Prior to ion etching, oxygen plasma pre-treatment reduces the PS sphere diameter to ∼400 nm. Subsequent Ar⁺ beam etching through this PS mask produces patterned BFO nanostructures featuring circular nanoislands with ∼400 nm diameter, ∼30 nm height, and ∼100 nm inter-island spacing. Following mask removal and subsequent immersion in deionized water for sacrificial layer dissolution, we obtain freestanding BFO nanoisland arrays retaining the SRO bottom electrode. Fig. 1(b) and (c) present scanning electron microscopy (SEM) images of the PS mask and the resulting BFO nanoislands, respectively. The freestanding membrane (outlined by the red dashed box in Fig. 1(d)) was transferred onto a flexible mica substrate. As shown in Fig. 1(e), the transferred membrane exhibits a remarkable capacity for bending deformation.

Fig. 1 (a) Schematic diagram illustrating the procedures of the freestanding SRO film with BFO nanoislands on a mica substrate. Scanning electron microscopy images of plasma-etched monolayer PS array (b) and the BFO nanoisland array (c) Scale bars: 500 nm. (d) Freestanding BFO/SRO film detached from the substrate. (e) Freestanding BFO/SRO film transferred onto a mica substrate, along with its flexibility bending test.

3. Results and discussion

Freestanding BFO epitaxial films were synthesized using a water-soluble Sr₂CaAl₂O₆ (SCAO) sacrificial layer, as schematically illustrated in Fig. 1(a) (see the Methods section for the detailed fabrication procedure). The fabricated BFO nanoisland array, supported on an SRO buffer layer, was successfully transferred onto a mica substrate for subsequent characterization. Pre-release morphological analysis presented in Fig. S2 (SI) confirms the exceptional epitaxial quality of the nanostructures.

The morphological and structural characteristics of the transferred freestanding BFO nanoisland array are shown in Fig. 2. Fig. 2(a) displays a morphological image captured under an optical microscope, illustrating that the sample remains largely intact across a wide range after being stripped. Moreover, the post-transfer nanoisland array (Fig. 2(b)) retains its structural periodicity ordering, confirming the methodological reliability for freestanding nanostructure transfer. Cross-sectional TEM micrographs of individual nanoislands (Fig. 2(c)) coupled with energy-dispersive X-ray spectroscopy (EDS) elemental mapping reveal distinct compositional stratification: Bi and Fe signals are concentrated in the BFO layer, while Sr is restricted to the SRO buffer layer. Post-release structural analysis through X-ray diffraction (XRD) and reciprocal space mapping (RSM) (Fig. 2(d) and (e)) confirms preserved epitaxial quality, yielding lattice parameters of a ≈ b ≈ 3.95 Å and c ≈ 3.98 Å. This indicates that the freestanding BFO nanoisland array adopts a more stable R-phase after substrate removal due to strain relaxation. Fig. 2(f) shows PFM amplitude–voltage loop (red) and phase–voltage hysteresis loop (blue) for a randomly selected nanoisland, demonstrating good ferroelectric properties.

Fig. 2 (a) Optical microscopy image for the BFO/SRO film on mica. (b) AFM morphological image for the BFO nanoisland array within a 5 × 5 µm² region selected from (a). (c) Cross-sectional TEM image of the BFO nanoisland with the corresponding chemical elemental mapping. (d) The θ–2θ XRD diffraction pattern and (e) a reciprocal space mapping (RSM) around (203) peak for the post-transfer BFO nanoisland array. (f) PFM amplitude–voltage loop (red) and phase–voltage hysteresis loop (blue) for a randomly selected nanoisland.

Initial domain characterization of as-grown BFO thin films was performed using piezoresponse force microscopy (PFM). As shown in Fig. S1 (SI), the pristine films exhibit mosaic-like domain configurations. Subsequent analysis of transferred nanoislands fabricated through BFO film etching revealed periodically ordered arrays with average diameters of ∼400 nm.

Vector PFM imaging, simultaneously capturing vertical and lateral piezoresponse signals, enabled comprehensive domain mapping of individual nanostructures. Fig. 3 presents vertical and lateral PFM phase images of the nanoisland array. The vertical PFM contrast (Fig. 3(a)) reveals cross-shaped antidomain textures in each nanoisland, exhibiting remarkable similarity to self-assembled BFO nanostructures on LaAlO₃ (LAO) and SrTiO₃ (STO) substrates.^9,23,32 Full domain reconstruction required lateral piezoresponse acquisition along two orthogonal cantilever orientations (0° and 90°), enabling three-dimensional polarization vector determination through combined vertical–lateral signal analysis.

Fig. 3 (a) Topography, vertical PFM phase and lateral PFM phase images captured at sample rotation angles of 0° and 90°, which were also superimposed with their 3D topographic images. (b) Vertical and lateral PFM phase images of a typical nanoisland by the blue circle in panel (a). (c) 2D vector contour mapping of the selected nanoisland converted from the combination of the lateral PFM with a sample rotation of 0° and 90°. (d) Schematic of the 3D domain structures.

A representative nanoisland with characteristic domain architecture was selected for detailed examination. As illustrated in Fig. 3(b), the PFM phase patterns demonstrate four-quadrant head-to-head polarization arrangements forming a center-convergent topological state, with vertical PFM contrast delineating cross-shaped antidomain boundaries separating quadrant domains. Fig. 3(c) and (d) schematically illustrates the two-dimensional and three-dimensional polarization configuration of this center-type domain structure, respectively. Two-dimensional polarization vector mapping was performed through MATLAB programing, following the method of Rodriguez and Kalinin.⁵⁴ By applying a negative tip bias (−4 V) during PFM writing, the domain structure of the nanoislands was successfully switched (see SI Fig. S3). Preliminary analysis suggests that the three-dimensional domain configuration exhibits a center convergent (with downward vertical polarization) topological state as shown in Fig. 3(d).

The transport properties of freestanding BFO nanoislands were investigated through conductive atomic force microscopy (CAFM). As shown in Fig. 2(f), polarization switching characteristics are evidenced by a typical phase–voltage hysteresis loop and butterfly-shaped amplitude response observed in a randomly selected nanoisland, with coercive voltage ∼ ±3 V. Therefore, the initial current of the nanoislands is almost zero when a readout field of −1.5 V (below the coercive voltage) is applied. After applying a tip voltage of −4 V (with +4 V bottom electrode bias in CAFM mode), a high conductivity region (marked by the blue dashed box) is detected, where the conductivity is enhanced by 3 orders of magnitude according to the CAFM image shown in Fig. 4(b) and (d).

Fig. 4 (a) Topography of freestanding BFO nanoislands obtained in AFM mode. (b) Corresponding CAFM image acquired with −4 V tip bias during writing (blue dashed box), readout tip bias maintained at −1.5 V. (c) The domain state of the nanoisland after writing a negative voltage (needle tip), along with its corresponding CAFM image. (d) Corresponding current profiles extracted from a high-conductivity channel and initial nanoisland showing current intensity for on/off state, respectively. (e) 2D vector mapping (using the MATLAB program based on the PFM image from the region selected by the red dashed box in (c)). (f) Magnified 2D vector mapping of the red-circled region in (e).

To illustrate the correlation between domain structure and conduction characteristics, Fig. 4(c) presents a comparative analysis of lateral PFM images recorded at two cantilever angles for a representative nanoisland alongside its corresponding CAFM current mapping. As revealed in Fig. 4(e), the nanoisland exhibits center divergent domain configuration, with detailed domain features of the center core region presented in Fig. 4(f). Notably, the polarization vector distribution in the central core area demonstrates strong spatial correlation with the enhanced conductivity regions identified in the CAFM current map (Fig. 4(c)).

In our previous work,⁵⁵ we have established the correlation between high-conductivity channels and topological core structures (quadrant vortex domains and center domains) in high-quality BFO nanoislands. The present investigation reveals that these conductive channels similarly originate from charge carrier dynamics within central core regions.^22,24,53 In this work, BFO is deposited by PLD at a relatively high temperature of 730 °C, which contain a limited number of Bi vacancies that produce holes in the nanoisland. Upon negative bias application, the polarization switched into center-divergent domains with tail-to-tail charged walls/cores, where hole carriers migrate to screen bound negative charges. Under sustained bias, progressive hole accumulation at this area not only stabilizes the charged domain walls/cores but also facilitates conductive filament formation through carrier aggregation. Similar conduction behaviors were reported in earlier literature addressing the tail-to-tail charge domain walls in BFO nanoislands.^23,56 It is worth noting that the domain structure formed after the polarization reversal is not regular, with divergent topological domains predominantly localized in the central nanoisland region. Furthermore, the resolution of domain wall conductance mapping is inherently constrained by scanning probe tip dimensions. This may explain why no apparent conductivity was observed in the domain walls connected to center core region.

The one-to-one correspondence between the topological core and enhanced conductivity allows controlled domain reconfiguration to modulate conduction states, paving the way for next-generation non-volatile memory devices. Manipulating the domain walls/cores and their conduction states by an electric field is the most straightforward approach. Thus, the operational feasibility of freestanding BFO nanoisland array for ferroelectric domain wall (DW) memory applications is demonstrated through controlled write/erase cycling, as illustrated in Fig. 5. In pristine states, all nanoisland units exhibit uniformly low conductivity corresponding to high-resistance states (HRS). Application of −4.0 V write bias (with +4.0 V bottom electrode bias in CAFM mode) to the nanoisland units induces formation of high-conductivity channels in CAFM images, marking the transition to low-resistance states (LRS) through center-divergent domain states. Subsequent +4.0 V erase bias (with −4.0 V bottom electrode bias in CAFM mode) eliminates these conductive channels, reverting devices to HRS via head-to-head domain wall reconfiguration. Reversible switching between memory states is achieved through polarity-controlled bias application, confirming reliable non-volatile memory operation. The high ON/OFF ratio observed in current profiles characteristics (Fig. 4(d)) further validates robust data readout functionality, establishing this architecture's potential for nanoelectronic memory applications.

Fig. 5 Schematics of the DW memory based on a high-conductivity channel. Manipulation of conductive states via controlled creation and elimination of center-type topological states. (a) Initial high resistance state with center convergent domains. (b) Low resistance state with center divergent domains by applying −4.0 V scanning bias (Readout voltage: −1.5 V) (c) High resistance state with center convergent domains by applying a scanning bias of +4.0 V (readout voltage: +1.5 V). (d) Low resistance state with center divergent domains after applying a -4.0 V bias voltage (readout voltage: −1.5 V).

Additional studies on the device's functional flexibility are summarized in Fig. S7–S11. Evaluation under sustained bending confirms that the central topological domains are stable and the conductive channels endure read–write cycles without significant degradation (Fig. S9). Additionally, the domain structure remains stable across 1 × 10³ bending cycles (Fig. S10). Moreover, while the onset and read voltages increase slightly after repeated bending (10² to 1 × 10³ cycles, Fig. S11), the device retains its ability to perform stable erase–write operations, underscoring its practical relevance. The above results suggest the potential for developing domain wall memories on a flexible substrate, which not only introduces new opportunities for research in flexible electronics, but also establishes a new paradigm for developing nanoelectronic devices with programmable functionalities based on topological domains.

4. Conclusions

In summary, we demonstrate a scalable fabrication strategy for ordered BFO nanoisland memory arrays featuring center-type topological domains on flexible mica substrates through the dissolution of the sacrificial layer and etching. Furthermore, the nanoisland memory units can be reversibly and repeatedly switched between a divergent state with a high-conductivity channel around center core area and a convergent state with low conductivity under electric field control. The topological protection mechanism effectively safeguards polarization configuration in the central domain thereby stabilizing and optimizing conductive channel formation. Complemented by a high switching ratio and robust read/write cyclability, these functional nanoislands establish a promising platform for implementing conduction domain walls/cores in next-generation flexible electronics and hybrid silicon-based architectures.

5. Methods

5.1. Freestanding BFO nanoisland array preparation

Freestanding BFO epitaxial films were successfully fabricated with the assistance of a water-soluble sacrificial layer calcium strontium aluminate (Sr₂CaAl₂O₆:SCAO). Firstly, the as-grown BFO (30 nm)/SRO (20 nm) double-layer heterostructure was synthesized on a SCAO (10 nm) buffered (001) STO substrate by pulsed laser deposition. Before BFO/SRO deposition, a thin SCAO layer was deposited on the STO substrate at 750 °C in 0.1 Pa oxygen using PLD. Next, the SRO was deposited at 680 °C in 15 Pa and the BFO was deposited at a growth temperature of 730 °C in an oxygen atmosphere of 20 Pa. Subsequently, the BFO layer covered with PS spheres as the template on the surface was etched via an Ar⁺ ion beam for appropriate times. Finally, the as-prepared sample was dissolved in deionized water to remove the SCAO layer and the freestanding BFO nanoisland array was transferred to a mica substrate.

5.2. Ion beam etching process

The BFO film covered with the PS template was etched by an Ar⁺ ion beam at a vacuum pressure of 1.0 × 10⁻⁴ Pa at room temperature. The optimized etching parameters were a cathode current of 15.8 A, a neutralization current of 13 A, a bias current of 1.2 A, an anode voltage of 50 V, a plate voltage of 300 V, and an ion accelerating voltage of 250 V.

5.3. Structure and morphological analysis

The crystalline structures of samples were characterized by X-ray diffraction and reciprocal space mapping (PANalytical X’Pert PRO). The morphology of the BFO nanoislands was characterized using the atomic force microscopy mode of an Asylum Research scanning probe microscope (Asylum Cypher SPM) and a Zeiss SEM and TEM.

5.4. PFM and CAFM analysis

The local piezoresponse loops and vector polarization maps of the BFO nanoislands were obtained using the PFM mode (Asylum Cypher PFM). In constructing the domain structure of the BFO nanoislands, an angle-resolved PFM technique was adopted with two lateral PFM images obtained at different sample orientation angles. Cr–Pt-coated conducting tips (Nano Word) acted as the top electrode in all the PFM and CAFM measurements.

Author contributions

Jun Jin and Houlin Zhou contributed equally to this work. Jun Jin: investigation, data curation, formal analysis, writing – review & editing. Houlin Zhou: investigation, data curation, formal analysis, writing – original draft. Yuyin Yang: formal analysis, data curation. Jiaqi Zhang: formal analysis, data curation. Xingchen Zhang: formal analysis, data curation. Shuoshuo Ma: formal analysis, data curation. Jianbiao Xian: formal analysis, data curation. Yihang Guo: formal analysis, data curation. Ji-Yan Dai: funding acquisition, project administration. Guo Tian: conceptualization, funding acquisition, investigation, project administration, writing – original draft, writing – review & editing.

Conflicts of interest

The authors declare no conflict of interest.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: see the supplementary material for details on the structure, domain states and functional flexibility of the BFO nanoislands. See DOI: https://doi.org/10.1039/d5tc03316k.

Acknowledgements

The authors would like to thank the National Key Research and Development Programs of China (No. 2022YFB3807603), the National Natural Science Foundation of China (No. 92163210 and U22A20117), the Science and Technology Projects in Guangzhou (No. 202201000008), and the Guangdong Basic and Applied Basic Research Foundation (No. 2023B1515130003 and 2024A1515011608), and G. T. acknowledges support from the Hong Kong Scholar Program (No. XJ2022004).

References

1. C.-L. Jia, K. W. Urban, M. Alexe, D. Hesse and I. Vrejoiu, Science, 2011, 331, 1420–1423.
2. Y. L. Tang, Y. L. Zhu, X. L. Ma, A. Y. Borisevich, A. N. Morozovska, E. A. Eliseev, W. Y. Wang, Y. J. Wang, Y. B. Xu, Z. D. Zhang and S. J. Pennycook, Science, 2015, 348, 547–551.
3. A. Schilling, D. Byrne, G. Catalan, K. G. Webber, Y. A. Genenko, G. S. Wu, J. F. Scott and J. M. Gregg, Nano Lett., 2009, 9, 3359–3364.
4. A. K. Yadav, C. T. Nelson, S. L. Hsu, Z. Hong, J. D. Clarkson, C. M. Schlepütz, A. R. Damodaran, P. Shafer, E. Arenholz, L. R. Dedon, D. Chen, A. Vishwanath, A. M. Minor, L. Q. Chen, J. F. Scott, L. W. Martin and R. Ramesh, Nature, 2016, 530, 198–201.
5. B. J. Rodriguez, X. S. Gao, L. F. Liu, W. Lee, I. I. Naumov, A. M. Bratkovsky, D. Hesse and M. Alexe, Nano Lett., 2009, 9, 1127–1131.
6. G. Tian, D. Chen, H. Fan, P. Li, Z. Fan, M. Qin, M. Zeng, J. Dai, X. Gao and J.-M. Liu, ACS Appl. Mater. Interfaces, 2017, 9, 37219–37226.
7. W. Geng, X. Guo, Y. Zhu, Y. Tang, Y. Feng, M. Zou, Y. Wang, M. Han, J. Ma, B. Wu, W. Hu and X. Ma, ACS Nano, 2018, 12, 11098–11105.
8. Z. Li, Y. Wang, G. Tian, P. Li, L. Zhao, F. Zhang, J. Yao, H. Fan, X. Song, D. Chen, Z. Fan, M. Qin, M. Zeng, Z. Zhang, X. Lu, S. Hu, C. Lei, Q. Zhu, J. Li, X. Gao and J.-M. Liu, Sci. Adv., 2017, 3, e1700919.
9. G. Tian, X. Yi, Z. Song, W. Yang, J. Xian, J. Jin, S. Ning, Z. Hou, D. Chen, Z. Fan, M. Qin, G. Zhou, J. Dai, X. Gao and J.-M. Liu, Appl. Phys. Rev., 2023, 10, 021413.
10. H. Chen, G. Tian, W. Yang, Z. Mo, L. Zhang, Y. Chen, C. Chen, Z. Hou, D. Chen, Z. Fan, X. Gao and J.-M. Liu, J. Appl. Phys., 2020, 128, 224103.
11. S. Das, Y. L. Tang, Z. Hong, M. A. P. Gonçalves, M. R. McCarter, C. Klewe, K. X. Nguyen, F. Gómez-Ortiz, P. Shafer, E. Arenholz, V. A. Stoica, S.-L. Hsu, B. Wang, C. Ophus, J. F. Liu, C. T. Nelson, S. Saremi, B. Prasad, A. B. Mei, D. G. Schlom, J. Íñiguez, P. García-Fernández, D. A. Muller, L. Q. Chen, J. Junquera, L. W. Martin and R. Ramesh, Nature, 2019, 568, 368–372.
12. L. Han, C. Addiego, S. Prokhorenko, M. Wang, H. Fu, Y. Nahas, X. Yan, S. Cai, T. Wei, Y. Fang, H. Liu, D. Ji, W. Guo, Z. Gu, Y. Yang, P. Wang, L. Bellaiche, Y. Chen, D. Wu, Y. Nie and X. Pan, Nature, 2022, 603, 63–67.
13. S. Das, Z. Hong, V. A. Stoica, M. A. P. Gonçalves, Y. T. Shao, E. Parsonnet, E. J. Marksz, S. Saremi, M. R. McCarter, A. Reynoso, C. J. Long, A. M. Hagerstrom, D. Meyers, V. Ravi, B. Prasad, H. Zhou, Z. Zhang, H. Wen, F. Gómez-Ortiz, P. García-Fernández, J. Bokor, J. Íñiguez, J. W. Freeland, N. D. Orloff, J. Junquera, L. Q. Chen, S. Salahuddin, D. A. Muller, L. W. Martin and R. Ramesh, Nat. Mater., 2021, 20, 194–201.
14. R. Zhu, Z. Jiang, X. Zhang, X. Zhong, C. Tan, M. Liu, Y. Sun, X. Li, R. Qi, K. Qu, Z. Liu, M. Wu, M. Li, B. Huang, Z. Xu, J. Wang, K. Liu, P. Gao, J. Wang, J. Li and X. Bai, Phys. Rev. Lett., 2022, 129, 107601.
15. W. R. Geng, Y. L. Zhu, M. X. Zhu, Y. L. Tang, H. J. Zhao, C. H. Lei, Y. J. Wang, J. H. Wang, R. J. Jiang, S. Z. Liu, X. Y. San, Y. P. Feng, M. J. Zou and X. L. Ma, Nat. Nanotechnol., 2025, 20, 366–373.
16. Y. J. Wang, Y. P. Feng, Y. L. Zhu, Y. L. Tang, L. X. Yang, M. J. Zou, W. R. Geng, M. J. Han, X. W. Guo, B. Wu and X. L. Ma, Nat. Mater., 2020, 19, 881–886.
17. J. Yin, H. Zong, H. Tao, X. Tao, H. Wu, Y. Zhang, L.-D. Zhao, X. Ding, J. Sun, J. Zhu, J. Wu and S. J. Pennycook, Nat. Commun., 2021, 12, 3632.
18. Q. Zhang, L. Xie, G. Liu, S. Prokhorenko, Y. Nahas, X. Pan, L. Bellaiche, A. Gruverman and N. Valanoor, Adv. Mater., 2017, 29, 1702375.
19. S. R. Bakaul, S. Prokhorenko, Q. Zhang, Y. Nahas, Y. Hu, A. Petford-Long, L. Bellaiche and N. Valanoor, Adv. Mater., 2021, 33, 2105432.
20. I. Luk’yanchuk, Y. Tikhonov, A. Razumnaya and V. M. Vinokur, Nat. Commun., 2020, 11, 2433.
21. Y.-J. Wang, Y.-P. Feng, Y.-L. Tang, Y.-L. Zhu, Y. Cao, M.-J. Zou, W.-R. Geng and X.-L. Ma, Nat. Commun., 2024, 15, 3949.
22. J. Seidel, L. W. Martin, Q. He, Q. Zhan, Y.-H. Chu, A. Rother, M. E. Hawkridge, P. Maksymovych, P. Yu, M. Gajek, N. Balke, S. V. Kalinin, S. Gemming, F. Wang, G. Catalan, J. F. Scott, N. A. Spaldin, J. Orenstein and R. Ramesh, Nat. Mater., 2009, 8, 229–234.
23. J. Ma, J. Ma, Q. Zhang, R. Peng, J. Wang, C. Liu, M. Wang, N. Li, M. Chen, X. Cheng, P. Gao, L. Gu, L.-Q. Chen, P. Yu, J. Zhang and C.-W. Nan, Nat. Nanotechnol., 2018, 13, 947–952.
24. N. Balke, B. Winchester, W. Ren, Y. H. Chu, A. N. Morozovska, E. A. Eliseev, M. Huijben, R. K. Vasudevan, P. Maksymovych, J. Britson, S. Jesse, I. Kornev, R. Ramesh, L. Bellaiche, L. Q. Chen and S. V. Kalinin, Nat. Phys., 2012, 8, 81–88.
25. A. K. Yadav, K. X. Nguyen, Z. Hong, P. García-Fernández, P. Aguado-Puente, C. T. Nelson, S. Das, B. Prasad, D. Kwon, S. Cheema, A. I. Khan, C. Hu, J. Íñiguez, J. Junquera, L.-Q. Chen, D. A. Muller, R. Ramesh and S. Salahuddin, Nature, 2019, 565, 468–471.
26. Q. He, C.-H. Yeh, J.-C. Yang, G. Singh-Bhalla, C.-W. Liang, P.-W. Chiu, G. Catalan, L. W. Martin, Y.-H. Chu, J. F. Scott and R. Ramesh, Phys. Rev. Lett., 2012, 108, 067203.
27. A. Chaudron, Z. Li, A. Finco, P. Marton, P. Dufour, A. Abdelsamie, J. Fischer, S. Collin, B. Dkhil, J. Hlinka, V. Jacques, J.-Y. Chauleau, M. Viret, K. Bouzehouane, S. Fusil and V. Garcia, Nat. Mater., 2024, 23, 905–911.
28. N. Domingo, S. Farokhipoor, J. Santiso, B. Noheda and G. Catalan, J. Phys.: Condens. Matter, 2017, 29, 334003.
29. J. Seidel, D. Fu, S.-Y. Yang, E. Alarcón-Lladó, J. Wu, R. Ramesh and J. W. Ager, Phys. Rev. Lett., 2011, 107, 126805.
30. F. Zhuo and C.-H. Yang, Phys. Rev. B, 2020, 102, 214112.
31. W. Yang, G. Tian, H. Fan, Y. Zhao, H. Chen, L. Zhang, Y. Wang, Z. Fan, Z. Hou, D. Chen, J. Gao, M. Zeng, X. Lu, M. Qin, X. Gao and J. Liu, Adv. Mater., 2022, 34, 2107711.
32. K.-E. Kim, S. Jeong, K. Chu, J. H. Lee, G.-Y. Kim, F. Xue, T. Y. Koo, L.-Q. Chen, S.-Y. Choi, R. Ramesh and C.-H. Yang, Nat. Commun., 2018, 9, 403.
33. K.-E. Kim, Y.-J. Kim, Y. Zhang, F. Xue, G.-Y. Kim, K. Song, S.-Y. Choi, J.-M. Liu, L.-Q. Chen and C.-H. Yang, Phys. Rev. Mater., 2018, 2, 084412.
34. B. C. Jeon, D. Lee, M. H. Lee, S. M. Yang, S. C. Chae, T. K. Song, S. D. Bu, J. Chung, J. Yoon and T. W. Noh, Adv. Mater., 2013, 25, 5643–5649.
35. J. Wang, Z. Liu, Q. Wang, F. Nie, Y. Chen, G. Tian, H. Fang, B. He, J. Guo, L. Zheng, C. Li, W. Lü and S. Yan, Adv. Sci., 2024, 11, 2401657.
36. X. Wu, L. Qi, M. A. Iqbal, S. Dai, X. Weng, K. Wu, C. Kang, Z. Li, D. Zhao, W. Tang, F. Zhuge, T. Zhai, S. Ruan and Y.-J. Zeng, ACS Appl. Mater. Interfaces, 2024, 16, 14038–14046.
37. X. Jia, R. Guo, J. Chen and X. Yan, Adv. Funct. Mater., 2025, 35, 2412887.
38. B. Huang, Y. Yu, F. Zhang, Y. Liang, S. Su, M. Zhang, Y. Zhang, C. Li, S. Xie and J. Li, Adv. Mater., 2023, 35, 2305766.
39. C. Chen, H. Liu, Q. Lai, X. Mao, J. Fu, Z. Fu and H. Zeng, Nano Lett., 2022, 22, 3275–3282.
40. W. Ming, B. Huang, S. Zheng, Y. Bai, J. Wang, J. Wang and J. Li, Sci. Adv., 2022, 8, eabq1232.
41. Y. Liu, A. N. Morozovska, A. Ghosh, K. P. Kelley, E. A. Eliseev, J. Yao, Y. Liu and S. Kalinin, ACS Nano, 2023, 17, 22004–22014.
42. W. Peng, S. Y. Park, C. J. Roh, J. Mun, H. Ju, J. Kim, E. K. Ko, Z. Liang, S. Hahn, J. Zhang, A. M. Sanchez, D. Walker, S. Hindmarsh, L. Si, Y. J. Jo, Y. Jo, T. H. Kim, C. Kim, L. Wang, M. Kim, J. S. Lee, T. W. Noh and D. Lee, Nat. Phys., 2024, 20, 450–455.
43. G. Tian, S. Zheng, Z. Mo, J. Xian, C. Chen, Z. Fan, M. Qin, J. Dai, J. Wang, J. Liu and X. Gao, Adv. Funct. Mater., 2025, 2416311.
44. X. Liang, H. Dong, Y. Wang, Q. Ma, H. Shang, S. Hu and S. Shen, Adv. Funct. Mater., 2024, 34, 2409906.
45. H. Shang, H. Dong, Y. Wu, F. Deng, X. Liang, S. Hu and S. Shen, Phys. Rev. Lett., 2024, 132, 116201.
46. I. Naumov and H. Fu, Phys. Rev. Lett., 2007, 98, 077603.
47. I. I. Naumov, L. Bellaiche and H. Fu, Nature, 2004, 432, 737–740.
48. W.-R. Geng, X. Guo, Y.-L. Zhu, D. Ma, Y.-L. Tang, Y.-J. Wang, Y. Wu, Z. Hong and X.-L. Ma, Nat. Commun., 2025, 16, 2804.
49. D. P. Chen, Y. Zhang, X. M. Zhang, L. Lin, Z. B. Yan, X. S. Gao and J.-M. Liu, J. Appl. Phys., 2017, 122, 044103.
50. Y. Nahas, S. Prokhorenko, L. Louis, Z. Gui, I. Kornev and L. Bellaiche, Nat. Commun., 2015, 6, 8542.
51. L. Zhang, G. Tian, W. Yang, D. Zheng, C. Lin, J. Xian, Y. Guo, X. Zhang, X. Qiu, L. Zhang, Z. Fan, D. Chen, Z. Hou, M. Qin, J.-M. Liu and X. Gao, J. Materiomics, 2023, 9, 56–61.
52. L. Zhang, X. Zhang, J. Xian, R. Chen, G. Tian, C. Li, J.-M. Liu and X. Gao, Appl. Phys. Rev., 2025, 12, 031406.
53. G. Tian, W. Yang, X. Song, D. Zheng, L. Zhang, C. Chen, P. Li, H. Fan, J. Yao, D. Chen, Z. Fan, Z. Hou, Z. Zhang, S. Wu, M. Zeng, X. Gao and J. Liu, Adv. Funct. Mater., 2019, 29, 1807276.
54. S. V. Kalinin, B. J. Rodriguez, S. Jesse, J. Shin, A. P. Baddorf, P. Gupta, H. Jain, D. B. Williams and A. Gruverman, Microsc. Microanal., 2006, 12, 206–220.
55. W. Yang, G. Tian, Y. Zhang, F. Xue, D. Zheng, L. Zhang, Y. Wang, C. Chen, Z. Fan, Z. Hou, D. Chen, J. Gao, M. Zeng, M. Qin, L.-Q. Chen, X. Gao and J.-M. Liu, Nat. Commun., 2021, 12, 1306.
56. J. Wang, J. Ma, H. Huang, J. Ma, H. M. Jafri, Y. Fan, H. Yang, Y. Wang, M. Chen, D. Liu, J. Zhang, Y.-H. Lin, L.-Q. Chen, D. Yi and C.-W. Nan, Nat. Commun., 2022, 13, 3255.

---

Footnote

† These authors contributed equally.

---