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In-plane charged domain walls with memristive behaviour in a ferroelectric film


Domain-wall nanoelectronics is considered to be a new paradigm for non-volatile memory and logic technologies in which domain walls, rather than domains, serve as an active element. Especially interesting are charged domain walls in ferroelectric structures, which have subnanometre thicknesses and exhibit non-trivial electronic and transport properties that are useful for various nanoelectronics applications1,2,3. The ability to deterministically create and manipulate charged domain walls is essential to realize their functional properties in electronic devices. Here we report a strategy for the controllable creation and manipulation of in-plane charged domain walls in BiFeO3 ferroelectric films a few nanometres thick. By using an in situ biasing technique within a scanning transmission electron microscope, an unconventional layer-by-layer switching mechanism is detected in which ferroelectric domain growth occurs in the direction parallel to an applied electric field. Based on atomically resolved electron energy-loss spectroscopy, in situ charge mapping by in-line electron holography and theoretical calculations, we show that oxygen vacancies accumulating at the charged domain walls are responsible for the domain-wall stability and motion. Voltage control of the in-plane domain-wall position within a BiFeO3 film gives rise to multiple non-volatile resistance states, thus demonstrating the key functional property of being a memristor a few unit cells thick. These results promote a better understanding of ferroelectric switching behaviour and provide a new strategy for creating unit-cell-scale devices.

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Fig. 1: Real-time observation of ferroelectric domain switching behaviour.
Fig. 2: Layer-by-layer domain-wall migration with multiple resistance states.
Fig. 3: Atomic structure and behaviour of domain walls with varying BFO film thickness.

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The data generated and analysed during the current study are available from the corresponding authors on reasonable request.


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We thank G. V. Tendeloo, S. Liu and F. Lin for helpful suggestions regarding revisions to our manuscript. This work was financially supported by the National Key R&D Programme of China (grant no. 2021YFA1500800), the National Natural Science Foundation of China (grant no. 12125407 and no. 52272129), China Postdoctoral Science Foundation (grant no. 2022M722716), Joint Funds of the National Natural Science Foundation of China (grant no. U21A2067), the Fundamental Research Funds for the Central Universities and the Zhejiang Provincial Natural Science Foundation (grant no. LD21E020002 and no. LR21E020004). J.S.C. acknowledges the financial support from the Singapore Ministry of Education MOET2EP50121-0024, MOE Tier 1-22-4888-A0001, A*STAR AMRIRG (grant no. A1983c0036); RIE2020 Advanced Manufacturing and Engineering (AME) Programmatic Grant no. A20G9b0135; and the Singapore National Research Foundation under a CRP Award (grant no. NRF-CRP23-2019-0070). The research work at the University of Nebraska-Lincoln was supported by the National Science Foundation (NSF) through the EPSCoR RII Track-1 (NSF Award OIA-2044049) and MRSEC (NSF Award DMR-1420645) programmes.

Author information

Authors and Affiliations



Z.Z. and H.T. conceived and designed this work. Z.L. performed and analysed the in situ STEM, EDX and EELS experiments, analysed the electrical measurements and wrote the manuscript. H.W. and J.C. prepared the samples and performed the characterization. M.L., L.T., T.R.P. and E.Y.T. performed the DFT calculations and data interpretation. H.Y. and Y.W. performed the in-line electron holography measurements. S.H., M.Z. and Y.X. carried out the electrical measurements. Z.R. co-wrote the manuscript. All authors contributed to the manuscript and the interpretation of the data.

Corresponding authors

Correspondence to Evgeny Y. Tsymbal, Jingsheng Chen, Ze Zhang or He Tian.

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Extended data figures and tables

Extended Data Fig. 1 Growth of BFO ultrathin films.

a, AFM image of Nb·STO/SRO/BFO/SRO. b, AFM images of the morphology of (001) STO substrate. c, RHEED intensity oscillation during the growth of SRO and four unit cell BFO. Insets of (b, c) show RHEED patterns of the substrate before and after SRO and BFO deposition respectively. d, Magnified STEM image of Nb·STO/SRO/BFO/SRO.

Extended Data Fig. 2 In-situ STEM experiments.

a, STEM image of conductive tungsten probe and of FIB sample lamella. The electrical path is marked with white lines. b, Magnified STEM image of partition area highlighted with a dashed blue square in (a). Capping Pt (blue) and sample (red) are cut out until the partition touches the substrate. c, Magnified STEM image of the tip with a schematic electrical path (red lines), which highlighted by a white square in (a). d, Magnified STEM image of SRO/BFO/SRO structure. e, Related schematic diagram of (d). f, Photograph of Hysitron PI-95 TEM Picoindenter with Electrical Characterization Module (ECM).

Extended Data Fig. 3 Changing of individual lattice parameter c and a during domain switching.

ac, HAADF-STEM images of SRO/BFO/SRO which are the same as Fig. 1d–f during polarization switching. Scale bars, 2 nm. df, Maps of c lattice parameter in (ac). gi, Maps of a lattice parameter in (ac). To avoid the drift in sample recording, the images are obtained using various beam scanning directions.

Extended Data Fig. 4 Exhibition of BFO film with tail-to-tail domain wall on large scale and in long time.

a, The HAADF-STEM image of BFO film with atomically flat charged domain wall on a large scale. Scale bars, 5 nm. b, The charged domain wall in BFO film after 24 months. The area is highlighted by a yellow rectangle in (a). Tail-to-tail state still maintained for over 24 months. Scale bars, 2 nm.

Extended Data Fig. 5 EELS analysis of Fe-L and O-K edges in different tail-to-tail domain wall states.

ac, Atomic resolution line scanning EELS of Fe-L2,3 edges taken along BFO film in Fig. 2a–c. Each spectrum is demonstrated from the signal summing up of one layer of Fe. The shifts of Fe-L edges are less than 0.2 eV, reflecting the unchanged valence state in Fe. df, Atomic resolution line scanning EELS of O-K edges taken along BFO unit cells in Fig. 2a–c. Original signals are drawn by grey dots, superposed by smoothed spectra. gi, The intensity ratio of peak A and peak B for O-K edges in (df). The ratio is calculated as IA/IB, indicated by black circles (filled circles: domain wall regions). Error bars are the standard error for determining the IA/IB over five measurements. Two features can be found in the O-K spectra: the pre-peak A, and the post-peak B. The relative intensity of peak A (IA) and peak B (IB), displayed as IA/IB, is used to evaluate the oxygen vacancy population42. In our case, an increased IA/IB corresponds to excess of oxygen vacancies. The relative intensities are sizably enhanced at the domain wall area (Fig. S2g–i). These quantified results confirm the accumulation of oxygen vacancies where the charged domain walls are created.

Extended Data Fig. 6 Distortion of oxygen octahedron in BFO during domain-wall migration.

a, The integrated differential phase contrast (iDPC) STEM image of the uniformly polarized state. Inset presents unit cell schemes with Bi, Fe, O, Sr, and Ru atoms (red, green, blue, yellow, and dark blue, respectively). Polarization vectors are presented by blue and red arrows at left. b, The iDPC-STEM image of “tail-to-tail” polarized state with schemes of atoms and polarization vectors. Scale bars (a,b), 1 nm. c, The distances of top and bottom oxygen atoms for each BFO layer in “tail-to-tail” state from experimental and calculation results. The error bars are the standard error of mean in each layer. d, The comparison of experiment and DFT calculation off-centre displacement of oxygen octahedra and Fe atoms for each BFO layer in “tail-to-tail” state. Off-center displacement is defined as a distance from the centre of oxygen octahedra (or Fe atoms) to the center of the Bi lattices. Along with the accumulation of oxygen vacancies, the distortion of oxygen octahedra in BFO is also observed. The positions of oxygen atoms are precisely determined using iDPC-STEM imaging technique. Using a 4-quadrant detector, the iDPC-STEM imaging technique can observe both light and heavy elements with clear contrast. The light elements have a higher signal to dose ratio in iDPC imaging, which makes oxygen visible43. In the tail-to-tail state, the distances between the top and bottom oxygen atoms are decreased at the domain wall, showing a clear compression of oxygen octahedra. Accompanied by the compression at the domain wall, oxygen octahedra at the BFO/SRO interfaces are stretched, leading to larger off-centre displacements. The lattice deformation across the domain wall is further confirmed by our DFT calculations (Fig. S7c,d), which demonstrate the quantitative agreement with experimental data. Previous works also indicated that missing oxygen atoms in perovskite unit cells lead to oxygen octahedra to be compressed44,45. The observed lattice distortion and the accumulation of oxygen vacancies around the tail-to-tail domain wall are the structural and electrical factors for the creation and manipulation of charged domain wall, respectively.

Extended Data Fig. 7 DFT calculations of the atomic structure in different polarized states in SRO/BFO/SRO.

Fully relaxed atomic structure for single-domain structure (a,b) and tail-to-tail domain wall structure (c,d). VO denotes the oxygen vacancy at the first (b), second (c), and central (d) BiO layer. The arrows schematically denote the layer-resolved polarization and the length of arrows scales with the magnitude of displacements. When the uniform polarization state is sustained in 4-unit-cell BFO film, a tail-to-tail domain wall configuration is unstable. This behaviour changes when oxygen vacancies are deposited at the domain wall. Ionized oxygen vacancies provide a positive ionic charge which screens the negative polarization charge at the tail-to-tail domain wall, resulting in a stable domain wall configuration. For the oxygen vacancy located in the first BiO monolayer from the interface, the atomic displacements near the oxygen vacancy are enhanced, but the BFO layer maintains a single domain structure. However, for the oxygen vacancy placed in the second or central BiO monolayer, the atomic displacements are pointing away from the oxygen vacancy layer, as expected from the positive charge of the ionized oxygen vacancy, forming a tail-to-tail domain wall structure.

Extended Data Fig. 8 Measured current and resistance in SRO/BFO/SRO film.

a, Current versus voltage curves measured by AFM on 4-u.c. SRO/BFO/SRO film, 0.5 V/s. Loops are displayed in chronological order. During the applied voltage cycles, I-V curves exhibit the pinched hysteresis character in memristor. b, Digital meter measurement in SRO/BFO/SRO film. The measured I-V curve using digital meter (details see below). The current exhibit jumps during positive sweeping, which are indicated by red arrows. Black arrows show the sweeping direction of voltages. Inset shows the diagram of measurement. c, The measurement of resistance during in-situ biasing process. The voltage-time curve illustrates the write and read voltage sequences for measurements of resistance. After applying the constant write voltage on film, the resistance is read between −0.1 V and +0.1 V. Sketches of equivalent circuit diagrams for three typical polarization states are exhibited at d, corresponding to the high resistance state (High R), low resistance state (Low R) and intermediate states in R-V curves. The change of polarization states is discovered simultaneously with the change of resistance in in-situ test, which is consistent with the in-situ imaging in Fig. 2a–c. The vertical I-V measurement is performed at room temperature. The bottom and surface electrodes of the sample are silver paste and a 50-nm-silver film (about 0.17 square millimeter in area) prepared by e-beam evaporation, respectively. The DC voltage across the contacts is applied to bias the sample, and then the current is measured by a digital meter (Keithley 2611B). The sweeping direction of the voltage is from positive to negative and finally returns to the initial state, e.g. from 0 volts to +1 volts to −1 volts and back to 0 volts. We choose AFM test, in-situ test and digital meter test to confirm the current and resistance character in BFO film. AFM probe measurement is used to examine the fine feature of I-V curve. In-situ probe measurement is used to examine the correspondence of resistance change and domain wall dynamic behavior. Digital meter measurement is used to examine the repeatability of I-V character in a large area of sample.

Extended Data Fig. 9 BFO films with asymmetric terminations.

a-b, The HAADF-STEM images of SRO/BFO/SRO film with asymmetric terminations. Film shows single domain states all the time under similar in-situ electric operation. c, The elemental EDX maps of (a,b) with false-colour overlaid on Bi (red), Fe (green), Sr (yellow), and Ru (blue). The films have asymmetric terminations. In the upper SRO/BFO interface, the termination is FeO2, while the bottom interface shows BiO termination. Scale bars, 1 nm. Without the symmetric termination, BFO exhibits a uniform polarization.

Extended Data Fig. 10 BFO films with various thicknesses after applied voltage.

ac, HAADF images of 2-unit cells thick, 5-unit cells thick, and 6-unit cells thick BFO films, respectively. Domain wall (red dashed line) and polarization vectors (red arrows for polarized up and blue for polarized down) are superposed. Scale bars, 2 nm.

Extended Data Fig. 11 Domain wall formation in different heterostructures.

a, The magnified STEM image of La0.7Sr0.3MnO3/BiFeO3/La0.7Sr0.3MnO3 (LSMO/BFO/LSMO) structure. bc, The atomic-scale HAADF-STEM images of LSMO/BFO/LSMO film at 0 V and 5 V, respectively. The direction of polarization is marked by red and blue arrow. Domain wall is marked by dashed red line. Interfaces are indicated by dashed white lines. Scale bars, 1 nm. BFO shows uniform polarization at initial state. After applying voltage of 5 volt, a tail-to-tail in-plane charged domain wall is found. d, The magnified STEM image of SRO/BFO/SRO structure with thick SRO electrodes. The thickness of SRO electrode is more than 14 nm. e-f, Atomic-scale HAADF-STEM images of SRO/BFO/SRO film at 0 V and 5 V, respectively. Scale bars, 2 nm. A tail-to-tail in-plane charged domain wall is still formed when SRO electrodes become thicker. g, The magnified STEM image of SrRuO3/BaTiO3/SrRuO3 (SRO/BTO/SRO) structure. h-i, Atomic-scale HAADF-STEM images of SRO/BTO/SRO film at 0 V and 5 V, respectively. Scale bars, 2 nm. BTO shows uniform polarization at initial state. After applying voltage of 5 volt, a head-to-head in-plane charged domain wall is found. j, The magnified STEM image of SrTiO3/BiFeO3/SrTiO3 (STO/BFO/STO) structure. k-l, Atomic-scale HAADF-STEM images of STO/BFO/STO film at 0 V and 10 V, respectively. Interfaces of STO/BFO are indicated by dashed white lines. Scale bars, 1 nm. BFO is switched without charged domain wall after applying voltage of 10 volt. Without conducting electrodes such as SRO and LSMO in film, BFO switches from the uniform polarization to the opposite without forming charged domain wall.

Extended Data Fig. 12 Ferroelectricity of SRO/4 u.c. BFO/SRO film.

Out-of-plane SS-PFM amplitude (half-filled olive square) and phase (filled blue circle) loop are measured in air.

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Liu, Z., Wang, H., Li, M. et al. In-plane charged domain walls with memristive behaviour in a ferroelectric film. Nature 613, 656–661 (2023).

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