Tailoring polarization homogeneity in discontinuous-columnar Bi(Fe,Mn)O_3 thin films via dislocation engineering with controlled self-assembly

Domain: physics
Published: 2026-01-15
Editorial outcome: major_revision

Abstract
Defect microstructures, particularly dislocations, are pivotal in determining the functional properties of ferroelectric thin films. While their density is routinely considered, the critical role of their spatial configuration has remained largely unexplored and difficult to control. Here, we develop a controlled self-assembly strategy for dislocations in Bi(Fe,Mn)O3 thin films on Ni-Cr that directly addresses this challenge. By employing a LaNiO3 buffer layer, we template a discontinuous-columnar grain structure and guide the self-assembly of edge dislocations along grain boundaries in a topologically-protected configuration. The resulting ordered microstructure promotes a more uniform strain field and more coherent FeO6 octahedral tilting, significantly enhances polarization homogeneity, leading to a lower domain-switching barrier and a more uniform domain pinning effect. Consequently, the BFMO thin film exhibits dramatically superior aging stability after 60 days at 60 °C, exhibiting far smaller reductions in remanent polarization (~20%) and coercive field (~35%) compared to the BFMO thin film grown directly on Ni-Cr. These findings establish a defect engineering paradigm wherein the deliberate dislocation rearrangement is leveraged to unlock superior ferroelectric performance.

Introduction
The functional performance of ferroelectric materials is governed by their microstructure, with strain-polarization coupling being one of the characteristics widely utilized in non-volatile memory applications1,2. Defects, which vary from zero-dimensional point defects to two-dimensional interfaces, are inherent in these materials and significantly influence their functional characteristics. Among these defects, one-dimensional topological defects, such as dislocations, have recently gained attention not merely as defects, but as core elements whose configuration can be engineered to tailor material performance3–5.

Traditionally, dislocations have been viewed as harmful, with most defect engineering strategies merely focused on reducing their density to enhance material properties6,7. However, recent studies have revealed that strategically engineering dislocation configurations can actually improve functionality. This paradigm shift is particularly relevant in ferroelectrics, where the spatial rearrangement of dislocations is as critical as their density. A low density of randomly-distributed dislocations can suppress random strain fluctuations and promote uniform domain ordering. However, this configuration typically results in higher energy requirements for domain switching and thus a higher coercive field (Ec)8–13. In contrast, a high density of random dislocations can facilitate strain transfer and reduce switching barriers through interaction with domain wall motion, but may also generate random strain field that lead to nanoscale polarization vortex, resulting in decreased remnant polarization (Pr) and accelerated aging process14.

The profound impact of lattice control on ferroelectric properties is classically demonstrated by applying strain. In ferroelectrics like BiFeO3 (BFO), strain-induced templates can selectively manipulate FeO6 octahedral rotation modes. A striking manifestation occurs in epitaxially constrained BFO thin films under strong compressive strain, which stabilize a metastable tetragonal-like polymorph exhibiting both an exceptionally large axial ratio (c/a ~1.23) and fundamentally distinct oxygen octahedral rotation patterns compared to the rhombohedral bulk phase. This “super-tetragonal” phase, first predicted theoretically in the mid-2000s, exhibits not only giant polarization but also reconstructed rotation symmetries, demonstrating dual role of strain in modifying both polar and rotational order parameters15. Similarly, in displacement-type ferroelectrics such as BaTiO3 (BTO), the interaction between strain and lattice distortions becomes particularly crucial for optimizing distortion pathways. First-principles calculations reveal that uniaxial c-axis strain promotes cooperative Ti-O displacements that linearly enhance polarization, while multiaxial (abc) strain triggers discontinuous polarization jumps through anomalous oxygen displacements16.

Building on the established foundation of strain engineering, recent advances have identified dislocation engineering as a frontier for controlling ferroelectric properties, shifting the focus from applying uniform global strain to deliberately designing nanoscale dislocation configurations17–19. This innovative approach enables the conversion of dislocation configurations from randomly distributed defects into purposefully crafted functional elements, providing pathway to simultaneously enhance key memory parameters: increasing Pr to broaden memory windows, tuning Ec for efficient switching, and significantly improving aging stability. By leveraging the unique, topologically protected behavior of dislocations, guided dislocation self-assembly provides a pathway to control local octahedral tilting and lattice distortions in ferroelectrics15,16,20,21. Such precise control over local structural distortions represent the central goal of modern defect engineering.

Bismuth ferrite (BiFeO3, BFO) is well-suited for memory applications due to its intrinsic properties, such as high intrinsic Pr exceeding 100 μC/cm2 and low Ec below 100 kV/cm22. However, the integration of BFO into thin-film devices presents significant challenges, primarily due to interfacial mismatch strain, which can induce defects during crystallization23. These defects can markedly impair the ferroelectric properties, leading to issues such as severe leakage current, accelerated aging in polarization, diminished Pr and increased Ec values24. Addressing these issues by defect engineering provides a strategy to concurrently optimize polarization parameters, paving the way for developing more reliable and efficient ferroelectric memory devices.

To address the limitations in ferroelectric performance of BFO thin films, one must reconsider the interactions among defect configurations and ferroelectric polarization. A key focus lies in understanding how the configurations influence ferroelectric polarization. A major challenge lies in the fabrication of BFO thin films with controlled defect configurations that can effectively regulate interactions across various levels, from atomic distortions to domain structures and overall ferroelectric polarization.

Here, we have developed an innovative strategy of dislocation engineering via controlled self-assembly to overcome the limitations of conventional defect density-control approaches in Bi(Fe,Mn)O3 (BFMO) thin films. Unlike previous studies that employed SrTiO3 (STO) substrates to achieve low dislocation densities and improve ferroelectric properties25–27, we selected a face-centered cubic (FCC) Ni-Cr substrate to deliberately introduce lattice and thermal expansion mismatch with the rhombohedral (R3c) BFMO thin film. This mismatch is not a defect but a design feature, serving as a source to generate a high density of dislocations for configuration control. These dislocations provide a unique way of probing dislocation-polarization interaction and the impact on ferroelectric behaviors. Furthermore, the metallic nature of Ni-Cr substrate offers inherent potential as a built-in electrode for future studies on interfacial charge behavior, while its mechanical properties also make it a promising candidate for explorations into flexible ferroelectric electronics. We then incorporated a LaNiO3 (LNO) buffer layer, which reduced BFMO/Ni-Cr lattice mismatch from ~3.8% to ~1.0%. This promoted the formation of a discontinuous-columnar grain structure, which in turn provided fundamental control over the dislocation configuration, guiding the subsequent self-assembly.

The strain energy anisotropy effect of LNO plays a pivotal role in guiding the formation of discontinuous-columnar grains in BFMO, facilitating the self-assembly of topologically-protected dislocations along grain boundaries. This interaction between dislocations and grain boundaries introduces an innovative mechanism for regulating functional properties, enabling the dissipation of strain energy through a more uniform strain field, more coherent FeO6 octahedral tilting, and enhanced macroscopic polarization homogeneity. Consequently, the LNO-buffered BFMO thin film aged for 60 days at 60 °C exhibits robust aging resistance, with only ~20% and ~35% reductions in Pr and Ec, while the LNO-free thin film suffers severe degradation of ~90% and ~80%, respectively. These findings challenge the conventional perspective of defects as purely detrimental, instead presenting a design approach focused on controlling dislocation configurations to optimize ferroelectric properties.

Results
In perovskite ferroelectric thin films, where multiple dislocation types typically coexist, edge dislocations are particularly influential due to their distinct mechanistic attributes. The characteristic extra half-plane structure in edge dislocations generates substantial strain gradients, quantified by pronounced shear stress and asymmetry normal stress near the dislocation core28,29. This anisotropic strain field breaks local symmetry and induces polarization gradients, establishing edge dislocations as effective tools to tailor ferroelectric polarization. The resulting strain-polarization coupling further enables deterministic control of dynamic responses to external stimuli, offering valuable opportunities for exploring defect-ferroelectric interactions.

To explore these effects at a fundamental level and provide a basis for their engineering, we established a 2D slice model of BFMO single crystal viewed along [100] direction, allowing us to effectively isolate and examine the intrinsic edge dislocation effects on ferroelectric polarization. The [100] direction is specifically chosen for reasons as follows: (i) the Burgers vector (b‖[100]) lies entirely within the observation plane while the dislocation line (t) aligns with [010], and (ii) it provides optimal strain field decoupling. Besides, the [100] direction enables clear separation between transverse strain (εxx) and longitudinal strain (εyy), respectively around edge dislocations, while also allowing distinct visualization of domain wall strains (primarily εxx). This geometric selectivity permits effective isolation of defect interactions and precise analysis of edge dislocation effects on polarization.

We compare characteristic electric field-dependent interactions between an edge dislocation (marked as black “T” symbol, where the vertical stem of “T” indicates the extra half-plane and the horizontal bar shows the termination line of the dislocation) and a ferroelectric domain wall (where ferroelectric domain is the region with uniform polarization orientation indicated by arrows and domain wall represents boundary between adjacent domains), as shown in Fig. 1a,b. Phase-field simulations reveal the fundamental mechanisms underlying defect-polarization interaction, providing critical insights into their role in modulating ferroelectric properties.

The results demonstrate that when the applied electric field (E) is below the critical pinning strength (E<Ec, where Ec is the coercive field), the strain field generated by the edge dislocation creates a significant energy barrier that strongly pins the domain wall at the dislocation core. This pinning effect primarily stems from the strong coupling between the local strain field induced by the dislocation and change in polarization across the domain wall. As the E value increases beyond the critical value (E>Ec), the domain wall undergoes a dynamic de-pinning process, characterized by local deformation near the dislocation core and eventual release through characteristic structural transformations. Notably, in the defect-free BFMO (Fig. 1a), polarization vortices emerge, only when the E value reaches a critical threshold value. In contrast, in BFMO containing an edge dislocation (Fig. 1b), distinct polarization vortices are readily detectable near the dislocation even in the absence of E. Without defects, the formation of polarization vortices relies entirely on E overcoming the energy barrier of the uniform polarization state. However, with an edge dislocation, the strong localized strain field introduced by an edge dislocation couples significantly with the ferroelectric order parameter, markedly promoting formation of vortex through strain-polarization interactions. More importantly, this localized strain field provides an additional topological protection, enhancing the stability of the formed polarization vortices. This process aligns with classical domain wall pinning process but highlights the unique strain effects from dislocations. These insights not only deepen our understanding of defect-polarization interactions but also establish the foundational principles for the dislocation engineering approaches demonstrated in this work30.

To further explore this mechanism at the atomic scale, DFT calculations were performed (Fig. 1c) to simulate atomic-scale edge dislocation configurations, which directly correlate with the edge dislocation observed in Fig. 1b. Comparing the pristine (c1) and slip-dislocated (c2) BFMO systems, where the latter was constructed by cleaving the BFMO crystal along the (001) plane, the dislocated configuration (c2) mimics the core characteristic of edge dislocation through a relative in-plane shear displacement (marked by ←/→ arrows) across a defined interface (indicated by the black-dashed line). This structure mismatch reflects the extra half-plane characteristic of an edge dislocation, indicated by the black “T” symbol in Fig. 1b, where the black-dashed interface line corresponds to the horizontal bar of the “T” notation. The anti-parallel displacements explicitly represent Burgers vector components of neighboring dislocation cores, introducing a shear-liked distortion at the interface that may influence local polarization. Fig. S2 reveals the corresponding electrostatic potential distributions with the statistical-box normal plots (Fig. 1d) to show the potential fluctuation. The significantly enhanced electrostatic potential fluctuations in the slip-dislocated structure are evidenced by extended box ranges and flattened normal distribution profiles, which fundamentally reflect charge redistribution and built-in electric field modification. Additionally, the differential charge density analysis (Fig. S3) reveals distinct localized charge accumulation around O sites and depletion near Fe cations, demonstrating that these variations originate from the significant electron redistribution primarily from Fe-3d to O-2p orbitals. This charge transfer, driven by FeO6 octahedral tilting [arrows in Fig. 1(c2)], couples with ionic displacement-induced dipole re-alignment to stabilize the observed electronic configuration. The resulting symmetry-breaking shear distortion creates polarization disorder, providing direct evidence for how an edge dislocation fundamentally modulates ferroelectric behavior through local structural and electronic modifications.

The influence of edge dislocations on the domain structure (Fig. 2a,b), ferroelectric polarization (Fig. 2c) and local strain field (Fig. 2d) in BFMO single crystal were investigated using phase-field simulations based on Ginzberg-Landau equations. In the absence of edge dislocations, the saturated polarization (Ps) forms a stable equilibrium configuration with well-defined straight 90° domain walls (Fig. 2a). In contrast, phase-field simulations of an active slip system (Fig. 2b) containing randomly-distributed edge dislocations (Burgers vector |b|=2ai, where i=1, 2, 3) reveal that domain walls become distorted and broadened near dislocation cores, forming kinked, bulged configurations. This results in significantly enhanced fluctuations of local ferroelectric polarization. The corresponding polarization switching dynamics under super-coercive electric field was systematically investigated to elucidate the pinning effects of edge dislocations on domain switching (Fig. 2c). Compared to the pristine one, BFMO containing edge dislocations exhibits reduced remnant polarization (Pr) and increased coercive field (Ec), highlighting the strong pinning imposed by dislocations on domain wall motion. Further analysis of the local strain field (Fig. 2d) shows that dislocations introduce significant elastic distortions that influence domain behavior, causing domain walls to bend along the isoenergy contours of the strain field, where elastic strain energy is minimized. Without dislocations, only minor transverse strain (εxx) variations are observed around the domain walls, while the longitudinal strain (εyy) remains essentially unchanged. The introduction of edge dislocations with specific geometric configurations (Burgers vector b‖[100], dislocation line t‖[010]) generates significant εyy and coupled εxx at the dislocation cores. This complex strain field presents a fundamental challenge for ferroelectric modulation.

As shown in Fig. 2(e), in the absence of dislocations, the εxx observed at domain walls originates from cooperative lattice distortions that accommodate polarization switching between adjacent ferroelectric domains, primarily manifesting as transverse lattice stretching or compression. While, the negligible εyy reflects minimal polarization-induced variation in the out-of-plane lattice parameters. Upon introducing edge dislocations with b‖[100] and t‖[010] in Fig. 2(e2), the characteristic “extra half-plane” disrupts lattice periodicity, generating substantial longitudinal compression or tension at the dislocation core. This strong localized distortion, through Poisson coupling, further induces εxx, creating a three-dimensional strain field with significantly greater intensity than domain wall induced local strains.

These results demonstrate that the configuration of edge dislocations exerts a much stronger localized influence on ferroelectric polarization than domain walls alone, as its associated three-dimensional strain field directly impacts both longitudinal and transverse directions.

Structural mechanisms of BFMO thin films
Building on the principle that ferroelectric polarization is governed by dislocation configuration, we designed a heterostructure (Fig. 3) to actively engineer these arrangements. The introduction of a LaNiO3 (LNO) buffer layer between the BFMO thin film and Ni-Cr substrate fundamentally modifies the interfacial constraints (Fig. 3a,b). In the Au/BFMO/Ni-Cr structure (Fig. 3a), direct contact between BFMO and Ni-Cr results in a severe lattice mismatch (Δa/a₀~3.8%). By contrast, the Au/BFMO/LNO/Ni-Cr (Fig. 3b) reduces this mismatch to Δa/a₀~1.0% through LNO’s intermediate lattice parameter, enabling near-coherent hetero-epitaxial growth through optimized lattice parameter matching. XRD analysis confirms that both BFMO thin films possess phase-pure polycrystalline perovskite structures, consistent with the reference (#PDF01-072-7680, Fig. S4). With the introduction of LNO, the BFMO thin film exhibits significantly enhanced intensity and sharpness of diffraction peaks, particularly (012), (104), and (110), compared to the LNO-free one. This improvement stems from the better lattice matching between LNO and BFMO, which lowers the nucleation energy barrier and promotes hetero-epitaxial growth of BFMO31–33.

To further understand the stress environment, we developed a mechanical model treating BFMO thin film (estimated thickness h≈600 nm) as an Euler-Bernoulli beam on a Winkler foundation (Ni-Cr and LNO/Ni-Cr, estimated thickness H≈50 μm), where the axial force (N) and induced bending moment (M) collectively determine the deflection profile ω(x) (Fig. 3c)34. For simplicity, the structure is treated as one-dimensional and symmetric, with interfacial stress originating from the BFMO-foundation boundary and acting uniformly at BFMO. This symmetric stress distribution induces upward buckling of BFMO. Leveraging the symmetry, we restrict our analysis to the right half-region (x≥0), with the symmetry axis fixed at x=0 and the region of interest spanning xє[0, L]. The deflection profile ω(x) of BFMO thin films on the Winkler foundation is governed by Eq. (1).

EIω'''' (x) + Nω'' (x) + kω = 0 (1)

k = E/H (2)

where E is the Young’s modulus of BFMO, I is the moment of inertia, N characterizes the interfacial stress, and k is the elastic constant of the foundation. For the thin-sheet foundation, k is simplified by Eq. (2). We derive the analytical solution under the boundary condition of an applied moment M at x=L. This model directly correlates lattice matching at the interface with stress relaxation on the macroscopic scale, establishing a multiscale framework for understanding how interfacial constraints can be tailored to engineer defects.

Building upon the mechanical model described in Fig. 3c, we perform a systematic comparison of stress distribution within BFMO thin films (Fig. 3d–f). It reveals that the BFMO grown on LNO/Ni-Cr exhibits a distinct multi-directional load transfer pathway, forming a characteristic “square star-shaped” configuration (Fig. 3e). This contrasts sharply with the uniaxial, striped stress distribution observed in BFMO directly on Ni-Cr (Fig. 3d). This fourfold symmetric stress distribution not only provides clear orientation guidance for engineering defects, but also demonstrates improved strain energy dissipation through modified geometric patterning, mirroring reported stress-relief strategies35–38. Besides, the BFMO on LNO/Ni-Cr exhibits smoother deflection gradient with reduced slope dω/dx (Fig. 3f) across the whole thin film, potentially enabling multi-directional strain delocalization. This behavior, which creates a more favorable environment for controlled dislocation self-assembly, merits further investigation through Geometric Phase Analysis (GPA).

To compare the crystallinity of BFMO thin films grown on Ni-Cr and LNO/Ni-Cr substrates, bright-field (BF) and dark-field (DF) TEM imaging were performed (Fig. 4a–c). Both thin films demonstrate excellent compositional homogeneity across their thicknesses (Fig. S5). The thicknesses of BFMO and LNO layer are approximately 650 nm and 100 nm, respectively. BF-TEM and DF-TEM of BFMO thin film on LNO/Ni-Cr reveal discontinuous-columnar grains (Fig. 4b–c, S6, S7), demonstrating epitaxial registry between BFMO and LNO, which is consistent with previous reports39–41. The vertical growth of discontinuous-columnar grains establishes a longitudinal grain boundary network spanning the film thickness. Local selected-area electron diffraction (SAED) of region (c1) (Fig. 4c) shows superlattice diffraction spots with two sets of Bravais lattices, attributed to FeO6 octahedral tilting, which is a hallmark of the high-symmetry R3c phase in BFO derivatives42,43. HRTEM images (Fig. 4d,e) reveal well-defined lattice fringes with interplanar spacings (e.g., (012), (104), (110), (102¯)) matching well with the reference perovskite structure (PDF#01-072-7680). SAED confirms the crystallographic orientations: [22¯1] for BFMO/Ni-Cr and [010] for BFMO/LNO/Ni-Cr, both consistent with the R3c symmetry.

The IFFT reconstructions (Fig. 4g–i) highlight characteristic edge dislocations, marked by white “T” symbols, where an extra atomic half-plane terminates within the crystal lattice, which is a common feature in perovskite ferroelectrics44. Critically, a stark contrast in their configuration is observed: the BFMO on Ni-Cr exhibits a high density of randomly-distributed dislocations, whereas in BFMO/LNO/Ni-Cr, they are preferentially assembled along a discontinuous-columnar grain boundary marked with the red-dashed line in Fig. 4f. This transition from disorder to order directly correlates with the macroscopic strain state. As evidenced by GPA (Fig. 4j,k), the randomly-distributed dislocations in BFMO/Ni-Cr induce a pronounced spatial variation in εxy and εyy, while the self-assembled dislocations in BFMO/LNO/Ni-Cr give rise to a uniform strain distribution. We attribute this to the templating effect of LNO layer during growth. The LNO promotes near-single-crystal order within individual grains. Under the influence of the anisotropic stress distribution (Fig. 3e), this structure actively guides dislocations to migrate and self-assemble along discontinuous-columnar grain boundaries (Fig. S8), using the grain boundaries as effective sinks for defect isolation.

Electrical properties of BFMO thin films
High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was employed to map spontaneous polarization vectors via tracking B-site cation displacements (Fig. 5a,d) for BFMO thin films on Ni-Cr and LNO/Ni-Cr. The corresponding atomic brightness contrast directly visualizes spatial variations in polarization amplitude and angle (Fig. 5b,c,e,f). Regions from Fig. 4(a1) and (c1) were specifically selected to investigate the local influence of dislocation configurations on polarization (Fig. S9). In BFMO/Ni-Cr, which contains a high density of randomly-distributed dislocations (Fig. 4g), the polarization vectors exhibit significant spatial disorder (Fig. 5a). This disorder arises from irregular B-site cation displacements relative to the A-site lattice, where localized lattice distortions near edge dislocations disrupt the coherent ionic off-centering, creating competing polarization variants evident as random brightness contrast (Fig. 5b,c). In stark contrast, the BFMO/LNO/Ni-Cr thin film, featuring a microstructure with dislocations self-assembly along discontinuous-columnar grain boundaries (Fig. 4i), exhibits remarkable uniformity in both polarization vector alignment and angular distribution (Fig. 5d–f). This direct correlation between the engineered dislocation configuration and the enhanced polarization homogeneity demonstrates that defect engineering is a key to optimize ferroelectric performance. The reduction of randomly-distributed dislocations and their self-assembly along discontinuous-columnar grain boundaries minimizes the random local strain fluctuations that disrupt long-range polarization ordering.

This defect engineering strategy is fundamentally validated by combining it with DFT calculations (Fig. 1c–d, S3). The calculations confirm that a single edge dislocation induces a localized symmetry-breaking distortion, primarily manifested as FeO6 octahedral tilting and the resultant charge redistribution, which collectively stabilize a disordered polarization configuration. In BFMO/Ni-Cr, the collective effect of a high density of randomly-distributed dislocations creates overlapping disruptive fields, accounting for the severe macroscopic polarization disorder. Therefore, the reduction in randomly-distributed dislocations and their self-assembly achieved in the LNO-buffered BFMO thin film effectively mitigate this collective detrimental impact, directly enabling the observed polarization homogeneity.

To characterize the polarization behavior of the fresh BFMO thin films, we measured P-E loops at their respective breakdown strengths (Fig. 5g). The BFMO thin film on LNO/Ni-Cr exhibits reduced coercive field (Ec) with markedly higher Pr and Pm at room temperature. This indicates a lower domain-switching barrier, which aligns with the reduced pinning from the controlled dislocation configuration (Fig. 4i), in contrast to the strong pinning imposed by the high density of randomly-distributed dislocations in BFMO/Ni-Cr (Fig. 4g). Additionally, it also helps in reducing the leakage current density in BFMO on LNO/Ni-Cr, being one order of magnitude lower than that of the BFMO on Ni-Cr (Fig. S10).

Having established the superior initial ferroelectric properties of the LNO-buffered BFMO thin film, we evaluated the stability under accelerated aging conditions at multiple temperatures (RT, 60, 120, and 180°C) for 60 days (Fig. 5h,i). The performance of the two thin films diverges significantly. The BFMO/Ni-Cr thin film suffered severe ferroelectric degradation and ultimately failed at elevated temperatures, while the BFMO/LNO/Ni-Cr thin film demonstrated remarkably superior aging resistance, maintaining functionality even at 180°C. A notable contrast occurs at 60°C. The BFMO thin film on Ni-Cr suffers a severe ~90% reduction in Pr and ~80% in Ec, whereas the LNO-buffered thin film maintains a stable state with only ~20% and ~35% reductions, respectively. We attribute this dramatic difference to their distinct dislocation configurations (Fig. 4). In BFMO/Ni-Cr, the high density of randomly-distributed dislocations creates heterogeneous and thermally unstable pinning sites that are easily de-pinned, leading to rapid polarization degradation. In contrast, the reduced randomly-distributed dislocations and their self-assembly along discontinuous-columnar grain boundaries in BFMO/LNO/Ni-Cr creates a more uniform and coherent microstructure. This engineered configuration minimizes random local strain fluctuations and establishes a stable pinning environment that is robust against thermal stress, thereby ensuring the observed aging resistance.

In situ piezoelectric force microscope (PFM) was performed to probe the domain stability and switching reversibility (Fig. S11). After partial poling with opposite voltages, the BFMO/LNO/Ni-Cr thin film exhibited robust stability, with the PFM phase and amplitude of the switched domains remaining nearly unchanged for over 40 min. In stark contrast, the PFM signals from BFMO/Ni-Cr showed significant degradation within 30 min, indicating substantial back-switching of the ferroelectric domains. This distinct relaxation behavior is directly linked to their dislocation configurations. The dislocation self-assembly along grain boundaries in BFMO/LNO/Ni-Cr creates a stable energy landscape that effectively pins the domain walls, suppressing back-switching. Conversely, the high density of randomly-distributed dislocations in BFMO/Ni-Cr generates a heterogeneous and unstable pinning environment, which facilitates the depolarization fields that drive domain back-switching.

Methods
Mn-doped BiFeO3 (BFMO) thin film preparation
The 3 mol.% Mn-doped BiFeO3 (BFMO) thin film was synthesized via sol-gel method combined with layer-by-layer annealing. This optimal concentration was determined through preliminary experiments to effectively suppress leakage current density while significantly enhancing ferroelectric properties (Fig. S12). High-purity bismuth nitrate (99.99%, Aladdin, with 8 mol.% excess added to compensate for Bi volatilization during annealing), iron nitrate (99.99%, Aladdin), and manganese acetate (99.0%, Aladdin) were stoichiometrically weighed. The solvent system consisted of ethylene glycol (99.8%), acetylacetone (99.6%), and acetic acid (99.5%) in a 1:3:8 volume ratio. Bismuth nitrate was dissolved in the mixture of ethylene glycol and acetate under stirring at 70°C, while iron nitrate was premixed with acetylacetone at room temperature. The iron solution was incorporated into the bismuth solution, followed by addition of manganese acetate. After aging for 48 h, the sol was spin-coated onto 10×10 mm2 Ni-Cr substrate at 4000 rpm for 30 s and dried at 250°C for 180 s. Each layer underwent rapid thermal processing (RTP) immediately after deposition. The RTP steps for each layer were as follows: (i) preheating at 200°C for 60 s, (ii) pyrolysis at 350°C for 600 s, and (iii) annealing at 525°C for 480 s. During the annealing of each layer, the underlying crystallized layers experience a repeated thermal cycle. This process provides necessary driving force for the reorganization and propagation of structural defects, such as dislocations, across the film thickness, originating from the lattice and thermal mismatch at the progressive crystallization interface between successive layers. Both the deposition and annealing cycle were repeated 10 times to achieve the desired thickness.

Fabrication of a LaNiO3 (LNO) buffer layer
The LNO buffer layer was deposited between BFMO and Ni-Cr substrate using lanthanum nitrate (99.999%, Aladdin) and nickel acetate (99.9%, Aladdin). Precursors were homogenized in the mixture of 2-methoxyethanol and acetic acid under rotation at 60°C for 2 h, followed by 24 h aging at room temperature. Spin-coating at 3000 rpm for 30 s and drying at 300°C for 180 s were performed with the following RTP steps: (i) preheating at 200°C for 60 s, (ii) pyrolysis at 350°C for 1500 s, and (iii) annealing at 650°C for 480 s. Both the deposition and heat treatment cycle were repeated 3 times.

Structure characterization
The crystal structures were characterized by using X-ray diffractometer (XRD) with Cu Kα radiation (λ=1.5406 Å) (6°/min, Bruker D8 Discover, Germany). The microstructure of the samples was observed by a transmission electron microscope (TEM, FEI Talos F200X, USA). High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images were taken by a condenser spherical aberration-corrected transmission electron microscope (STEM, Thermo Spectra 200, USA).

Electrical measurements
The response of domains to electric field after a certain relaxation time was studied using a piezoresponse force microscopy (PFM, Bruker Dimension Edge, Germany) with the writing voltage of ±10 V. For the electrical measurements, Au top electrodes were sputtered onto the top surface with a shadow mask (~1 mm in diameter) to obtain the Au/BFMO/Ni-Cr and Au/BFMO/LNO/Ni-Cr structures. The polarization-electric field (P-E) loops and leakage current density were derived from the ferroelectric measurement system (Radiant RTI-Multiferroic, USA). For comparing the polarization stability, the BFMO thin films were first characterized at RT as the fresh reference, then aged at RT for 60 days, and the corresponding P-E loops were tested. Furthermore, P-E loops were also measured at elevated temperatures (e.g., 60, 120 and 180°C) to further evaluate their stability.

Phase-field simulations of the evolution of polarization behaviors
In the phase-field simulations, the ferroelectric polarization was simulated by solving the time-dependent (Ginzburg-Landau) (TDGL) equation for the temporal evolution of the polarization vector field. More details can be found in the Supplementary Information.

DFT simulations
All calculations were carried out using the Vienna Ab initio Simulation Package (VASP). We employed the projector augmented wave (PAW) method to simulate the electronic behavior of BFMO, with the generalized gradient approximation (GGA) and the Perdew-Burke-Ernzerhof (PBE) functional describing electron exchange-correlation (XC) interactions depending on the calculation type. More details can be found in the Supplementary Information.

Modeling BFMO as Euler-Bernoulli beam on a winkler foundation (Ni-Cr or LNO/Ni-Cr)
The mechanical behavior of BFMO was modeled as an Euler-Bernoulli beam resting on a Winkler foundation (Ni-Cr and LNO/Ni-Cr substrates). The governing differential equation was numerically solved using a custom-developed PYTHON-based framework. More details can be found in the Supplementary Information.

Calculation of polarization vector
To analyze the positions and shapes of atomic columns in STEM images, we used ATOMAP, a free and open-source software tool based on 2D elliptical Gaussian fitting. The method involves iteratively fitting the most intense atomic columns, subtracting them from the image, and then extracting the positions of the remaining atoms. More details can be found in the Supplementary Information.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript describes an interesting approach to improving the ferroelectric properties of Bi(Fe,Mn)O₃ (BFMO) films grown on Ni-Cr substrates by employing a LaNiO₃ (LNO) buffer layer. The LNO buffer layer is applied for strain engineering to reduce the dislocation density near the BFMO/Ni-Cr interface (reduced-dislocation self-assembly strategy), thereby mitigating degradation of the electrical properties.\nOverall, the work is promising and may be acceptable after addressing the following points:\nComments\n1. One important challenge for BiFeO3 (BFO) and related compounds in electronic device applications, including memory devices, is the issue of large leakage current (as described in line. 101). It would strengthen the manuscript if the authors could clarify whether the proposed “reduced-dislocation self-assembly strategy” also helps in reducing leakage current.\n2. Previous studies have reported that epitaxially grown BFO on SrTiO3 (STO), with lower defect density at the interface, can exhibit improved Pr and better electrical properties. Since such results are not cited here, it would be helpful for the authors to include relevant references and also to explain their motivation for employing the Ni-Cr substrate, which is less commonly used in Si-based electronic devices.\n3. Because the electrical properties of BFO, particularly leakage current, are sensitive to Mn doping concentration, it would be helpful if the authors could explain why 3 mol% Mn doping was chosen.\n4. The phrase “industry-standard 60 °C after 60-day aging” might be somewhat misleading. Typically, device reliability tests are carried out at higher temperatures (e.g., 150–200 °C), considering an activation energy of about 1 eV. A clarification would improve the accuracy of this description.\n5. In Figures 5a–f, it is a little difficult to identify which regions (e.g., BFMO/Ni-Cr boundaries) are shown. Revising the figure captions for clarity would make the results easier to follow.", "reviewer_2": "Please find attachment", "reviewer_3": "This manuscript tries to deliver a new concept on self-assembly dislocation and strain field control to tune properties of BFMO films. Although the authors carried out comprehensive studies on the dislocation effects on strains and ferroelectric properties, I do not think this manuscript provides sufficient novelty that readers of Nature Communicaions expect. In addition, some of the statements are rather speculative. The detailed comments are as follows.\nI am convinced that the manuscript presents the consistency that the BFMO/LNO/Ni-Cr film is less dislocation density than the BFMO/Ni-Cr film and demonstrates the consequent stress uniformity and improvement of ferroelectric properties. However, I do not see how the authors engineered and leveraged the dislocations to control the strain field and improve the properties besides reducing the dislocations. Although the authors bring up \"reduced dislocation self-assembly mediated strain engineering\", the conclusion appears to be that a film with lower dislocation density (Fig. 4g and h) is better (Fig. 2c, Fig. 5g, h, and i), which is not a new concept. People have already developed high quality BFO films with lower coercive field and higher polarization (which is not easy to compare due to the orientation difference) even with chemical solution method [10.1002/smll.201903663].\nAlso, the dislocation self-assembly at grain boundaries is not fully convincing based just on Fig. h and f. To prove the self-assembly, the authors need more data for statistical analysis for any scientific publication.\nI am not fully convinced with the lattice matching mechanism for the dislocation reduction for those specific polycrystalline films. Firstly, I do not see the “discontinuous columnar grains” from Fig. 4b and c. To me they look more like granular microstructure. In case of granular grains, the lattice mismatch discussion that the author mention is invalid since the grains at the BFMO/LNO interface are only influenced. Next, even if they are columnar growth, the effects on the dislocation density at grains inside the film are questionable. The lattice mismatch induces misfit dislocations at the interface but does not necessarily produce them in the bulk.\nI am concerned with the dislocation effects on the aging and degradation effects (by the way, that experimentation is not for retention study). The films have neither same interface nor crystallinity, which may also affect the degradation after aging. The authors reason the dislocation contribution based on the Ec drop after aging, but it is invalid evidence because the P-E loops after aging (especially for 60 C) do not show proper ferroelectricity anymore. The statement “This distinct aging behavior directly correlates with dislocation configurations” is speculative."}, "author_response": "Overall Response to the Editor and Reviewers\nWe would like to express our sincere appreciation to all the reviewers for dedicating their time and efforts to evaluating our work and for providing valuable feedback. We have thoroughly addressed all the comments raised and made adequate revisions accordingly. In the following section, we provide point-by-point responses to each comment, detailing the changes made in response to the suggestions/comments from the reviewers. Additionally, all modifications in the revised manuscript are highlighted in red for easy reference.\nReviewer #1:\nGeneral Comment: This manuscript describes an interesting approach to improving the ferroelectric properties of Bi(Fe,Mn)O (BFMO) films grown on Ni-Cr substrates by employing a LaNiO (LNO) buffer layer. The LNO buffer layer is applied for strain engineering to reduce the dislocation density near the BFMO/Ni-Cr interface (reduced-dislocation self-assembly strategy), thereby mitigating degradation of the electrical properties. Overall, the work is promising and may be acceptable after addressing the following points:\nOverall response: We sincerely appreciate the reviewer for their highly positive evaluation of our manuscript, especially the remark: ''Overall, the work is promising and may be acceptable after addressing the following points.''. In the following, we have carefully addressed all of reviewer's comments.\nComment 1: One important challenge for BiFeO (BFO) and related compounds in electronic device applications, including memory devices, is the issue of large leakage current (as described in line. 101). It would strengthen the manuscript if the authors could clarify whether the proposed ''reduced-dislocation self-assembly strategy'' also helps in reducing leakage current.\nResponse: Thanks to the reviewer for the valuable suggestions. We fully agree that high leakage current is a critical issue in BiFeO (BFO)-based electronic devices [Adv. Mater. 23, 669–672 (2011) and Adv. Funct. Mater. 32, 2112944 (2022)]1,2.\nIn response to the reviewer's comment, we have conducted additional electrical measurements to compare the leakage current between BFMO thin films with high-dislocation (without self-assembly) and the one with reduced-dislocation self-assembly. The leakage current density was measured as a function of the applied electric field to obtain I-E curves for BFMO thin films on Ni-Cr and LNO/Ni-Cr, as shown in Fig. R1 (Revised Supplementary Materials marked Fig. S10). It is interesting to note that the leakage current density of BFMO thin film on LNO/Ni-Cr is nearly one order of magnitude lower than the one on Ni-Cr under the same electric field of 600 kV/cm. The results confirm that the BFMO thin film on LNO/Ni-Cr with reduced-dislocation self-assembly maintains a significantly lower leakage current density. The results clearly indicate that our ''reduced-dislocation self-assembly strategy'' contributes to a notable reduction in leakage current density. On one hand, the strategy significantly reduces the dislocation density, thereby diminishing the number of defects that can serve as leakage current pathways [Nat. Commun. 11, 1762 (2020) and Nat. Commun. 15, 479 (2024)]3,4. More critically, the self-assembly process drives the dislocations to transition from a chaotic, random distribution into a highly ordered, isolated, and periodic arrangement. This ordered structure effectively disrupts the continuous percolation network that readily forms between randomly-distributed dislocations. Consequently, even if charge carriers enter a specific dislocation line, they cannot find a complete conductive path spanning the entire thin film, leading to a significant suppression of leakage current. In other words, self-assembly not only reduces the number of leakage paths but also prevents the formation of an \"interconnected network\" by reorganizing the pathway, thereby effectively blocking leakage current.\nFig. R1 (Revised Supplementary Materials Fig. S10) Leakage current density versus applied electric field (I-E) curves of BFMO thin films on Ni-Cr and LNO/Ni-Cr.\nFollowing the reviewer's suggestion, the I-E curves have been added into the revised Supplementary Materials marked Fig. S10 considering the limited space availability. Additionally, we have added discussions, reads as: ''Additionally, the reduced-dislocation self-assembly strategy also helps in reducing the leakage current density in BFMO on LNO/Ni-Cr, being one order of magnitude lower than its counterpart on Ni-Cr substrate (Fig. S10).''.\nComment 2: Previous studies have reported that epitaxially grown BFO on SrTiO (STO) substrates, with lower defect density at the interface, can exhibit improved P and better electrical properties. Since such results are not cited here, it would be helpful for the authors to include relevant references and also to explain their motivation for employing the Ni-Cr substrate, which is less commonly used in Si-based electronic devices.\nResponse: We thank the reviewer for raising this critical point, which correctly identifies an oversight in our literature citations and the important issue of substrate selection. We will update the references and explain the motivation for our choice of Ni-Cr substrate.\n(1) About references and discussions regarding high-quality BFO on SrTiO (STO) substrates\nWe fully agree with the reviewer's suggestion. The work on growing high-quality BFO thin films epitaxially on STO substrates is indeed foundational research that reveals the intrinsic ferroelectric properties of BFO and is considered a classic in the field of ferroelectrics. These studies leveraged the excellent lattice matching between STO and BFO along with high-quality epitaxial growth to reduce interface defect density, resulting in BFO thin films with nearly perfect crystal structure and high remanent polarization (P), among other excellent electrical properties [Science 299, 1719–1722 (2003) and Appl. Phys. Lett. 90, 212902 (2007)]5,6. These related works have established a foundation for subsequent research on BFO-based thin films.\nFollowing the reviewer's suggestion, we have added the sentence ''Unlike previous studies that employed SrTiO (STO) substrates to achieve low dislocation densities and improve ferroelectric properties25–27, we selected a face-centered cubic (FCC) Ni-Cr substrate to deliberately introduce lattice and thermal expansion mismatch with the rhombohedral (R3c) BFMO film. This mismatch is not a defect but a design feature, enabling strain engineering and generating a relatively high density of dislocations. These dislocations provide a unique way of probing dislocation-polarization interactions and strain-mediated ferroelectric behaviors. Furthermore, the metallic nature of Ni-Cr substrate offers inherent potential as a built-in electrode for future studies on interfacial charge behavior, while its mechanical properties also make it a promising candidate for explorations into flexible ferroelectric electronics.'' into the Part of Introduction of the revised manuscript to highlight the classical approach of using STO for high-quality epitaxial growth and enhanced electrical performance, and then to underscore our innovative strategy of utilizing Ni-Cr to pioneer a strain and defect engineering pathway.\n(2) About the motivation regarding the choice of Ni-Cr substrate\nThe reviewer's concern regarding the relatively limited application of Ni-Cr substrates in Si-based technology makes really good sense. However, our choice of Ni-Cr substrate is driven by a specific scientific motivation that differs from conventional approaches, which also represents one of the key innovations of this study:\nI. It allows us to introduce a specific strain state and a high density of defects. There exists a significant lattice mismatch and difference in thermal expansion coefficients between the Ni-Cr substrate with a face-centered cubic (FCC) structure and BFO thin film with rhombohedral (R3c) structure. We intentionally leverage this substantial mismatch to introduce a relatively high density of dislocations and strain fields into the BFO thin film. As demonstrated in our study, this distinctive microstructure is not an indicator of \"poor quality\". Instead, it serves as an essential prerequisite for controlling dislocation density, enabling dislocation reconfiguration, and consequently investigating the physical mechanisms of interaction between dislocations and ferroelectric polarization. Our objective is to explore the influence of defect engineering on ferroelectric polarization, rather than merely pursuing low defect density.\nII. It enables the possibility for subsequent device integration. Although Ni-Cr is not compatible with Si, it can serve as a bottom electrode directly for devices given its nature as a metallic alloy substrate. This allows us to construct a simple metal/ferroelectric prototype device for studying physical processes such as charge injection and interfacial transport, a functionality not directly attainable using insulating substrates like STO.\nIII. It provides a way to explore potential pathways for BFO-based applications in flexible electronics. Ni-Cr offers favorable mechanical strength and flexibility. Compared with rigid substrates (such as STO), integrating functional oxide thin films on flexible Ni-Cr represents an emerging research direction in the field of flexible electronics. Our work provides a foundational technical exploration in this regard. In future studies, we will further investigate the mechanical properties of Ni-Cr (such as elastic modulus and yield strength) and their influence on the microstructure, ferroelectric domain switching, and the stability of the piezoelectric response of BFO thin film under repeated bending deformation. This ongoing work aims to clarify the failure mechanisms of thin films on flexible substrates under mechanical stress and to establish a foundation for developing flexible ferroelectric devices with superior performance and exceptional reliability.\nIn summary, the choice of Ni-Cr substrate represents a non-conventional design strategy. The core concept is to \"turn a drawback into an advantage\" by leveraging the significant lattice mismatch to deliberately introduce defects and strain, thereby enabling the exploration of novel physical phenomena that cannot be observed in single crystals or epitaxial thin films without defect (or with low defect density).\nWe have included this explanation regarding the motivation for substrate selection in the Introduction of the revised manuscript, reads as: ''Here, we have developed an innovative strategy termed \"reduced-dislocation self-assembly mediated strain engineering\" to overcome the limitations of conventional defect-control approaches in Bi(Fe,Mn)O (BFMO) thin films. Unlike previous studies that employed SrTiO (STO) substrates to achieve low dislocation densities and improve ferroelectric properties25–27, we selected a face-centered cubic (FCC) Ni-Cr substrate to deliberately introduce lattice and thermal expansion mismatch with the rhombohedral BFMO film. This mismatch is not a defect but a design feature, enabling strain engineering and generating a relatively high density of dislocations. These dislocations provide a unique way of probing dislocation-polarization interactions and strain-mediated ferroelectric behaviors. Furthermore, the metallic nature of Ni-Cr substrate offers inherent potential as a built-in electrode for future studies on interfacial charge behavior, while its mechanical properties also make it a promising candidate for explorations into flexible ferroelectric electronics.''. We hope this content can effectively addresses reviewer's concern and better highlights the novelty and contribution of our work. Once again, we sincerely thank the reviewer for helping improve the quality and clarity of our paper.\nComment 3: Because the electrical properties of BFO, particularly leakage current, are sensitive to Mn doping concentration, it would be helpful if the authors could explain why 3 mol. % Mn doping was chosen.\nResponse: We thank the reviewer for pointing out the need to provide justification for choosing 3 mol. % Mn doping. As the reviewer highlighted, the electrical properties of BFO, particularly leakage current, are sensitive to Mn doping concentration.\nWe introduced a certain amount of Mn primarily to effectively address the inherent high leakage current issue in the sol-gel derived BFO thin films, which is a fundamental requirement and basis for obtaining measurable and highly reliable ferroelectric performance.\nOur experimental results identified 3 mol. % as the optimal Mn doping concentration. In preliminary tests across rigid (Pt/Ti/SiO₂/Si) and flexible (LNO/Ni-Cr) substrates, 3 mol. % Mn effectively reduced leakage current to a level that allows reliable ferroelectric measurement in Figs. R2 a,b. This concentration also produced a significant enhancement in ferroelectric properties, as seen in the modulated remanent polarization (P) and coercive field (E ) in Figs. R2 c,d. This optimal performance at 3 mol.% is attributed to the balanced role of Mn ions, which can effectively compensate for charge-compensating oxygen vacancies that cause leakage, without introducing a high density of new point defects that would act as strong pinning centers and hinder domain switching.\nFig. R2 (Revised Supplementary Materials Fig. S12) Electrical performance measurements of BFMO thin films with Mn doping contents of 1, 3, and 5 mol. %, respectively. a,b Leakage current density versus applied electric field (I-E) curves of BFMO on rigid Pt/Ti/SiO /Si and flexible LNO/Ni-Cr, respectively, c,d P-E loops of BFMO on rigid Pt/Ti/SiO /Si and flexible LNO/Ni-Cr at 10 kHz, respectively.\nFollowing the reviewer's suggestion, Fig. R2 has been added into the revised Supplementary Materials marked Fig. S12 considering the limited space availability. Additionally, we have added discussions, reads as: ''This optimal concentration was determined through preliminary experiments to effectively suppress leakage current while significantly enhancing ferroelectric properties (Fig. S12).'' into the Part of ''Mn-doped BiFeO (BFMO) Thin Film Preparation'' in the Methods of the revised manuscript.\nComment 4: The phrase ''industry-standard 60 °C after 60-day aging'' might be somewhat misleading. Typically, device reliability tests are carried out at higher temperatures (e.g., 150–200 °C), considering an activation energy of about 1 eV. A clarification would improve the accuracy of this description.\nResponse: We sincerely thank the reviewer for raising this highly professional comment. This is absolutely correct, given the activation energy of ~1 eV, industry-standard reliability tests are indeed typically conducted at higher temperatures (e.g., 150–200 °C) to accelerate the aging process. We have carefully addressed this inaccuracy in the revised manuscript and sincerely apologize for this oversight.\nFig. R3 (Revised Manuscript Fig. 5 h,i) P-E loops of BFMO thin films measured at 10 kHz before/after aging (@RT, 60, 120, and 180 °C). a On Ni-Cr, b on LNO/Ni-Cr. It demonstrates superior aging resistance of the LNO-buffered sample.\nIn the study, we have conducted aging tests on BFMO thin films deposited on both Ni-Cr and LNO/Ni-Cr substrates at multiple temperatures (RT, 60, 120, and 180 °C) at 10 kHz, as shown in Fig. R3. It reveals that at temperatures exceeding 60 °C, the BFMO thin film on Ni-Cr suffered from severe degradation in ferroelectricity, ultimately leading to sample failure. In contrast, the film on LNO/Ni-Cr demonstrated remarkably superior aging resistance, maintaining functional performance even at 180 °C.\nWhile the contrast in aging resistance is most pronounced at elevated temperatures (120 and 180 °C), in the original manuscript, we only selected RT and 60 °C as they provide the most instructive basis for comparison. At RT, both thin films retain functionally measurable and directly comparable ferroelectric properties, thereby enabling a quantitatively rigorous and scientifically equitable evaluation. It turns out that RT condition represents a \"relatively moderate aging state\" where a valid comparative analysis between the two types remains possible. This is the reason why we selectively presented only RT and 60 °C results in the original manuscript. This striking contrast provides meaningful evidence for our core argument that the BFMO thin films grown on LNO/Ni-Cr, which are characterized by reduced-dislocation self-assembly, exhibit significantly superior aging resistance at elevated temperatures.\nIn response to the reviewer's suggestion, we have corrected the inaccurate statements and systematically reorganized all the aging data from RT to 180 °C. Accordingly, we have replaced the original Figs. 5 h,i with Figs. R3 a,b. The discussions, reads as: ''Having established the superior initial ferroelectric properties of the LNO-buffered BFMO thin film, we further evaluated the stability under accelerated aging conditions. Aging tests are conducted for both BFMO thin films at multiple temperatures (RT, 60, 120, and 180 °C) for 60 days (60 d) at 10 kHz, as illustrated in Figs. 5 h,i. It reveals that at temperatures exceeding RT, the BFMO thin film on Ni-Cr suffered from severe degradation in ferroelectricity, ultimately leading to sample failure. In contrast, the film on LNO/Ni-Cr demonstrated remarkably superior aging resistance, maintaining functional performance even at 180 °C. Notably, their performance diverges significantly at 60 °C: the film on Ni-Cr suffers a severe ~90% reduction in P and ~80% reduction in E , compared to a more stable state with ~20% reduction in P and ~35% reduction in E for the LNO-buffered film. We attribute this to their microstructure (Fig. 4) with distinct dislocation configurations. The former's high-density, randomly-distributed dislocations create heterogeneous pinning sites that are susceptible to thermal de-pinning. The latter's stability arises from a uniform pinning effect generated by dislocation self-assembly and a discontinuous-columnar grain structure, which suppresses defect migration.'' has been added in the revised manuscript. We thank the reviewer once again for the valuable comment, which has greatly enhanced the accuracy and completeness of our manuscript.\nComment 5: In Figures 5a–f, it is a little difficult to identify which regions (e.g., BFMO/Ni-Cr boundaries) are shown. Revising the figure captions for clarity would make the results easier to follow.\nResponse: We are grateful to the reviewer for this constructive suggestion.\nFollowing the reviewer's suggestion, we have revised the figure captions of Figures 5a–f to make the identified regions clearer and the results easier to follow, reads as: ''Fig. 5 Polarization analysis of BFMO thin films. a,d Spontaneous polarization vectors (derived from B-site cation displacements) overlaid on HAADF-STEM images (Fig. S6) for a a randomly selected small grain on Ni-Cr marked as (a ) in Fig. 4a, and d a discontinuous-columnar grain on LNO/Ni-Cr marked as (c ) in Fig. 4c, where BFMO on LNO/Ni-Cr exhibits uniformity in both polarization vector alignment and angular distribution, confirming enhanced long-range polarization ordering compared to the disordered configuration on Ni-Cr, b,e corresponding atomic brightness contrast maps showing polarization amplitude, c,f corresponding atomic brightness contrast maps showing polarization angle. g P-E hysteresis loops of BFMO on Ni-Cr measured at 10 kHz (@RT). h,i P-E hysteresis loops of BFMO on Ni-Cr and LNO/Ni-Cr measured at 10 kHz before/after aging (@RT, 60, 120, and 180 °C), demonstrating superior aging resistance of the LNO-buffered sample.''.\nReferences\n1. Shelke, V. et al. Reduced coercive field in BiFeO thin films through domain engineering. Adv. Mater. 23, 669–672 (2011).\n2. Barrios, Ó. et al. A sustainable self-induced solution seeding approach for multipurpose BiFeO active layers in flexible electronic devices. Adv. Funct. Mater. 32, 2112944 (2022).\n3. Bencan, A. et al. Domain-wall pinning and defect ordering in BiFeO probed on the atomic and nanoscale. Nat. Commun. 11, 1762 (2020).\n4. Husain, S. et al. Low-temperature grapho-epitaxial La-substituted BiFeO on metallic perovskite. Nat. Commun. 15, 479 (2024).\n5. Wang, J. et al. Epitaxial BiFeO multiferroic thin film heterostructures. Science 299, 1719–1722 (2003).\n6. Bose, S. et al. Improved ferroelectric and leakage properties in symmetric BiFeO /SrTiO superlattice. Appl. Phys. Lett. 90, 212902 (2007).\nReviewer #2:\nGeneral Comments: The authors have grown BFMO thin films on Ni-Cr substrates and have done some detailed analysis of defect engineering that explains the enhancement in ferroelectric properties. There are quite a lot of interesting results and analysis pertaining to the sample is carried out and which would definitely be interesting to the researchers working on defect engineering of multifunctional oxides. However, the density of data and analysis is highly packed in the manuscript, that it can be presented in a better manner.\n………..\nOverall, it's a very interesting study and provides a different perspective and analysis. However I feel the draft is too much packed with data and analysis, the overall presentation for the convenience of the reader can be improved. Most importantly some of the technical questions raised above would enhance the rigor of the manuscript. Hence, I accept this manuscript with major mandatory revision.\nOverall response: We would like to express our gratitude for the valuable and constructive feedback provided by the reviewer, and emphasize that ''There are quite a lot of interesting results and analysis pertaining to the sample is carried out and which would definitely be interesting to the researchers working on defect engineering of multifunctional oxides.'' and ''Overall, it's a very interesting study and provides a different perspective and analysis. I accept this manuscript with major mandatory revision.''. In the following, we carefully address all comments from the reviewer.\nComment 1: The manuscripts never provide a justification on the choice of Mn and the specific atomic percentage (3 at.%) of Mn chosen to substitute in BFO.\nResponse: We thank the reviewer for raising this important point regarding the rationale behind the selection of Mn as the doping element and its concentration (3 at. %). We agree that clarifying this aspect is crucial for understanding our experimental design.\n(1) The reason for the selection of Mn as the doping element\nThe selection of Mn is grounded in its established role as an effective dopant for mitigating the high leakage current in BFO, a necessity for measuring ferroelectric properties. This is based on two key mechanisms supported by literature [Ceram. Int. 41, S234-S239 (2015) and J. Alloy. Compd. 886, 161168 (2021)]1,2.\nI. Charge compensation. Mn ions substitute on Fe-site, and their mixed valence states effectively compensate for the charge from oxygen vacancies, significantly reducing leakage current, an effect robustly demonstrated in prior works [Ceram. Int. 41, S234-S239 (2015)]1.\nII. Structural stabilization. The strong Mn-O bond energy can enhance the stability of the perovskite structure [J. Alloy. Compd. 886, 161168 (2021)]2.\nConsequently, Mn doping was chosen to solve the fundamental problem of high leakage in the sol-gel derived BFO thin films, enabling ferroelectric characterization.\n(2) The reason for determining Mn doping concentration\nFig. R4 (Revised Supplementary Materials Fig. S12) Electrical performance measurements of BFMO thin films with Mn doping contents of 1, 3, and 5 mol. %, respectively. a,b Leakage current density versus applied electric field (I-E) curves of BFMO on rigid Pt/Ti/SiO /Si and flexible LNO/Ni-Cr, respectively, c,d P-E loops of BFMO on rigid Pt/Ti/SiO /Si and flexible LNO/Ni-Cr at 10 kHz, respectively.\nThe 3 mol. % (the same 3 at. %) Mn doping concentration was selected as the optimal compromise for sol-gel derived BiFeO thin films. This concentration effectively suppresses leakage current suppression to enable valid ferroelectric characterization, while minimizing the introduction of additional point defect that could interfere with polarization switching.\nTo identify the optimal doping level, we systematically prepared and compared BFO thin films with Mn concentrations of 1, 3, and 5 mol.%, respectively on both rigid (Pt/Ti/SiO /Si) and flexible (LNO/Ni-Cr) substrates. As shown in Figs. R4 a,b, at 3 mol. % Mn doping, the leakage current is reduced to a level that allows reliable ferroelectric testing, accompanied by significant modulation of coercive field (E ) and remanent polarization (P), resulting in significantly optimized ferroelectric properties (Figs. R4 c,d). This optimal performance at 3 mol. % is attributed to the balanced role of Mn ions. They suppress leakage by compensating for the oxygen vacancies, without introducing excessive additional point defects that would otherwise act as strong pinning centers that impede subsequent domain switching.\nFollowing the reviewer's suggestion, Fig. R4 has been added into the revised Supplementary Materials as Fig. S12 considering the limited space availability. Additionally, we have added discussions, reads as: ''Preliminary experiments have determined that this optimal concentration can effectively suppress leakage current while significantly enhancing ferroelectric properties (Fig. S12).'' into the Part of ''Mn-doped BiFeO (BFMO) Thin Film Preparation'' in the Methods of the revised manuscript.\nComment 2: Most importantly, Mn is expected to increase the point defect densities, which in turn is expected to influence the electrical behavior. No mentioning on the role of Mn induced defects especially, considering the oxidation state changes that comes with Mn substitutions. A detailed analysis on octahedral distortions due to point defects can also be discussed and mentioned in the DFT studies.\nResponse: We thank the reviewer for this insightful comment regarding the role of Mn-induced point defects. We agree that their impact on defect densities, oxidation states, and local structure is indeed important for understanding the electrical behavior.\nIn response, we have revisited our prior DFT calculations, performed using the Vienna Ab initio Simulation Package (VASP) on Mn doped BFO with phase of R3c. These calculations utilized models constructed as a 1×2×3 supercell from the Materials Project database. Mn doping was introduced by substituting atoms at specific lattice sites. The electron exchange-correlation interactions were treated with the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) and the projector augmented-wave (PAW) pseudopotential method. A plane-wave cutoff energy of 500 eV was used, and the self-consistent field calculations were converged until the energy change was below 10-5 eV.\nOur analysis indicates that Mn doping introduces highly localized electronic states within the bandgap. As shown in Fig. R5, the overall band structure along the high-symmetry path Γ–X|Y–Γ–Z|R–Γ–T|U–Γ–V and fundamental bandgap remain largely unchanged upon Mn doping, suggesting that Mn predominantly acts as localized defect center, most consistently with a stable oxidation state (e.g., Mn3+). This strong localization of charge implies that the associated point defects and any charge fluctuations are confined to the immediate atomic environment. Consequently, while Mn doping increases point defect density, the electronic impact is localized, and this localization correspondingly suppresses long-range octahedral distortions in the average crystal structure.\nFig. R5 Band structures along the high-symmetry path Γ-X|Y-Γ-Z|R-Γ-T|U-Γ-V. a BFO, b BFMO.\nWe fully agree with the reviewer's insight regarding the necessity to precisely quantify local octahedral distortions induced by point defects. While the current DFT study successfully establishes the connection between electron localization and macroscopic structural stability, we acknowledge that a detailed quantitative analysis of the local atomic structure requires further investigation. Consequently, we have designated this as a key objective for our forthcoming research, planning to employ extended X-ray absorption fine structure (EXAFS) spectroscopy to directly probe the Mn coordination environment.\nComment 3: The authors have written a statement ''Anisotropic strain field breaks the local symmetry and induce polarization gradients'' In principle yes, it’s a known phenomenon, however, the authors do not mention about the size of the polarization gradient and the strain gradients used in the calculations.\nResponse: We thank the reviewer for highlighting this important aspect regarding the quantification of polarization gradient and strain gradient. We agree that specifying the magnitude of these parameters is essential for a comprehensive understanding of the calculated effects, and we appreciate the opportunity to clarify this point.\nTab. 1 Landau free energy coefficients for BFO at 25 °C3\nCoefficients BFO\nα (C-2·m2·N) -3.73×108\n1\nα (C-4·m6·N) 2.29×108\n11\nα (C-4·m6·N) 3.064×108\n12\nα (C-6·m10·N) 5.99×109\n111\nα (C-6·m10·N) -3.34×108\n112\nα (C-6·m10·N) -1.778×109\nComment 4: Most importantly, does the polarization gradient and strain gradient have the same directional features-not necessarily so. It would be nice if the authors can comment on the following:\na) What is the size of polarization gradient? And the size of strain gradient?\nb) Do they have the same direction or what is the angular relation between them if the gradients are positioned in different directions?\nc) Do they interact with each other?\nResponse: We sincerely thank the reviewer for these insightful and critical questions regarding the directional relationship and interaction between polarization gradient and strain gradient. We have conducted further analysis based on phase-field simulations to address these specific points, as detailed below.\nThe phase-field simulations provide quantitative analysis of the polarization gradient and strain gradient induced by the dislocation cores, as shown in Fig. R6. The results indicate that the local polarization gradient is within the range of 108–109 C·m-3, while the corresponding strain gradient reaches a magnitude on the order of 108 m-1. Regarding the directional relationship, our analysis reveals that the polarization gradient and strain gradient do not exhibit a fixed angular correlation. Their spatial orientations are governed by distinct mechanisms: the strain gradient is primarily determined by the local lattice distortion around dislocations, whereas the polarization gradient follows the symmetry-breaking direction of the spontaneous polarization. Furthermore, within the framework of our model and the observation scale, no direct coupling interaction was found between these two gradient fields. Their evolutions appear to be driven by separate energetic contributions in the current system.\nFig. R6 Phase-field simulations of polarization gradients and strain gradients induced by dislocation cores. a–d Spatial distributions of polarization gradient components: a ∂Pₓ/∂x, b ∂Pₓ/∂y, c ∂Pᵧ/∂x, and d ∂Pᵧ/∂y. The polarization gradient magnitude is on the order of 108–109 C·m-3, reflecting the variation in local polarization due to symmetry breaking around dislocations. e–h Corresponding strain gradient components: e ∂εₓₓ/∂x, f ∂εₓₓ/∂y, g ∂εᵧᵧ/∂x, and h ∂εᵧᵧ/∂y. The strain gradient magnitude reaches 108 m-1, representing the lattice distortion induced by dislocation strain fields.\n∼\nComment 5: The values of n, u used in strain gradients and the values of x used in polarization gradients and how does the free energy changes with varying values of n, u and x should be presented and discussed (in supplementary or in main manuscript) to truly appreciate the spontaneity of defect arrangements and alignments if any in the system.\nResponse: We are grateful to the reviewer for this insightful comment regarding the parameterization of the phase-field simulations. We agree that providing the specific values of key parameters and discussing their influence on the free energy of the system is essential for understanding the energetic driving defect arrangements.\n(1) The values of n, u used in strain gradient and the values of x used in polarization gradient\nTo prevent any potential confusion with the spatial coordinate \"x\" used in the Part of \"Phase-Field Simulations of the Evolution of Polarization Behaviors\" in the revised Supplementary Materials, the parameter originally denoted as \"x\" in the polarization gradient description has been systematically replaced with \"a \" in the revised Supplementary Materials. This adjustment ensures clarity while presenting the complete parametrization. We have included a comprehensive parameter discussion as detailed below and also in the revised Supplementary Materials.\nThe elastic energy density can be expressed as:\nε ε ε ε ε ε\n1 0 d 0 d\nwhere is the elafs e t l i a c s s=tiffnCe i s jk s l (ten ij s−or, ij − re ij p)r(es k e l n−ts t k h l e− tot k a l l) elastic strain, is the eigenstrain expressed as , is the strain caused by dislocation, represents theε lijatt=iceQ pijakrlPakmPelt eεri,j = ∆na irie/puresents a dislocation that produces lattice spacings and defines the size of phase-field area. Here, is aii ∆naii set to 2 and defines as 16 nm in length. The primary variable parameter in our ∆n u ∆n analysis is , which directly modulates the strain distribution within the core region. u The shear deformation caused by dislocations is not considered.\n(2) Changes of free energy as functions of , u and x\n∆n\nFig. R7 Phase-field simulations of energy density evolution under varying Δn values. a Δn=0, b Δn=1, c Δn=3, d Δn=5.\nIn our phase-field simulations, serves as the only variable parameter. Accordingly, we have performed systematic phase-field simulations of the energy ∆n density evolution under varying values ( =0, 1, 3, and 5), which includes the Landau energy (f ), gradient energy (f ), electric energy (f ), and elastic energy (f ) to quantify its influence on the free energy (Fig. R7). The results reveal pronounced variations in these energy components across different values, underscoring the key role of dislocation-induced strain in modulating free energy of ∆n the system. The strong correlation between free energy minimization and the emergence of ordered dislocation configurations provides compelling thermodynamic evidence for spontaneous self-assembly. These results confirm that the observed patterning corresponds to an energetically favored state, establishing strain engineering via parameter control as a pathway to guide defect organization in functional oxides, thereby clarifying the spontaneity of the defect arrangements.\nWhile the phase-field simulations provide the distributions of both the polarization gradient and strain gradient, the direct calculation of the flexoelectric energy density is not feasible in the present study due to the lack of experimentally measured or reliably reported flexoelectric coefficients for this specific material system. In the future, our work will focus on quantitatively determining these coefficients and integrating them into our phase-field simulations, thereby enabling a complete thermodynamic description of electromechanical coupling in ferroelectric systems.\nComment 6: The direction of the electric field applied in phase field with respect to the geometry of the sample needs to be discussed and provided, in the form of a schematic and/or with coordinate axis along with the diagrams (Figure 1).\nResponse: We thank the reviewer for this valuable suggestion. We agree that clarifying the direction of the applied electric field relative to the sample geometry is essential for interpreting the phase-field simulations.\nFig. R8 (Revised Supplementary Materials Fig. S1) a Schematic diagram with coordinate axes and b direction of the applied electric field applied in phase-field simulations.\nAccordingly, we have now added a schematic diagram with coordinate axes and the direction of the applied electric field (Fig. R8). This revision provides a clear geometrical context for the phase-field simulations and ensures the boundary conditions are well defined.\nFollowing the reviewer's suggestion, Fig. R8 has been added into the revised Supplementary Materials marked Fig. S1 considering the limited space available. Additionally, we have revised the corresponding Figure Caption of Figs. 1 a,b in the revised manuscript, reads as: ''Fig. 1 Intrinsic effects of an edge dislocation on ferroelectric polarization in 2D slice of BFMO single crystal viewed along [100] direction. a,b Phase-field simulations of the sample without/with an edge dislocation-domain wall interaction under various applied electric fields, the coordinate system and direction of the applied electric field are defined in Fig. S1, where polarization vortices appear in b''.\nComment 7: Figure 3, d-e it is difficult to understand if the stress distribution is purely simulation or experimentally verified. Most importantly, the system is treated as continuum and the constants C , C ,C and C used to define the final deflections 1 2 3 4 ω(x) seems to be valid numerically, however what connections does these constants make with the material under study is not clear?\nResponse: We sincerely thank the reviewer for this insightful comment and apologize for the lack of clarity in our original manuscript regarding the nature of the stress distribution results. The stress distribution presented in Figs. 3d–e is obtained purely from simulation. We will provide a detailed description of the simulation methodology below to improve transparency.\n(1) Clarification for Figs. 3d–e\nThe stress distributions in Figs. 3d–e were obtained from a continuum analytical model: a thin film with bending stiffness , subject to an in-plane force per unit width , and coupled to a linear foundation of stiffness . The transverse deflection 𝐸𝐼 satisfies the fourth-order linear ODE with constant coefficients, so no empirical 𝑁 𝐾 fitting enters the stress fields themselves.\n𝜔(0)\nStresses then follow fro(m4) standard ′b′eam/plate relations, with the thickness 𝐸𝐼𝜔 (𝑥)−𝑁𝜔 (𝑥)+𝐾𝜔(𝑥) = 0 (1) coordinate.\n𝑧\nExperimental comparisons, ′w′ here provided, are used only to validate the 𝐾(𝑥) = 𝜔 (𝑥),𝜎𝑥𝑥(𝑥,𝑧) = −𝐸𝑧𝐾(𝑥) (2) continuum prediction and are not used to define .\n(2) General solution and material connection\n𝜔(𝑥)\nIntroducing , the characteristic equation is as follows:\n2\n𝑧 = 𝑟\nwith roots 2\n𝐸𝐼𝑧 −𝑁𝑧+𝐾 = 0 (3)\n2\n𝑁±√𝑁 −4𝐸𝐼𝐾\nHence, when 𝑧1,2 = (distinct r , e 𝑟 a1l = √𝑧1,𝑟2 = ), √𝑧2 (4)\n2𝐸𝐼\n2\n𝑁 −4𝐸𝐼𝐾 > 0 𝑟1,𝑟2 > 0\nWhen (co𝑟1m𝑥plex ro−o𝑟t1s𝑥 𝑟2𝑥 ), −𝑟2𝑥\n𝜔(x) = 𝐶1𝑒 +𝐶2𝑒 +𝐶3𝑒 +𝐶4𝑒 (5)\n2\n𝑁 −4𝐸𝐼𝐾 < 0 𝑟 = 𝛼±𝑖𝽁\n𝛼x −𝛼𝑥\nC𝜔ru(c𝑥ia)ll=y, 𝑒the (o𝐶n1lcyo psl(𝽁𝑥 )+𝐶1sin( 𝽁𝑥 )+𝑒 (𝐶3cos( 𝽁𝑥 )+𝐶4sin( 𝽁𝑥 )) (6)\nenter is through , (or , ); therefore the integration constants ,…, are 𝐸,𝐼,𝐾,𝑁\nnot material constants, but coefficients fixed by boundary/support conditions and 𝑟1 𝑟2 𝛼 𝽁 𝐶1 𝐶4\nloading given those materials-dependent wavenumbers.\n(3) How ,…, were determined\nLet the span be . Consider the four-order ODE is as follows:\n𝐶1 𝐶4\n𝑥є[0,𝐿]\nwhose characteristic equ(a4t)ion in ′′ is with roots:\n𝐸𝐼𝜔 (𝑥)−𝑁𝜔 (𝑥)+𝐾𝜔(𝑥) = 0 (7)\n2 2\n𝑧 = 𝑟 𝐸𝐼𝑧 −𝑁𝑧+𝐾 = 0\n2\n𝑁±√𝑁 −4𝐸𝐼𝐾\nwhen 𝑧1,2 = , the general solut i , o 𝑟 n1 = is √ 𝑧1,𝑟2 = √𝑧2 (8)\n2𝐸𝐼\n2\n𝑁 −4𝐸𝐼𝐾 > 0\nThe boundary conditions of𝑟 1t𝑥his work− 𝑟a1r𝑥e: 𝑟2𝑥 −𝑟2𝑥\n𝜔(x) = 𝐶1𝑒 +𝐶2𝑒 +𝐶3𝑒 +𝐶4𝑒 (9)\nat ,\nat ′ .\n𝑥 = 0:𝑤(0) = 0𝜔 (0) = 0;\nApplying these to′′ the exponen′′t′ial form yields four scalar equations:\n𝑥 = 𝐿:−𝐸𝐼𝑤 (𝐿) = 𝑀,𝑤 (𝐿) = 0\n(i) ,\n(ii) ,\n𝑤(0) = 𝐶1 +𝐶2 +𝐶3 +𝐶4 = 0\n′\n(iii) 𝑤 (0) = 𝑟1(𝐶1 −𝐶2)+𝑟2(𝐶3 −𝐶4) = 0 ,\n′′ 2 𝑟1𝐿 −𝑟1𝐿 2 𝑟2𝐿 −𝑟2𝐿 𝑀\n(iv) 𝑤 (𝐿) = 𝑟1(𝐶1𝑒 +𝐶2𝑒 )+𝑟2(𝐶3𝑒 +𝐶4𝑒 ) = 𝐸𝐼.\nFrom (′i′)′ and (ii),3 one c𝑟a1n𝐿 express− 𝑟1𝐿 and3 in𝑟2 t𝐿erms of− 𝑟2𝐿 and :\n𝑤 (𝐿) = 𝑟1(𝐶1𝑒 −𝐶2𝑒 )+𝑟2(𝐶3𝑒 −𝐶4𝑒 ) = 0\n𝐶2 𝐶4 𝐶1 𝐶3\n(𝑟1+𝑟2)𝐶1+2𝑟2𝐶3 −2𝑟1𝐶1 −(𝑟1 +𝑟2)𝐶3\nSubstitutin𝐶g2 th=ese into (iii)-(iv) gives ,t𝐶w4o= equations involving only and : (10)\n𝑟1−𝑟2 𝑟1 −𝑟2\n𝐶1 𝐶3\n2 𝑟1𝐿 −𝑟1𝐿 2 𝑟2𝐿 −𝑟2𝐿 𝑀\n𝑟1(𝐶1𝑒 +𝐶2𝑒 )+𝑟2(𝐶3𝑒 +𝐶4𝑒 ) = − (11)\n𝐸𝐼\nwhich determ3ine 𝑟1𝐿 and −𝑟1𝐿 algeb3raicall𝑟y2𝐿 in ter−m𝑟2s𝐿 of ( ).\n𝑟1(𝐶1𝑒 −𝐶2𝑒 )+𝑟2(𝐶3𝑒 −𝐶4𝑒 ) = 0 (12)\nBlack-substitution then gives and . In this way, the coefficients are not\n𝐶1 𝐶3 𝐸,𝐼,𝐾,𝑁,𝐿,𝑀\nmaterial constants, but rather, they are fixed by the boundary conditions and the\n𝐶2 𝐶4 𝐶𝑖\nmaterial/structural parameters through and .\nwhen and ,\n𝑟1 𝑟2\n2\n𝑁 −4𝐸𝐼𝐾 < 0 𝑟 = 𝛼 ±𝑖𝽁\n𝛼𝑥 −𝛼𝑥\nT𝑤he(n𝑥,) a=pp𝑒ly th(e𝐶 1cos( 𝽁𝑥 )+𝐶1sin( 𝽁𝑥 ))+𝑒 (𝐶3cos( 𝽁𝑥 )+𝐶4sin( 𝽁𝑥 )) (13)\n,…, (the algebra is analogous, with cos and sin replacing exponentials).\nFollowing the reviewer's suggestion, we have also updated the Part of \"Modeling 𝐶1 𝐶4\nBFMO as Euler-Bernoulli Beam on a Winkler Foundation (Ni-Cr or LNO/Ni-Cr)\" in the revised Supplementary Materials to further clarify the whole process.\nComment 8: The authors claim heteroepitaxial growth and which is a term used for thin films with a particular crystallographic growth direction and also possess a crystallographic relation with the substrates. Hence usage of heteroepitaxial growth term should be changed to growth of heterostructures. It provides wrong information about the sample.\nResponse: We sincerely appreciate the reviewer's insightful comment regarding the terminology used. We agree that \"heteroepitaxial growth\" may imply a specific, well-defined crystallographic relationship which was not sufficiently demonstrated in our original manuscript.\nFollowing the reviewer's suggestion, we have replaced \"heteroepitaxial growth\" by \"growth of heterostructure\" to more accurately describe the nature of the deposited thin films. This revision helps avoid potential misunderstanding and ensures precise communication of the structural characteristics of our samples.\nComment 9: How reproduceable or controllable is the self-assembly across different film thickness/lattice mismatches? Can thickness of LNO affect this self-assembly of dislocations?\nResponse: We thank the reviewer for raising this important question regarding the reproducibility and controllability of the self-assembly process. We address the points below.\n(1) How reproduceable or controllable is the self-assembly across different film thickness?\nRegarding the effect of BFMO thin film thickness, while a systematic variation was not the focus of this study, we can provide a reasonable argument based on the specificities of our sol-gel process.\nWe first wish to clarify that the microstructure observed in our films (e.g., in Fig. 4c) is not the classic, fully-vertically-aligned columnar grain, but rather what we term a \"discontinuous-columnar\" structure. Crucially, the formation of this distinct morphology is equally dependent on the repeated crystallization cycles inherent to our sequential deposition, including spin-coating and layer-by-layer annealing process. Each pre-deposited layer undergoes additional thermal cycles and grain growth as subsequent layers is annealed, which is essential for developing any form of vertically-oriented grain alignment, including our observed discontinuous-columnar grains [J. Appl. Phys. 101 132908 (2007)]3.\nWe posit that this discontinuous-columnar structure, analogous to its classic counterpart, provides the necessary geometric confinement and pathways for the dislocation self-assembly along the grain boundaries. Consequently, the total BFMO thin film thickness plays a key role. An insufficient thickness (i.e., too few deposited layers) would prevent the thin film experiencing the requisite number of thermal cycles to drive the evolution of this templating microstructure. Without this specific structure, the dislocation self-assembly would not occur.\nTherefore, within our processing paradigm, there exists a critical thickness for the phenomenon to manifest. The fact that we consistently observe the dislocation networks in samples of our reported thickness confirms that this threshold has been met and that the essential discontinuous-columnar template has formed. This demonstrates that the process is controllable and reproducible through the precise control of the final thickness (i.e., the number of layers). A detailed quantitative investigation into the relationship between thickness and the evolution of this specific microstructure represents a compelling direction for our future work.\n(2) How reproduceable or controllable is the self-assembly as a function of lattice mismatch?\nThe dislocation self-assembly process demonstrated in our work is highly reproducible and controllable, achieved through strain engineering by designing the interfacial mismatch.\nA significant inherent lattice and thermal expansion coefficient mismatch exists between the face-centered cubic (FCC) Ni-Cr substrate and the rhombohedral (R3c) BFMO thin film. Our strategy actively leverages this substantial mismatch to introduce a high density of dislocations and strain fields into the BFO thin film. The introduction of LNO layer enables fundamental control over dislocation density and distribution. The strain energy anisotropy effect of LNO plays a pivotal role in guiding the formation of discontinuous-columnar grains in BFMO, thereby facilitating the self-assembly of topologically protected dislocations along grain boundaries. Our results clearly demonstrate that in the BFMO thin film on Ni-Cr, dislocations exhibit high density and randomly-distributed distribution. In contrast, in the BFMO thin film on LNO/Ni-Cr, the dislocation self-assembly along grain boundaries results in an ordered \"dislocation-grain boundary\" interaction, effectively suppressing random dislocation distributions.\nTo confirm the reproducibility of this phenomenon, we independently reproduced BFMO thin films on LNO/Ni-Cr. To observe the dislocation self-assembly, it is essential to locate discontinuous-columnar grain boundaries in TEM and perform IFFT analysis. Following this approach, we randomly selected an additional region and again observed dislocation self-assembly along the grain boundaries (Fig. R9), providing direct evidence that the process is highly reproducible under our processing conditions.\nFig. R9 (Revised Supplementary Materials Fig. S8 a (a )–(a )) Microstructural characterization near discontinuous-columnar grain boundary in the BFMO thin film on LNO/Ni-Cr. a HRTEM image with white-dashed square demarcating the region near grain boundary, b enlarged area corresponding to the area with white-dashed square in a, where red line indicating the position of grain boundary. c IFFT image of the enlarged regions in b.\nWe fully agree with reviewer on the importance of systematically investigating the effects of varying lattice mismatch. This insight provides clear direction for our future work. We plan to precisely tune and broaden the range of lattice mismatch by systematically substituting substrates (e.g., Si, Mica, SrTiO , et al.) or incorporating buffer layers with different lattice constants (e.g., (La,Sr)MnO , LaAlO , et al.), thereby quantitatively elucidating the influence of lattice mismatch on the morphology, density, and spatial ordering of dislocation self-assembly in BFMO thin films.\n(3) The effects of LNO thickness on dislocation self-assembly\nThe role of LNO layer in templating columnar grain growth in BFO-based thin films is well-established, with studies indicating that a critical thickness is required to form a continuous and structurally coherent interface necessary for inducing such microstructure [Coatings 10, 438 (2020)]4 described as \"discontinuous-columnar\", characterized by segmented vertical alignment rather than fully continuous pathways, its development shares the fundamental templating dependence on the underlying layer. This confirms that a critical LNO thickness remains essential for inducing this specific, guided microstructure.\nBeyond its role in microstructural templating, the thickness of the LNO layer directly modulates the magnitude and distribution of strain transferred to the BFMO thin film. This strain gradient serves as the primary driving force for dislocation motion and their subsequent self-assembly along grain boundaries, where strain energy is minimized.\nThus, LNO thickness exerts a dual influence, governing both the formation of the discontinuous-columnar grain structure and the strain-driven assembly process. This synergy ultimately determines the reproducibility and controllability of the dislocation network, establishing LNO thickness as a critical parameter for controlling the dislocation self-assembly phenomenon. In future studies, we plan to systematically determine the critical thickness of LNO required for effective templating and strain-mediated dislocation self-assembly. This will be achieved by fabricating a series of heterostructures with precisely controlled LNO thicknesses, followed by comprehensive structural characterization (e.g., XRD, TEM) to correlate the LNO thickness with the evolution of grain morphology and the degree of dislocation ordering. Such an approach will allow us to establish a quantitative thickness-microstructure relationship and further optimize the controllability of the dislocation self-assembly process.\nComment 10: The growth of the samples provides an insight into the cross sectional TEM images. The sequential deposition of layers followed by annealing at every step has clearly introduced multiple interfaces across the sample as evidently seen from the cross sectional TEM studies. What is the role of the strain at these interfaces? Do they possess a key role on determining the distribution of dislocations? Can the study be carried out for a single total thickness without any sequential deposition and annealing? Would the results be similar?\nResponse: We thank the reviewer for the insightful questions regarding the role of interfacial strain and the design of our sample growth process. Below we provide a point-by-point response.\n(1) Overall comments on the sequential deposition process and the role of interfaces\nResponse: We fully agree with the reviewer's comment that \"The growth of the samples provides an insight into the cross-sectional TEM images. The sequential deposition of layers followed by annealing at every step has clearly introduced multiple interfaces across the sample as evidently seen from the cross-sectional TEM studies.\" The advantage of the sequential deposition lies in the fact that each annealing step aims to optimize the crystal quality of the current layer, turning it into a high-quality \"seeding layer\" or \"template\" upon which subsequent layers can achieve better growth. The multiple interfaces visible in the TEM images are the physical manifestation of this whole process. These interfaces primarily serve as evidence of high-quality crystallization and, secondly, as markers for analyzing the evolution of growth.\n(2) The role of strain at these interfaces\nResponse: From the perspective of \"providing a high-quality seeding layer,\" the management of interfacial strain is crucial, which will be analyzed from the two following aspects.\nI. Strain relaxation and lattice reorganization. Annealing immediately after the growth of each layer allows the material to undergo primary strain relaxation and the reorganization of defects (such as dislocations) in an independent stage. This means each layer is optimized after its specific deposition, rather than leaving all strain and defect issues to be addressed by a final single annealing process.\nII. Creating a superior starting point for upper layer growth. The annealed surface of the underlying layer has a lattice constant closer to its equilibrium state and a smoother surface morphology. This provides a starting point with a more stable strain state and higher crystal quality for the growth of the upper layer, significantly reducing the probability of introducing new defects into it. Consequently, the role of strain at the interfaces is transformed from a potentially detrimental factor into a beneficial one that is managed in a staged and effective manner.\n(3) The role of interface strain on dislocation distribution\nResponse: Yes, the strain at these interfaces possesses a key role in determining the distribution of dislocations. In traditional single-step growth, strain accumulates coherently throughout the thin film, allowing dislocations to generate and propagate across the entire thickness, ultimately forming a high density in the top layer. In the sequential deposition, the key is that the strain at the interfaces is deliberately relaxed at each stage through intermediate annealing. This controlled, layer-by-layer strain relaxation resets the strain field before the next layer grows, effectively blocking the propagation of dislocations across interfaces. Consequently, the distribution of dislocations is fundamentally altered such that each new layer starts from a state with low strain and few defects. This initiates a progressive improvement in crystal quality towards the surface and yields a significantly reduced dislocation density in the final top layer. The multiple interfaces therefore constitute the physical foundation for this stratified management of strain and defects.\n(4) Comparisons on single-step growth and sequential deposition\nResponse: This question \"Can the study be carried out for a single total thickness without any sequential deposition and annealing? Would the results be similar?\" raised by the reviewer is very important. And the question regarding the necessity of sequential deposition and annealing touches upon the core innovation of our work.\nLiterature confirms fundamental mechanistic differences between single-step growth and sequential deposition that lead to markedly divergent outcomes [Chem. Soc. Rev. 47 291–308 (2018)]5. The key distinction lies in strain management strategy, where single-step growth leads to continuous strain accumulation that relaxes primarily through high-density dislocation formation, creating deep-level defects that remain even after final annealing. In contrast, the sequential deposition enables stepwise strain relaxation after each deposition stage, achieving progressive crystal optimization. This controlled, intermittent relaxation is essential for forming the unique discontinuous-columnar grain structure with dislocation self-assembly along boundaries, which is a distinctive microstructure unattainable through single-step growth. It is this tailored microstructure that enables controlled dislocation self-assembly for ferroelectric polarization modulation, thereby realizing the novel functionality reported in our work. Therefore, sequential deposition represents not merely a fabrication choice, but rather the core technical pathway for achieving \"strain engineering\" and creating a \"superlattice-like\" architecture with periodic strain networks, which is fundamentally unattainable through single-step growth.\nComment 11: The authors have not provided evidences of compositional homogeneity cross the thicknesses and what if the highlighted defect regions are compositionally inhomogeneous? The authors can comment on this.\nResponse: We thank the reviewer for raising this important point. To directly address the concern of compositional homogeneity, we have performed additional EDS elemental mapping across the interface and the defect regions. As shown in Fig. R9, the distribution of all elements (Bi, Fe, Mn, O) is highly uniform. No evidence of compositional segregation or precipitation at the dislocation cores or interface was observed. This confirms that the contrast features in the TEM images are indeed due to crystal defects (dislocations and strain fields) rather than compositional variations.\nFig. R10 (Revised Supplementary Materials Fig. S5) TEM cross-sectional elemental analysis of BFMO thin film on LNO/Ni-Cr. a HAADF image, b–e corresponding EDS elemental maps for Bi, Fe, O, and Mn, f atomic fraction profile of each element along the yellow arrow indicated in a.\nFollowing the reviewer's suggestion, Fig. R10 has been added into the revised Supplementary Materials marked Fig. S5 considering the limited space available. Additionally, we have revised the following relevant description in the revised manuscript, reads as: ''Both thin films demonstrate excellent compositional homogeneity (Fig. S5) across their thicknesses as well as coherent growth, with respective thicknesses of ~650 nm for BFMO and ~100 nm for LNO.''.\nReferences\n1. Ren, Y. et al. Comparative study of Mn3+ and Mn2+ doping effects on structure and electrical properties of BiFeO thin films. Ceram. Int. 41, S234–S239 (2015).\n2. Liang, X. et al. Prominent ferroelectric properties in Mn-doped BiFeO spin-coated thin films. J. Alloy. Compd. 886, 161168 (2021).\n3. Wu, J. et al. Improved ferroelectric behavior in (110) oriented BiFeO thin films. J. Appl. Phys. 101 132908 (2007).\n4. Abramov, A. et al. Chemical solution deposition of BiFeO films with layer-by-layer control of the coverage and composition. Coatings 10, 438 (2020).\n5. Bretos, I. et al. Low-temperature crystallization of solution-derived metal oxide thin films assisted by chemical process. Chem. Soc. Rev. 47 291–308 (2018).\nReviewer #3:\nGeneral comments: This manuscript tries to deliver a new concept on self-assembly dislocation and strain field control to tune properties of BFMO films. Although the authors carried out comprehensive studies on the dislocation effects on strains and ferroelectric properties, I do not think this manuscript provides sufficient novelty that readers of Nature Communications expect. In addition, some of the statements are rather speculative. The detailed comments are as follows.\nOverall response: We sincerely thank the reviewer for the time and valuable feedback. We have carefully considered the comment regarding novelty and have significantly revised the manuscript to better articulate our core conceptual advance: the active and deterministic use of dislocation self-assembly as a primary tool for strain engineering, rather than treating them as passive defects. This paradigm shift from defect mitigation to defect utilization for property control is, we believe, a novel concept for the readership of Nature Communications. Additionally, we have rigorously revised the text to eliminate speculative claims, strengthening our arguments with additional data and clarified discussion, as detailed in our point-by-point response. We believe these comprehensive changes have fully addressed the reviewer's concerns and hope that the revised manuscript is now acceptable for publication.\nComment 1: I am convinced that the manuscript presents the consistency that the BFMO/LNO/Ni-Cr film is less dislocation density than the BFMO/Ni-Cr film and demonstrates the consequent stress uniformity and improvement of ferroelectric properties. However, I do not see how the authors engineered and leveraged the dislocations to control the strain field and improve the properties besides reducing the dislocations. Although the authors bring up \"reduced dislocation self-assembly mediated strain engineering\", the conclusion appears to be that a film with lower dislocation density (Fig. 4g and h) is better (Fig. 2c, Fig. 5g, h, and i), which is not a new concept. People have already developed high quality BFO films with lower coercive field and higher polarization (which is not easy to compare due to the orientation difference) even with chemical solution method [10.1002/smll.201903663].\nResponse: We sincerely thank the reviewer for this insightful comment. The reviewer correctly pointed out that demonstrating lower dislocation density and improved ferroelectric properties alone would not be considered as a novel contribution. We fully agree with this perspective and appreciate the opportunity to clarify the core innovation of our work.\nOur research aims to move beyond the traditional paradigm of \"defect elimination\" and explore a new strategy of proactive \"strain engineering\". The novelty of our work lies not in the result of reduced dislocation density, but in the unique design concept and the process of actively controlling and utilizing dislocation configurations. We will elaborate as below.\n(1) Research design of this work\nOur approach was fundamentally different from the conventional path of seeking \"perfect crystals\" on lattice-matched STO substrates [Science 299, 1719–1722 (2003) and Appl. Phys. Lett. 90, 212902 (2007)]1,2. As the reviewer commented, people have already developed high quality BFO thin films with low coercive field and high polarization even with chemical solution method [Small 17, 1903663 (2021)]3. We also thank the reviewer for bringing this highly relevant work to our attention and have accordingly included this reference in the revised manuscript to strengthen the background of our study.\nOur design was intentional and proactive:\nI. Intentional selection of a mismatched substrate. We deliberately chose Ni-Cr substrate with significant lattice and thermal expansion mismatch with BFMO. This strategy was to actively and controllably introduce an initial state with high density of dislocations and strong local strain fields. This initial \"high-defect\" state was the designed starting point for our subsequent control, not merely a sign of \"poor thin film quality\" in the traditional sense.\nII. Clear application orientation. The metallic nature of Ni-Cr offers built-in electrode potential for future interfacial charge studies, and its flexibility targets applications in flexible electronics. This underscores that the selection of the material was an active design based on functional goals.\n(2) Core innovation of this work\nThe key innovation lies in the precise control mechanism enabled by the LNO buffer layer:\nI. Active microstructural templating. The critical role of LNO was not only to reduce the lattice mismatch (from ~3.8% to ~1.0%) but more importantly, the strain energy anisotropy it introduced actively guided the microstructural evolution of the BFMO thin film. It promoted the formation of discontinuous-columnar grains. This specific grain morphology created unique spatial constraints for the dislocation self-assembly that will be discussed later.\nII. Achieving dislocation self-assembly. Under these controlled microstructural conditions, dislocations were not randomly eliminated but were guided to grain boundaries, forming an ordered, topologically protected self-assembly. This means we controlled not only the quantity of dislocations but also their spatial distribution and configuration. This is the specific physical meaning of self-assembly in our work and the essential difference from the simple concept of density reduction.\n(3) Innovative physical mechanism of this work\nWe not only controlled the dislocation arrangement but also revealed how to use this engineered dislocation structure to actively influence material properties. It is found that this controlled dislocation self-assembly interacting with grain boundaries creates a novel mechanism for strain field mediation. The dislocation self-assembly and grain boundaries work together to dissipate and redistribute the initially concentrated internal strain through periodic fluctuations and coordinated tilting of FeO octahedral.\nAccording to this feedback, we have revised the Introduction to better articulate the novelty of our work. The following paragraph has been added: ''Here, we have developed an innovative strategy—\"designed dislocation self-assembly mediated strain engineering\"—to overcome the limitations of conventional defect-control approaches in Bi(Fe,Mn)O (BFMO) thin films. Unlike previous studies that employed SrTiO (STO) substrates to minimize dislocations25–27, we deliberately employ a face-centered cubic (FCC) Ni-Cr substrate to create a lattice and thermal expansion mismatch with the rhombohedral (R3c) BFMO thin film. This mismatch is not a defect but a designed feature, enabling strain engineering and generating a controlled density of dislocations. These dislocations provide a unique way of probing dislocation-polarization interactions and strain-mediated ferroelectric behaviors. Furthermore, the metallic nature of Ni-Cr substrate offers inherent potential as a built-in electrode for future studies on interfacial charge behavior, while its mechanical properties also make it a promising candidate for explorations into flexible ferroelectric electronics.''. We believe this addition effectively addresses the reviewer's concern by clearly highlighting the novel approach and significant contribution of our work. Once again, we sincerely thank the reviewer for helping improve the quality and clarity of our paper.\nComment 2: Also, the dislocation self-assembly at grain boundaries is not fully convincing based just on Fig. h and f. To prove the self-assembly, the authors need more data for statistical analysis for any scientific publication.\nResponse: Thanks for this insightful comment. We fully acknowledge that statistical analysis would strengthen the reliability of our conclusions and therefore highly value the reviewer's suggestion regarding the statistical verification of dislocation self-assembly.\nWe would like to clarify that obtaining high-resolution images suitable for quantitative dislocation analysis is experimentally challenging due to the following constraints:\nI. Acquiring HRTEM images for quantitative dislocation analysis requires tilting the grain boundary to a specific zone-axis orientation, which was often unattainable due to the limited tilt range and fixed geometry of the FIB-prepared samples.\nII. Locating grains with specific orientation relationships in the FIB-prepared discontinuous-columnar grain structure is inherently difficult.\nIII. The small grain size in the BFMO thin films makes it impractical to pre-locate specific orientations via EBSD analysis prior to FIB sample preparation.\nDue to these limitations, a systematic statistical analysis is not presently feasible.\nDespite this constraint, we systematically screened dozens of grain boundaries. The images presented in Figs. 4f, i of the original manuscript and the newly provided Fig. R11 (Revised Supplementary Materials Fig. S8 b) represent the highest-quality examples we were able to obtain. We present this additional data to provide further evidence for the dislocation self-assembly at grain boundaries.\nFig. R11 (Revised Supplementary Materials Fig. S8 b (b )–(b )) Microstructural characterization near discontinuous-columnar grain boundary in the BFMO thin film on LNO/Ni-Cr. a HRTEM image with white-dashed square demarcating the region near grain boundary, b enlarged area corresponding to the area with white-dashed square in a, where red line indicating the position of grain boundary. c IFFT image of the enlarged regions in b.\nWe noted that some studies combine high-resolution images with lower-magnification dark-field images to demonstrate the macroscopic extent of dislocations, thereby confirming their structural features. However, the fine-grained nature of our thin films makes it challenging to apply this technique directly, as it is most effective for delineating features across distinct, large grains. Despite this experimental constraint, we are confident that the representative micrographs in Fig. R11 and Fig. 4 in the original manuscript provide clear and consistent evidence for dislocation self-assembly at grain boundaries, which underpins our proposed polarization regulation mechanism. We acknowledge that a full statistical analysis is an important goal, and we are committed to optimizing our methodology in future work to achieve this quantitative validation.\nFollowing the reviewer's suggestion, Fig. R11 has been added into the Supplementary Materials as Fig. S8 b considering the limited space available. Additionally, we have revised the following relevant description in the revised manuscript, reads as: ''Under the modulation of an anisotropic stress distribution, evidenced by the fourfold symmetric feature in Fig. 3e, these boundary-segregated dislocations self-assembled externally to the discontinuous-columnar grains. This phenomenon was consistently observed, with further representative examples provided in Fig. S8.''.\nComment 3: I am not fully convinced with the lattice matching mechanism for the dislocation reduction for those specific polycrystalline films. Firstly, I do not see the “discontinuous columnar grains” from Fig. 4b and c. To me they look more like granular microstructure. In case of granular grains, the lattice mismatch discussion that the author mentioned is invalid since the grains at the BFMO/LNO interface are only influenced. Next, even if they are columnar growth, the effects on the dislocation density at grains inside the film are questionable. The lattice mismatch induces misfit dislocations at the interface but does not necessarily produce them in the bulk.\nResponse: We thank the reviewer for raising these critical points regarding the microstructural interpretation and the proposed lattice mismatch mechanism. We appreciate the opportunity to clarify these aspects with additional evidence and mechanistic explanation.\n(1) Clarification on the \"discontinuous-columnar\" grain structure\nFig. R12 (Revised Supplementary Materials Fig. S7) Bright-field TEM images of BFMO on LNO/Ni-Cr at progressively higher magnifications.\nWe fully acknowledge the reviewer's observation that the grain morphology in Figs. 4b,c may appear to be granular within the limited field of view. To clearly demonstrate the \"discontinuous-columnar\" nature of the grains, we have performed additional dark-field TEM characterization.\nWe present a series of dark-field TEM images taken from the same sample region at progressively higher magnifications (Fig. R12). It provides a low-magnification overview, revealing the long-range vertical alignment of grains. Figs. R12 b,c show successive zoom-ins of the area marked in the previous image. These images clearly demonstrate that, although the grains do not form continuous columnar throughout the entire film thickness, they exhibit pronounced vertical alignment and elongation along a certain direction. This specific feature characterized by vertically correlated grains rather than fully isolated grains is precisely what we define as \"discontinuous-columnar\", representing a highly anisotropic, vertically interconnected microstructure distinct from classical continuous columnar grains.\n(2) Validity of the lattice mismatch\nWe understand the reviewer's concern that in conventional one-step epitaxial growth, misfit dislocations would be confined to the initial interface. However, the BFMO thin films in our work were fabricated via a sol-gel method combined with annealing layer-by-layer. This sequential deposition leads to a fundamentally different microstructural evolution mechanism. During the crystallization of each layer, new dislocations are generated at the \"fresh interface\" with the underlying crystallized layer due to lattice and thermal mismatch. As subsequent layer is annealed, the underlying layers undergo repeated annealing process. This repeated annealing process provides necessary energy and driving force for pre-existing dislocations to glide, reorganize, and propagate upward along the evolving discontinuous-columnar grain boundaries. Consequently, the observed dislocations result from the continuous generation, motion, and reorganization throughout the entire film growth process, not merely from initial misfit dislocations at the bottom interface. Furthermore, the lattice mismatch effect is transmitted continuously by a dynamically ascending \"interface\", which we called as the crystallization front between successive layers. This mechanism clearly explains the through-thickness distribution of dislocation beyond the substrate interface.\nFollowing the reviewer's feedback, Fig. R12 has been added into the revised Supplementary Materials as Fig. S7. It consists of dark-field TEM images of BFMO on LNO/Ni-Cr taken from the same sample region at progressively higher magnifications to provide more evidence for the discontinuous-columnar grains. Additionally, we have revised the following relevant description in the revised manuscript, reads as: ''BF-TEM and DF-TEM of BFMO thin film on LNO/Ni-Cr reveal discontinuous-columnar grains (Figs. 4b,c, S6), with an additional example provided in Fig. S7, demonstrating epitaxial registry between BFMO and LNO, which is consistent with previous reports39–41.''.\nAnd the content ''Each layer underwent rapid thermal processing (RTP) immediately after deposition. The RTP steps for each layer were as follows: (i) preheating at 200 °C for 60 s, (ii) pyrolysis at 350 °C for 600 s, and (iii) annealing at 525 °C for 480 s. During the annealing of each new layer, the underlying crystallized layers experience a repeated thermal cycle. The lattice and thermal mismatch at the growing film's interface provides necessary driving force for structural defects like dislocations to reorganize and propagate across the film thickness. Both the deposition and annealing cycle were repeated 10 times to build the film to its final thickness.'' has been added into the Part of ''Mn-doped BiFeO (BFMO) Thin Film Preparation'' in the Methods of the revised manuscript.\nComment 4: I am concerned with the dislocation effects on the aging and degradation effects (by the way, that experimentation is not for retention study). The films have neither same interface nor crystallinity, which may also affect the degradation after aging. The authors reason the dislocation contribution based on the E drop after aging, but it is invalid evidence because the P-E loops after aging (especially for 60 °C) do not show proper ferroelectricity anymore. The statement \"This distinct aging behavior directly correlates with dislocation configurations\" is speculative.\nResponse: We sincerely thank the reviewer for these insightful comments, which have helped us clarify key aspects of our work. We fully agree with the reviewer's points and have addressed them as follows.\n(1) Correction of technical terminology\nWe acknowledge that the word \"retention\" was inaccurate in describing our aging experiments. Following the reviewer's suggestion, we have revised the terminology throughout the manuscript to \"aging\" test to more accurately reflect the nature of the experiments.\n(2) Clarification on the link between dislocation configuration and aging behavior\nWe appreciate the reviewer's emphasis on the potential influences of interface and crystallinity. We agree that long-term stability is a multi-factorial phenomenon. Our goal, however, was not to dismiss other factors, but to specifically isolate and test the role of dislocations, which was predicted by our initial phase-field simulations to be a dominant factor during aging. The theoretical and experimental workflow is shown below.\nI. Theoretical prediction. Our phase-field simulations conducted prior to experimentation revealed that edge dislocations generate localized strain fields that strongly couple with polarization, enabling the formation of stabilized polarization vortices without external electric fields. This contrasts with defect-free systems where vortex nucleation requires energy-intensive polarization switching.\nII. Active material design. Based on this theoretical insight, we intentionally selected Ni-Cr substrate and LNO/Ni-Cr systems. We strategically leveraged the lattice mismatch and LNO-induced strain anisotropy to guide the formation of discontinuous-columnar grains in the BFMO thin films, which are accompanied by topologically protected dislocation self-assembly along grain boundaries. This engineered microstructure directly resulted in enhanced stabilization of ferroelectric polarization.\nIII. Experimental validation. The experimentally fabricated BFMO on LNO/Ni-Cr successfully realized the discontinuous-columnar grain structure with accompanying dislocation self-assembly along grain boundaries. Microstructural characterization confirmed that this specific feature effectively homogenized the spatial distribution of ferroelectric polarization, which consequently yielded remarkable aging resistance. In contrast, the BFMO on Ni-Cr, which developed microstructure with randomly-distributed dislocations, exhibited significantly faster degradation and less stable polarization behavior after aging. These results validate our phase-field simulations regarding strain-polarization coupling in the BFMO with dislocation self-assembly and demonstrate that guided microstructural design effectively achieves polarization homogeneity while simultaneously improving resistance to aging behavior.\n(3) Clarification on the dislocation-domain interaction mechanism in aging behavior\nWe thank the reviewer for raising this important point. We acknowledge that our original statement, \"This distinct aging behavior directly correlates with dislocation configurations,\" may have been imprecise in capturing the underlying physical mechanism, potentially giving the impression of being speculative. We have therefore rephrased the conclusion as: \"The distinct aging behavior is closely associated with the direct influence of different dislocation configurations on ferroelectric domain-switching dynamics.\".\nThis revision clarifies that dislocation configurations do not merely correlate with aging behavior, but rather lead to the observed performance differences through a specific physical process. The interaction between dislocation configurations and domain walls differs fundamentally. For the BFMO thin film on LNO/Ni-Cr, reduced dislocation self-assembly generate a relatively homogeneous strain field, leading to more uniform domain switching and a lower energy barrier for polarization reversal (manifested as a lower E ). In contrast, randomly-distributed dislocations with higher density in the BFMO thin film on Ni-Cr create highly localized, strong pinning sites, resulting in a higher and more broadly distributed energy barrier for domain switching (reflected by a higher E ). During the aging process, these intense and random pinning sites in the control sample cause irreversible charge carrier trapping and accelerated localized degradation, ultimately suppressing the ferroelectric polarization entirely. This reduced-dislocation self-assembly works to uniformly distribute strain and effectively delay the degradation process. Thus, the difference in E directly reflects the dislocation-domain wall interaction, and the superior aging resistance arises as a direct consequence of this tailored microstructure. Our conclusion is grounded in a clear structure-property relationship and reflects the fundamental physics of defect-domain interactions.\nReferences\n1. Wang, J. et al. Epitaxial BiFeO multiferroic thin film heterostructures. Science 299, 1719–1722 (2003).\n2. Bose, S. et al. Improved ferroelectric and leakage properties in symmetric BiFeO /SrTiO superlattice. Appl. Phys. Lett. 90, 212902 (2007).\n3. Yang, B. et al. Chemical solution route for high-quality multiferroic BiFeO thin films. Small 17, 1903663 (2021).\nBased on the reviewers' feedback, we have incorporated the above discussions in the revised manuscript. If there are any inappropriate points, please contact us.\nThanks again for your help!\nWith best regards,\nSincerely yours,\nHuiting Sui & Huajun Sun & Xiaoguang Ma & Shujun Zhang"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have responded well to my comments and have revised their manuscript appropriately. I believe the revised manuscript is suitable for publication.", "reviewer_2": "On reading the response to both the reviewers, I believe that the authors have addressed all the queries raised satisfactorily and hence the manuscript can be accepted for publication."}, "author_response": "Overall Response to the Editor and Reviewers\nWe would like to express our sincere appreciation to the reviewers for dedicating the time and efforts to evaluating our work and for providing valuable feedback. We have thoroughly addressed all the comments raised and made adequate revisions accordingly. In the following section, we provide point-by-point responses to each comment, detailing the changes made in response to the suggestions/comments from the reviewers. Additionally, all modifications in the revised manuscript are highlighted in red for easy reference.\nReviewer #1:\nGeneral Comment: The authors have responded well to my comments and have revised their manuscript appropriately. I believe the revised manuscript is suitable for publication.\nOverall response: We sincerely thank the reviewer for the positive feedback and for acknowledging our efforts in revising the manuscript. We are delighted to know that the reviewer found the revised manuscript suitable for publication. The insightful comments throughout the review process have been invaluable in helping us significantly improve the quality and clarity of our work.\nReviewer #2:\nGeneral Comment: On reading the response to both the reviewers, I believe that the authors have addressed all the queries raised satisfactorily and hence the manuscript can be accepted for publication.\nOverall response: We are very grateful to the reviewer for their time and for this positive assessment. We sincerely thank them for their valuable input during the review process, which has greatly strengthened our manuscript. We are pleased that the reviewer found all queries had been addressed satisfactorily and are honored by their recommendation for acceptance.\nReviewer #3:\nGeneral Comment: I appreciate the authors delivering clear explanations to the comments, although the response to the novelty concern is insufficient. I suggest either (1) adding more results showing evidence that the strain engineering associated with the grain boundary segregated dislocations indeed tunes the properties to verify the main concept \"designed dislocation self-assembly mediated strain engineering\", or (2) reframing the concept reflecting the existing results. The details are as follows.\nI understood the concept of strain engineering via dislocation arrangement, and the added paragraph in Introduction and responses clarify it well. However, I still think the presented results do not fully evidence the concept. Let me summarize the points presented in the results here first.\n1. Figure 2c shows that low randomly distributed dislocations decrease Pr and increase Ec. (Figures 1 and 2 do not consider grain boundary).\n2. Figures 4g, h, and i show the higher density of randomly distributed dislocations for BFMO/Ni-Cr than BFMO/LNO/Ni-Cr, and BFMO/LNO/Ni-Cr has high dislocation density at a grain boundary.\n3. Figure 4j and k show more uniform distribution in BFMO/LNO/Ni-Cr compared to BFMO/Ni-Cr due to the lower bulk (or randomly distributed) dislocation density.\n4. Figures 5b~f present more polarization disorder in BFMO/Ni-Cr than BFMO/LNO/NiCr associated with the lower bulk dislocation density.\n5. Figure 5g and h exhibit that BFMO/Ni-Cr has lower P and higher E than r c BFMO/LNO/Ni-Cr which can be explained by the point (1) above (attributed to randomly distributed dislocation density.)\nI see the fact that dislocations in BFMO/LNO/Ni-Cr preferably terminate the grain boundary interface (seen in 2), I don’t see any effect of the self assembled dislocations to properties in the current shape of manuscript, since the other results (2-5) can be explained merely by the reduction of the bulk dislocation density. I see the authors try to reason those behaviors with strain fields such as \"This enhancement originates from LNO-mediated defect organization, where the interlayer templates discontinuous-columnar grain growth with self-assembled dislocations along grain boundaries\" , \"The latter's stability arises from a uniform pinning effect generated by dislocation self assembly and a discontinuous-columnar grain structure, which suppresses defect migration\" , and \"The resulting periodic strain field will transform random FeO octahedral tilting into synchronized a a c octahedral rotation waves 6 that propagate throughout the whole thin film,” but they are rather speculative and not supported by the results. For example, what evidences the periodic strain field?\nThis evaluation made me bring up the novelty concern since bulk dislocation reduction is a known methodology at the first round, and that remains in the revision. To verify the design concept and claim \"actively controlling and utilizing dislocation configuration\", the authors need to present results evidencing the effects of the engineered dislocations at the grain boundary on the properties or functionalities.\nAlternatively, while careful reading, I see now \"bulk dislocation reduction with dislocation self assembly at grain boundary\" is well evidenced by Fig. 4g-k and consistent throughout the manuscript. I suggest reframing the main concept.\nOverall response: We sincerely thank the reviewer for the thoughtful and detailed feedback, which has been invaluable in improving our manuscript. We deeply appreciate the reviewer's efforts in carefully summarizing the key points of our results and providing clear, constructive suggestions for strengthening the work. The two proposed pathways: (1) adding more results showing evidence that the strain engineering associated with the grain boundary segregated dislocations indeed tunes the properties to verify the main concept \"designed dislocation self-assembly mediated strain engineering\", or (2) reframing the concept reflecting the existing results, have been particularly helpful in guiding our revisions.\nConsidering the significant challenge and time required for obtaining additional experimental results for strain engineering, and acknowledging that dislocation engineering inherently influences strain behavior, we have decided to reframe the study's focus, as suggested by the reviewer. Given that we have already validated the dislocation self-assembly and demonstrated its effect on material properties, we will emphasize dislocation engineering as the core concept. Accordingly, we have revised the manuscript to reframe the main idea from \"designed dislocation self-assembly mediated strain engineering\" to one that more accurately reflects our findings: dislocation engineering via controlled self-assembly. This adjustment aligns the narrative directly with the evidence presented, while still acknowledging the consequent tuning of strain and properties. The necessary conceptual and textual revisions have been implemented throughout the manuscript.\n1. The Title has been revised from \"Tailoring Polarization Homogeneity in Discontinuous-Columnar Bi(Fe,Mn)O Thin Films through Strain Engineering via 3 Controlled Dislocation Self-Assembly\" in the original manuscript to \"Tailoring Polarization Homogeneity in Discontinuous-Columnar Bi(Fe,Mn)O Thin Films via 3 Dislocation Engineering with Controlled Self-Assembly.\" in the revised manuscript. This change strategically shifts the focus from \"strain engineering\" as the primary mechanism to the active \"engineering of dislocations\", which we agree more accurately and robustly captures the core findings of our work.\n2. We have revised the Abstract to align with the new title and overall framework, as suggested. The content \"Strain engineering in ferroelectric thin films is crucial for advancing next-generation electronic devices, yet conventional approaches relying on dislocation-density approaches often compromise structural integrity and electromechanical performance. Here, we develop a reduced-dislocation self-assembly strategy for Bi(Fe,Mn)O (BFMO) thin films that overcomes these 3 constraints. By employing LaNiO (LNO) buffer layer, the interfacial lattice mismatch 3 between BFMO and Ni-Cr substrate is reduced from ~3.8% to ~1.0%, suppressing dislocation density while promoting strain anisotropy. This guides discontinuous-columnar grains in BFMO, promoting the self-assembly of edge dislocations along grain boundaries in a topologically-protected configuration. The interaction creates periodic strain fluctuations and coordinated FeO octahedral tilting, 6 significantly enhancing polarization homogeneity. Benefiting from this ordered microstructure, the BFMO thin film exhibits a lower domain-switching barrier and a more uniform domain pinning effect, which collectively enable a dramatically superior aging stability after 60 days at 60 °C, with far lower reductions in P (~20%) r and E (~35%) compared to its counterpart. These findings redefine defect c engineering paradigms, showing how controlled dislocation rearrangement and strain mediation can unlock superior ferroelectric performance.\" in the original manuscript has been replaced by \"Defect microstructures, particularly dislocations, are pivotal in determining the functional properties of ferroelectric thin films. While their density is routinely considered, the critical role of their spatial configuration has remained largely unexplored and difficult to control. Here, we develop a controlled self-assembly strategy for dislocations in Bi(Fe,Mn)O (BFMO) thin films on Ni-Cr 3 that directly addresses this challenge. By employing a LaNiO (LNO) buffer layer, we 3 template a discontinuous-columnar grain structure and guide the self-assembly of edge dislocations along grain boundaries in a topologically-protected configuration. The resulting ordered microstructure promotes a more uniform strain field and more coherent FeO octahedral tilting, 6 significantly enhances polarization homogeneity, leading to a lower domain-switching barrier and a more uniform domain pinning effect. Consequently, the BFMO thin film exhibits dramatically superior aging stability after 60 days at 60 °C, exhibiting far smaller reductions in remanent polarization (P) (~20%) and coercive field (E ) (~35%) compared to the BFMO thin r c film grown directly on Ni-Cr. These findings establish a new defect engineering paradigm wherein the deliberate dislocation rearrangement is leveraged to unlock superior ferroelectric performance.\" in the revised manuscript.\n3. The Introduction has been substantially revised in multiple sections to reflect the reframed focus. Specific changes are detailed below.\n3.1. The first paragraph \"Ferroelectric materials exhibit a strong coupling between strain and polarization, a characteristic widely utilized in non-volatile memory applications1,2. Defects, which vary from zero-dimensional point defects to two-dimensional interfaces, are inherent in these materials and significantly influence their functional characteristics. Among these defects, one-dimensional topological defects, such as dislocations, have recently gained attention as powerful tools for tailoring material performance due to the distinct strain field and extensive elastic interactions3-5.\" of the original manuscript has been changed into \"The functional performance of ferroelectric materials is governed by their microstructure, with strain-polarization coupling being one of the characteristics widely utilized in non-volatile memory applications1,2. Defects, which vary from zero-dimensional point defects to two-dimensional interfaces, are inherent in these materials and significantly influence their functional characteristics. Among these defects, one-dimensional topological defects, such as dislocations, have recently gained attention not merely as defects, but as core elements whose configuration can be engineered to tailor material performance3–5.\" in the revised manuscript.\n3.2. The sentences \"However, recent studies have revealed that strategically manipulating strain field can actually improve functionality. This paradigm shift is particularly relevant in ferroelectrics, where optimizing dislocation density is critical. A low dislocation density suppresses random strain fluctuations and supports uniform domain ordering, but results in higher energy requirements for domain switching and thus a higher coercive field (E )8–13.\" of the original manuscript has been modified as c \"However, recent studies have revealed that strategically engineering dislocation configurations can actually improve functionality. This paradigm shift is particularly relevant in ferroelectrics, where the spatial rearrangement of dislocations is as critical as their density. A low density of randomly-distributed dislocations can suppress random strain fluctuations and promote uniform domain ordering. However, this configuration typically results in higher energy requirements for domain switching and thus a higher coercive field (E )8–13.\" in the revised manuscript.\n3.3. The third paragraph \"Recent advances in dislocation engineering have reshaped our understanding of the interactions between strain and polarization, shifting the focus from general stress relief to the deliberate design of defect for precise strain field manipulation15–17. The innovative approach enables the conversion of dislocation configurations from random defects into purposefully crafted functional elements, providing new pathway to simultaneously enhance key memory parameters: increasing P to broaden memory windows, tuning E for efficient switching, and r c improving resistance to aging for the development of next-generation ferroelectric memory devices. By leveraging the unique topological protection behavior of dislocations, such as the conservation of Burgers vectors, disordered strain field can be reorganized to control octahedral tilting and lattice distortions in ferroelectrics18–21. In ferroelectrics like BiFeO (BFO), strain-induced templates can selectively 3 manipulate FeO oxygen octahedral rotation modes. A striking manifestation occurs in 6 epitaxially constrained BFO thin films under strong compressive strain, which stabilize in a metastable T-like (T′) polymorph exhibiting both an exceptionally large axial ratio (c/a ~1.23) and fundamentally distinct oxygen octahedral rotation patterns compared to the rhombohedral (R) bulk phase. This ''super-tetragonal'' phase, first predicted theoretically in the mid-2000s, exhibits not only giant polarization but also reconstructed rotation symmetries, demonstrating strain's dual role in modifying both polar and rotational order parameters20. In displacement-type ferroelectrics such as BaTiO (BTO), the interaction between strain and lattice distortions becomes 3 particularly crucial for optimizing distortion pathways. First-principles calculations reveal that uniaxial c-axis strain promotes cooperative Ti-O displacements that linearly enhance polarization, while multiaxial (abc) strain triggers discontinuous polarization jumps through anomalous oxygen displacements21. These findings establish strain engineering as a powerful and precise tool for manipulating ferroelectric distortion modes.\" of the original manuscript has been separated into two paragraphs, reads as \"The profound impact of lattice control on ferroelectric properties is classically demonstrated by applying strain. In ferroelectrics like BiFeO 3 (BFO), strain-induced templates can selectively manipulate FeO oxygen octahedral 6 rotation modes. A striking manifestation occurs in epitaxially constrained BFO thin films under strong compressive strain, which stabilize a metastable tetragonal-like polymorph exhibiting both an exceptionally large axial ratio (c/a ~1.23) and fundamentally distinct oxygen octahedral rotation patterns compared to the rhombohedral bulk phase. This ''super-tetragonal'' phase, first predicted theoretically in the mid-2000s, exhibits not only giant polarization but also reconstructed rotation symmetries, demonstrating dual role of strain in modifying both polar and rotational order parameters15. Similarly, in displacement-type ferroelectrics such as BaTiO 3 (BTO), the interaction between strain and lattice distortions becomes particularly crucial for optimizing distortion pathways. First-principles calculations reveal that uniaxial c-axis strain promotes cooperative Ti-O displacements that linearly enhance polarization, while multiaxial (abc) strain triggers discontinuous polarization jumps through anomalous oxygen displacements16.\nBuilding on the established foundation of strain engineering, recent advances have identified dislocation engineering as a new frontier for controlling ferroelectric properties, shifting the focus from applying uniform global strain to deliberately designing nanoscale dislocation configurations17–19. This innovative approach enables the conversion of dislocation configurations from randomly distributed defects into purposefully crafted functional elements, providing new pathway to simultaneously enhance key memory parameters: increasing P to broaden memory windows, tuning r E for efficient switching, and significantly improving aging stability. By leveraging the unique, topologically protected behavior of dislocations, guided dislocation self-assembly provides a pathway to control local octahedral tilting and lattice distortions in ferroelectrics15,16,20,21. Such precise control over local structural distortions represents the central goal of modern defect engineering.\" in the revised manuscript.\n3.4. The content \"Addressing these issues by controlling defects and targeting strain field regulation provides a novel strategy to concurrently optimize polarization parameters, paving the way for developing more reliable and efficient ferroelectric memory devices.\" of the original manuscript has been replaced by \"Addressing these issues by defect engineering provides a novel strategy to concurrently optimize polarization parameters, paving the way for developing more reliable and efficient ferroelectric memory devices.\" in the revised manuscript.\n3.5. The whole fifth paragraph \"To address the limitations in ferroelectric performance of BFO thin films, one must reconsider the interactions among strain field, defect and ferroelectric polarization. A key focus lies in understanding how the strain field is influenced by defects and how it correlates with ferroelectric polarization through defect manipulation. A major challenge lies in the fabrication of BFO thin films with controlled defects that can effectively regulate strain field and facilitate interactions across various levels, from atomic distortions to domain structures and overall ferroelectric polarization.\" of the original manuscript has been replaced by \"To address the limitations in ferroelectric performance of BFO thin films, one must reconsider the interactions among defect configurations and ferroelectric polarization. A key focus lies in understanding how the configurations influence ferroelectric polarization. A major challenge lies in the fabrication of BFO thin films with controlled defect configurations that can effectively regulate interactions across various levels, from atomic distortions to domain structures and overall ferroelectric polarization.\" in the revised manuscript.\n3.6. The last two paragraphs \"Here, we have developed an innovative strategy of dislocation engineering via controlled self-assembly to overcome the limitations of conventional defect density-control approaches in Bi(Fe,Mn)O (BFMO) thin films. 3 Unlike previous studies that employed SrTiO (STO) substrates to achieve low 3 dislocation densities and improve ferroelectric properties25–27, we selected a face-centered cubic (FCC) Ni-Cr substrate to deliberately introduce lattice and thermal expansion mismatch with the rhombohedral (R3c) BFMO thin film. This mismatch is not a defect but a design feature, serving as a source to generate a high density of dislocations for configuration control. These dislocations provide a unique way of probing dislocation-polarization interaction and the impact on ferroelectric behaviors. Furthermore, the metallic nature of Ni-Cr substrate offers inherent potential as a built-in electrode for future studies on interfacial charge behavior, while its mechanical properties also make it a promising candidate for explorations into flexible ferroelectric electronics. We then incorporated LaNiO (LNO) buffer layer, 3 which reduced BFMO/Ni-Cr lattice mismatch from ~3.8% to ~1.0% (Figs. 3a,b). This promoted the formation of a discontinuous-columnar grain structure, which in turn provided fundamental control over the dislocation configuration, guiding the subsequent self-assembly.\nThe strain energy anisotropy effect of LNO plays a pivotal role in guiding the formation of discontinuous-columnar grains in BFMO (Figs. 4c, S7), facilitating the self-assembly of topologically-protected dislocations along grain boundaries. This interaction between dislocations and grain boundaries introduces an innovative mechanism for regulating functional properties, enabling the dissipation of strain energy through a more uniform strain field, more coherent FeO octahedral tilting, 6 and enhanced macroscopic polarization homogeneity. Consequently, the LNO-buffered BFMO thin film aged for 60 days at 60 °C exhibits robust aging resistance, with only ~20% and ~35% reductions in P and E at 60 °C, while the r c LNO-free thin film suffers severe degradation of ~90% and ~80%, respectively. These findings challenge the conventional perspective of defects as purely detrimental, instead presenting a new design approach focused on controlling dislocation configurations to optimize ferroelectric properties.\" of the original manuscript has been changed into \"Here, we have developed an innovative strategy of dislocation engineering via controlled self-assembly to overcome the limitations of conventional defect density-control approaches in Bi(Fe,Mn)O (BFMO) thin films. 3 Unlike previous studies that employed SrTiO (STO) substrates to achieve low dislocation 3 densities and improve ferroelectric properties25–27, we selected a face-centered cubic (FCC) Ni-Cr substrate to deliberately introduce lattice and thermal expansion mismatch with the rhombohedral (R3c) BFMO thin film. This mismatch is not a defect but a design feature, serving as a source to generate a high density of dislocations for configuration control. These dislocations provide a unique way of probing dislocation-polarization interaction and the impact on ferroelectric behaviors. Furthermore, the metallic nature of Ni-Cr substrate offers inherent potential as a built-in electrode for future studies on interfacial charge behavior, while its mechanical properties also make it a promising candidate for explorations into flexible ferroelectric electronics. We then incorporated a LaNiO (LNO) buffer layer, 3 which reduced BFMO/Ni-Cr lattice mismatch from ~3.8% to ~1.0% (Figs. 3a,b). This promoted the formation of a discontinuous-columnar grain structure, which in turn provided fundamental control over the dislocation configuration, guiding the subsequent self-assembly.\nThe strain energy anisotropy effect of LNO plays a pivotal role in guiding the formation of discontinuous-columnar grains in BFMO (Figs. 4c, S7), facilitating the self-assembly of topologically-protected dislocations along grain boundaries. This interaction between dislocations and grain boundaries introduces an innovative mechanism for regulating functional properties, enabling the dissipation of strain energy through a more uniform strain field, more coherent FeO octahedral tilting, 6 and enhanced macroscopic polarization homogeneity. Consequently, the LNO-buffered BFMO thin film aged for 60 days at 60 °C exhibits robust aging resistance, with only ~20% and ~35% reductions in P and E , while the LNO-free r c thin film suffers severe degradation of ~90% and ~80%, respectively. These findings challenge the conventional perspective of defects as purely detrimental, instead presenting a new design approach focused on controlling dislocation configurations to optimize ferroelectric properties.\" in the revised manuscript.\n4. The corresponding revisions have been systematically implemented throughout the Results and Discussions. The key modifications are as follows.\nIn the part of \"Edge Dislocation Effects on Ferroelectricity for Bi(Fe,Mn)O 3 (BFMO)\":\n4.1. The sentence \"These insights not only deepen our understanding of defect-polarization interactions but also establish the foundational principles for the dislocation engineering approaches demonstrated in this work30.\" has been added behind the third sentence in the revised manuscript.\n4.2. The content \"Whereas the introduction of edge dislocations with specific geometric configurations (Burgers vector b‖[100], dislocation line t‖[010] generates simultaneous significant ε and coupled ε at the dislocation core.\" in the fifth yy xx paragraph in the original manuscript is changed into \"The introduction of edge dislocations with specific geometric configurations (Burgers vector b‖[100], dislocation line t‖[010]) generates significant ε and coupled ε at the dislocation yy xx cores. This complex strain field presents a fundamental challenge for ferroelectric modulation.\" in the revised manuscript.\n4.3. The last paragraph \"These results demonstrate that edge dislocations can exert much stronger localized influence on ferroelectric polarization than domain walls alone, due to their ability to generate pronounced strain field in both longitudinal and transverse directions. This underscores their critical role in modulating ferroelectric properties through \"defect-strain-polarization\" coupling.\" has been replaced by \"These results demonstrate that the configuration of edge dislocations exerts a much stronger localized influence on ferroelectric polarization than domain walls alone, as its associated three-dimensional strain field directly impacts both longitudinal and transverse directions.\" in the revised manuscript.\nIn the part of \"Structural Mechanisms of BFMO Thin Films\":\n4.4. The content \"As revealed by the phase-field simulations, edge dislocations can precisely modulate ferroelectric polarization through their localized strain field. By further controlling both dislocation density and alignment, it becomes possible to programmable manipulation of polarization distributions. This motivates our design of a heterostructure (Fig. 3), where the introduction of LaNiO (LNO) buffer layer 3 between Bi(Fe,Mn)O (BFMO) thin film and Ni-Cr substrate fundamentally modifies 3 interfacial strain distribution (Fig. 3a,b).\" in the first paragraph in the original manuscript has been modified as \"Building on the principle that ferroelectric polarization is governed by dislocation configuration, we designed a heterostructure (Fig. 3) to actively engineer these arrangements. The introduction of LaNiO (LNO) 3 buffer layer between the Bi(Fe,Mn)O (BFMO) thin film and Ni-Cr substrate 3 fundamentally modifies the interfacial constraints (Figs. 3a,b).\" in the revised manuscript.\n4.5. The paragraphs \"The IFFT reconstructions (Fig. 4g,h) highlight characteristic edge dislocations, marked by white \"T\" symbols, where an extra atomic half-plane terminates within the crystal lattice. Similarly, edge dislocations have been observed in perovskite ferroelectric thin films, such as 0.7Bi(Mg Ti )O -0.3SrTiO , 0.5 0.5 3 3 often associated with non-stoichiometric ratio44.\nNotably, the BFMO thin film on Ni-Cr exhibits higher density of randomly-distributed edge dislocations, enabling faster stress relaxation, which is consistent with the macroscopic stress profiles shown in Fig. 3f. GPA (Fig. 4j-k) reveals stark contrasts in stress distribution, where the BFMO thin film on Ni-Cr possesses a pronounced spatial variation in shear stress (ε ) and normal (ε ) stress, xy yy while the BFMO on LNO/Ni-Cr exhibits more uniform stress distribution.\nCritically, Fig. 4(f) reveals a clear contrast in dislocation density across the red-dashed grain boundary, where dislocations preferentially terminate along the discontinuous-columnar interface. The abrupt transition from a high-density dislocation network on one side to a low-defect region on the other is visually evident, with dislocations consistently ending at the marked boundary. During the growth of heterostructure, the LNO layer acts as a template, promoting near-single-crystal order within grains and driving defects (dislocations, vacancies) toward boundaries. Under the modulation of an anisotropic stress distribution, evidenced by the fourfold symmetric feature in Fig. 3e, these boundary-segregated dislocations self-assembled externally to the discontinuous-columnar grains. We observed this phenomenon consistently, with further examples provided in Fig. S8. This process resulted in an ordered ''dislocation-grain boundary'' interaction that suppressed randomly-distributed dislocation distributions (Fig. 4h). Collectively, these results demonstrate that LNO layer promotes strain delocalization via discontinuous-columnar grain-enabled stress redistribution, ultimately stabilizing the \"square star-shaped\" configuration and gradual deflection behavior observed in Fig. 3e–f.\" in the original manuscript have been tuned into \"The IFFT reconstructions (Figs. 4g–i) highlight characteristic edge dislocations, marked by white \"T\" symbols, where an extra atomic half-plane terminates within the crystal lattice, which is a common feature in perovskite ferroelectrics44. Critically, a stark contrast in their configuration is observed: the BFMO on Ni-Cr exhibits a high density of randomly-distributed dislocations, whereas in BFMO/LNO/Ni-Cr, they are preferentially assembled at a discontinuous-columnar grain boundary (marked with the red-dashed line in Fig. 4f). This transition from disorder to order directly correlates with the macroscopic strain state. As evidenced by GPA (Figs. 4j–k), the randomly-distributed dislocations in BFMO/Ni-Cr induce a pronounced spatial variation in shear strain (ε ) and ε , while the self-assembled xy yy dislocations in BFMO/LNO/Ni-Cr give rise to a uniform stress distribution. We attribute this to the templating effect of LNO layer during heterostructure growth. The LNO promotes near-single-crystal order within individual grains. Under the influence of the anisotropic stress distribution (Fig. 3e), this structure actively guides dislocations to migrate and self-assemble along the discontinuous-columnar grain boundaries (Fig. S8), using the grain boundaries as effective sinks for defect isolation.\" in the revised manuscript.\nThe discussion in part \"Electrical Properties of BFMO Thin Films\" has been rewritten to emphasize the connection between dislocation configuration and functional performance, as reflected in the updated text that follows:\nHigh-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was employed to map spontaneous polarization vectors via tracking B-site cation displacements (Figs. 5a,d) for BFMO thin films on Ni-Cr and LNO/Ni-Cr. The corresponding atomic brightness contrast directly visualizes spatial variations in polarization amplitude and angle (Figs. 5b,c,e,f). Regions from Figs. 4(a ) 1 and (c ) were specifically selected to investigate the local influence of dislocation 1 configurations on polarization (Fig. S9). In BFMO/Ni-Cr, which contains a high density of randomly-distributed dislocations (Fig. 4g), the polarization vectors exhibit significant spatial disorder (Fig. 5a). This disorder arises from irregular B-site cation displacements relative to the A-site lattice, where localized lattice distortions near edge dislocations disrupt the coherent ionic off-centering, creating competing polarization variants evident as random brightness contrast (Figs. 5b–c). In stark contrast, the BFMO/LNO/Ni-Cr film, featuring a microstructure with dislocations self-assembled at discontinuous-columnar grain boundaries (Fig. 4i), exhibits remarkable uniformity in both polarization vector alignment and angular distribution (Figs. 5d–f). This direct correlation between the engineered dislocation configuration and the enhanced polarization homogeneity demonstrates that defect engineering is a key to optimize ferroelectric performance. The reduction of randomly-distributed dislocations and their self-assembly at discontinuous-columnar grain boundaries minimizes the random local strain fluctuations that disrupt long-range polarization ordering.\nThis defect engineering strategy is fundamentally validated by combining it with DFT calculations (Figs. 1c–d, S3). The calculations confirm that a single edge dislocation induces a localized symmetry-breaking distortion, primarily manifested as FeO octahedral tilting and the resultant charge redistribution, which collectively 6 stabilize a disordered polarization configuration. In BFMO/Ni-Cr, the collective effect of a high density of randomly-distributed dislocations creates overlapping disruptive fields, accounting for the severe macroscopic polarization disorder. Therefore, the reduction in randomly-distributed dislocations and their self-assembly achieved in the LNO-buffered BFMO thin film effectively mitigate this collective detrimental impact, directly enabling the observed polarization homogeneity.\nTo characterize the polarization behavior of the fresh BFMO thin films, we measured P-E loops at their respective breakdown strengths (Fig. 5g). The BFMO thin film on LNO/Ni-Cr exhibits reduced coercive field (E ) with markedly higher P c r and P at room temperature. This indicates a lower domain-switching barrier, which m aligns with the reduced pinning from the controlled dislocation configuration (Fig. 4i), in contrast to the strong pinning imposed by the high density of randomly-distributed dislocations in BFMO/Ni-Cr (Fig. 4g). Additionally, it also helps in reducing the leakage current density in BFMO on LNO/Ni-Cr, being one order of magnitude lower than that of the BFMO on Ni-Cr (Fig. S10).\nHaving established the superior initial ferroelectric properties of the LNO-buffered BFMO thin film, we evaluated the stability under accelerated aging conditions at multiple temperatures (RT, 60, 120, and 180 °C) for 60 days (Figs. 5h–i). The performance of the two thin films diverges significantly. The BFMO/Ni-Cr thin film suffered severe ferroelectric degradation and ultimately failed at elevated temperatures, while the BFMO/LNO/Ni-Cr thin film demonstrated remarkably superior aging resistance, maintaining functionality even at 180 °C. A notable contrast occurs at 60 °C. The BFMO thin film on Ni-Cr suffers a severe ~90% reduction in P r and ~80% in E , whereas the LNO-buffered thin film maintains a stable state with c only ~20% and ~35% reductions, respectively. We attribute this dramatic difference to their distinct dislocation configurations (Fig. 4). In BFMO/Ni-Cr, the high density of randomly-distributed dislocations creates heterogeneous and thermally unstable pinning sites that are easily de-pinned, leading to rapid polarization degradation. In contrast, the reduced randomly-distributed dislocations and their self-assembly at discontinuous-columnar grain boundaries in BFMO/LNO/Ni-Cr creates a more uniform and coherent microstructure. This engineered configuration minimizes random local strain fluctuations and establishes a stable pinning environment that is robust against thermal stress, thereby ensuring the observed aging resistance.\nIn situ piezoelectric force microscope (PFM) was performed to probe the domain stability and switching reversibility (Fig. S11). After partial poling with opposite voltages, the BFMO/LNO/Ni-Cr thin film exhibited robust stability, with the PFM phase and amplitude of the switched domains remaining nearly unchanged for over 40 min. In stark contrast, the PFM signals from BFMO/Ni-Cr showed significant degradation within 30 min, indicating substantial back-switching of the ferroelectric domains. This distinct relaxation behavior is directly linked to their dislocation configurations. The dislocation self-assembly at grain boundaries in BFMO/ LNO/Ni-Cr creates a stable energy landscape that effectively pins the domain walls, suppressing back-switching. Conversely, the high density of randomly-distributed dislocations in BFMO/Ni-Cr generates a heterogeneous and unstable pinning environment, which facilitates the depolarization fields that drive domain back-switching.\n5. The Conclusions in the original manuscript has been re-written as \"In this work, we have established a dislocation engineering paradigm via controlled self-assembly for designing high-performance BFMO ferroelectric thin films. By employing LNO buffer layer to tailor the interfacial constraints, we guided the formation of discontinuous-columnar grain structure and the self-assembly of dislocations at grain boundaries. This engineered microstructure characterized by a low density of randomly-distributed dislocations and ordered self-assembly characteristics, directly resulted in enhanced polarization homogeneity and superior aging stability. Our findings demonstrate that controlling the spatial configuration of dislocations, rather than merely reducing their density, is the key to unlocking superior ferroelectric performance. This defect engineering approach establishes a new design principle for functional oxide thin films, paving the way for next-generation memory and electronic devices.\" in the revised manuscript.\nWe have carefully considered the reviewer's insightful comment. In response, we have integrated the above discussion and reframed the central narrative from strain engineering to dislocation engineering, which provides a more precise description of our mechanistic insight. Importantly, this adjustment enhances the clarity of our contribution without altering the novelty, key findings, or conclusions of the work.\nThanks again for your help!\nWith best regards,\nSincerely yours,\nHuiting Sui & Huajun Sun & Xiaoguang Ma & Shujun Zhang"}, {"round": 3, "reviewer_comments": {"reviewer_3": "I have no further comments at this stage."}, "author_response": ""}]

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