Introduction

Dislocation, a structure commonly present in crystals, has been widely exploited from material design to optimization. For metal materials, dislocations have been extensively studied and utilized to refine their hardness1,2, fatigue performance3,4, and ductility5,6. The presence of controllable high-density dislocations in metals is attributed to the non-directional and non-specific nature of metallic bonds. By contrast, ferroelectric crystals generally have rigid ionic or covalent bonds, exhibit anisotropic properties, and rely on domain switching and domain wall movement to release stress, making the formation of high-density dislocations (Nd > 1015 m−2) energetically unfavorable, and their manipulation is technically more challenging7. The effective control of dislocations in ferroelectric crystals is of great significance for fine-tuning their polarization8, domain wall dynamics9, thermoelectric properties10, piezoelectric response11, thermal conductivity12, and other potential applications yet to be identified. Therefore, growing efforts have been directed towards engineering dislocations in ferroelectric crystals.

Theoretically, the generation of dislocations in crystalline materials typically occurs when applied tensile, compressive, or shear stresses exceed the material’s yield point. For dielectric crystals, mechanical loading remains a primary method for dislocation introduction13,14,15, with controlled stress application techniques such as nanoindentation enabling precise control over the position of dislocations through localized plastic deformation16,17. Contemporary materials engineering has further developed alternative dislocation induction strategies that circumvent direct mechanical loading, such as doping18,19, heat treatment20,21, electric field22, and high-energy particle irradiation23,24. These non-mechanical approaches provide complementary pathways for tailoring dislocation architectures while preserving structural integrity in sensitive materials systems. Despite these efforts, current methods largely rely on non-spatially selective energy deposition and thus usually lose precision and controllability when inducing dislocations deep inside the crystal matrix. So far, a general technological platform that enables precise manipulation of high-density dislocations in 3D free space with multi-degree-of-freedom controllability remains elusive.

Recently, ultrafast laser-driven material modification has been established as a precise and versatile tool for reshaping the functionalities of transparent media by inducing non-stoichiometric modification in the matrix25,26,27,28. In general, ultrafast laser pulses interact with transparent materials via nonlinear optical absorption, where multiple laser parameters, such as laser polarization, pulse energy, pulse duration, and pulse number, as well as properties of target materials, can be applied to tune the local energy deposition, leading to flexible manipulation of the produced structures. The spatial selectivity and threshold effect of ultrafast laser-matter interaction potentially offer precise, multi-degree-of-freedom controllability, yet mostly unexplored, for dislocation engineering in ferroelectric crystals. In this study, using PMN-PT crystal as a model ferroelectric system, notable for its pronounced anisotropic characteristics (e.g., polarization and mechanical anisotropy) and recent breakthroughs in optical transparency29, we developed a straightforward ultrafast laser irradiation technique that enables reversible 3D writing of high-density dislocations with multidimensional controllability in free-space configurations.

Results

Figure 1 illustrates spatial morphology and typical manipulation modes of ultrafast laser-induced high-density dislocations in a PMN-PT single crystal. The dislocation-formed zone in 3D free space (the dark contrast regions in the optical images) exhibits significant anisotropy with the spatial sizes at the micrometer level (Fig. 1a). Any possible artifacts from domain patterns or lateral microcracks have been excluded through piezoresponse force microscopy (PFM) and dark-field optical imaging on the laser-modified zone (Supplementary Fig. 1). High-resolution transmission electron microscopy (HRTEM) characterization of the dislocation-formed zone indicates that the dislocation density is as high as ~3.6 × 1016 m−2 (Supplementary Note 1). According to laser incidence, laser parameters, and ferroelectric domain orientation, the dislocation distribution exhibits three typical states: perpendicular to laser polarization, parallel to laser polarization, and parallel to the poling direction. This observation is attributed to a competition mechanism between different types of local field enhancement during the interaction of a linearly polarized ultrafast laser with unpoled and electrically poled PMN-PT crystals. In addition, the induced dislocations can be in situ erased and rewritten through secondary irradiation with different laser parameters (Fig. 1b), achieved by leveraging the annihilation behavior of high-density dislocations. The seemingly non-erasable point-shaped feature does not belong to the dislocation-formed zone. Instead, it is an amorphous region formed at the center of the Gaussian ultrafast laser-irradiated zone (Supplementary Fig. 4).

Fig. 1: All-optical induction and manipulation of dislocations in PMN-PT crystal.
figure 1

a Schematic of ultrafast laser inducing dislocations in 3D space. Insets: images showing the front view and side view of dislocation-formed zone. Arrows and circles point to dislocations. b Fundamental approaches for manipulating dislocations, including polarization-dependent control, poling direction-dependent alignment, and in-situ modification through erasure and rewriting processes. E and P represent the laser electric field and the poling direction of crystal, respectively. Scale bars: 5 µm. c HRTEM image of a dislocation-formed zone and partially magnified view of the selected area. Scale bars: 10 nm, 3 nm. d Inverse fast Fourier transform (IFFT) images of the selected area in c and Burgers vectors analyzed in different crystal planes (b = [010]; b = [100]; \({{\bf{b}}}=\frac{1}{2}\left[1\bar{1}0\right]\); and \({{\bf{b}}}=\frac{1}{2}[110]\), in (010), (100), \((1\bar{1}0)\), and (110) crystal planes, respectively).

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Figure 1c, d showcase the ultrafast laser-induced high-density dislocations and their Burgers vectors. We reveal that there are dislocations distributed in different crystal planes, including (010), (100), (\(1\bar{1}0\)), and (110) planes, which belong to different slip systems. Specifically, for ABO3 perovskites, the dislocations identified in the (\(1\bar{1}0\)) and (110) planes belong to the {110} < 110> slip system, which is a room-temperature system. While the dislocations identified in the (010) and (100) planes belong to the {100} < 100> slip system, which is a high-temperature system. The appearance of <100> dislocations as well as dislocation line features in weak-beam dark-field images (Supplementary Fig. 5) jointly indicates that the ultrafast laser-based dislocation writing presented in our study is largely driven by thermal effects. Our systematic experiments using laser repetition rate as a control variable further confirm that thermal effects are necessary for dislocation induction (Supplementary Fig. 6).

As ultrafast lasers have ultra-high peak power and electric field intensity30, this dislocation induction approach can benefit from the rich nonlinear effects excited by strong field-matter interaction in the focal volume to offer multidimensional controllability. We reveal that this controllability arises from the synergistic interaction between polarization-dependent focal light field modulation and both the intrinsic and externally induced anisotropy of the PMN-PT crystal. Typically, when tightly focused inside transparent materials, the ultrafast laser pulses initiate multiphoton ionization, generating plasmas at the center of the focal volume31. This ionized region in turn disrupts the incoming pulses, leading to a redistribution of the light field within the focal volume. Two fundamental scenarios can be identified (Fig. 2a). When the carrier density is low (e.g., ~1026 m−3), the excited plasma is considered underdense32,33. In this condition, the light field intensity is enhanced along the orientation perpendicular to laser polarization (underdense mode) (Fig. 2a, up). By contrast, when the irradiation area is fully excited (carrier density > 1028 m−3), the ionized zone could exhibit a metallic state34,35, and the resultant plasmonic resonance-induced local field enhancement is parallel to laser polarization (plasmonic mode) (Fig. 2a, below). This polarization-dependence shift is essentially attributed to the resonant mode conversion caused by the change in dielectric properties of the central excited zone (Supplementary Note 2). Under the continuous action of the modulated ultrafast light field, anisotropic high temperature and high pressure are induced in the irradiated area, such that the dislocations are expected to preferentially emerge along the direction where the light field is enhanced.

Fig. 2: Dislocation manipulation driven by laser polarization and domain orientation.
figure 2

a Simulation results depicting the local field enhancement modes: underdense mode (up) at a low carrier density and plasmonic mode (below) at a high carrier density. E and k represent the laser electric field and the laser incident direction, respectively. Scale bars: 100 nm. b–e Schematics of the domain orientations (red arrows) in unpoled, [010]-poled, and [001]-poled PMN-PT crystals as well as dislocation-formed zones written with different laser polarization directions and pulse energies, corresponding to the four schematic diagrams on the left. The subscript c denotes pseudo-cubic coordinates. k and P represent the laser incident direction and the poling direction of PMN-PT crystal, respectively. The pulse duration and pulse number for dislocation induction are 885 fs and 150k, respectively. Scale bars: 10 µm.

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The anisotropic mechanical properties of the PMN-PT crystal significantly influence the dislocation generation. The Knoop hardness of PMN-PT single crystal is much lower on the (100) and (010) crystal planes36, indicating that the interatomic bonding strength on these crystal planes is weaker than others. The non-equilibrium stress caused by transient high temperature and high pressure at the focus could drive the crystal to preferentially cleave along these two crystal planes (Supplementary Fig. 7). During this process, the stretching and distortion of the crystal lattice will lead to the emergence of dislocations. Hence, when ultrafast lasers with different polarization directions are focused inside the PMN-PT crystal, the dislocation distribution does not depend solely on the polarization direction but is determined by the contrast of laser polarization components in the [100] and [010] directions (Fig. 2b–e). Regardless of variations in laser polarization direction, dislocations are primarily generated along the [100] or [010] directions. Due to the intrinsic anisotropy of the crystal, two types of polarization dependence arise depending on the applied pulse energy. Specifically, at low pulse energies (e.g., ~1 μJ), dislocation formation occurs in the underdense mode, resulting in a dislocation-formed zone perpendicular to the main component of laser polarization (Fig. 2b). In contrast, at higher pulse energies (e.g., ~5 μJ), the plasmonic mode becomes predominant, causing the dislocation formation zone to align parallel to the main component of laser polarization (Fig. 2c and Supplementary Fig. 8).

Ferroelectric domains also play a crucial role in dislocation control. Due to the spontaneous polarization of ferroelectric crystals, unpoled PMN-PT crystals contain numerous randomly oriented domain walls (Supplementary Fig. 9), leading to a high degree of local stress concentration37. Thus, additional randomly oriented dislocation-formed zones emerge around the main dislocation distribution along the [100] or [010] direction, which deteriorates the regularity of the dislocation distribution. We propose that by electrically poling the crystal to align the orientation of ferroelectric domains, the randomly oriented domain walls can be largely eliminated29, thereby greatly improving the regularity of dislocation arrangement (Fig. 2d, e). When the crystal is poled along the [100] or [010] direction (perpendicular to the laser incidence), dislocation generation becomes independent of laser polarization because the domain switching toughening effect38 from the aligned ferroelectric domains inhibits cleavage in other directions (Fig. 2d). Therefore, we use the PMN-PT crystal poled along the [001] direction (along the laser incidence) to maintain the controllability arising from laser polarization dependence. Importantly, in electrically poled ferroelectric crystals, there is a depolarization field (Ep) generated by opposite bound charges inside the crystal. The presence of Ep facilitates the separation and migration of free electrons and holes during ultrafast laser irradiation39,40, resulting in a significant increase in the carrier density of the ionized zone. Consequently, focal light field modulation in a poled PMN-PT crystal occurs under the plasmonic mode, whereby the induced dislocation distribution is parallel to laser polarization (Fig. 2e).

In summary, the spatial distribution of ultrafast laser-induced dislocations in PMN-PT crystal is mainly determined by three factors: laser polarization, the anisotropic mechanical properties of the matrix, and the orientation of ferroelectric domains, which confer our method additional control degrees of freedom in dislocation manipulation.

Generally, the writing of dislocations in perovskite oxide ferroelectrics is irreversible, as these dislocations are highly stable and exhibit very low mobility in the lattice structure and electrical domain environments. Here, we achieve dislocation erasing and rewriting in the PMN-PT crystal by using the annihilation behavior of high-density dislocations (Fig. 3 and Supplementary Movie 1). Dislocation annihilation is essentially caused by the encounter of complementary dislocations, necessitating the motion and interaction of dislocations. Specifically, when the spacing of two dislocations with opposite Burgers vectors is less than a certain value, namely, the critical annihilation distance (~1.5–1.6 nm)41,42,43, their stress fields superimpose and partially cancel, significantly reducing the total elastic strain energy of the system. This energy minimization generates a strong attractive interaction between the dislocations that overcomes the Peierls barrier and drives the dislocations to approach spontaneously, resulting in the annihilation of both dislocations.

Fig. 3: Erasure mechanism of high-density dislocations.
figure 3

a–d Simulated high-density dislocation distribution in the 100 × 100 nm square (up) and calculated the probability distribution of the dislocation spacing at different dislocation densities (below), corresponding to dislocation writing and erasing. The initial dislocation density is 3.6 × 1016 m−2, and 1t, 2t, 3t, 4t represent 1, 2, 3, and 4 times of the initial dislocation density, respectively. The dotted yellow region represents the critical distance range for dislocation annihilation. Inset: experimental results of dislocation erasing by multiplying the irradiation time. The irradiation time for dislocation writing is set to 1 s, and secondary irradiation time for dislocation erasing is 1 s, 2 s, and 3 s, respectively. Scale bars: 5 µm. e Optical microscopic images, HRTEM images, IFFT images showing dislocation-formed (left) and -erased (right) zones. Scale bars: 10 µm, 10 nm, 2 nm, respectively. f Birefringence signals of dislocation-formed (left) and -erased (right) zones. Scale bars: 10 µm. Source data are provided as a Source Data file.

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In this work, two main features allow for the reversible writing of dislocations in all-inorganic ferroelectric crystals. First, the density of ultrafast laser-induced dislocations in PMN-PT crystals is considerably high and can reach a level of ~1016 m−2. In this condition, the average spacing between dislocations is already less than 4 nm, which lays the foundation for further reducing the spacing of dislocations to below the critical value for activating dislocation interaction. Second, dislocation writing based on single-beam ultrafast laser static irradiation has considerably high positioning accuracy and repeatability, making it possible to superpose higher-density dislocations within the previously formed dislocation zone. Based on statistical methodology, we propose a secondary in-situ irradiation strategy to further increase the dislocation density in the dislocation-formed area and reduce the average spacing of dislocations below the critical annihilation distance, thereby achieving the erasure of dislocations.

As shown in Fig. 3a–d, guided by experimentally identified dislocation density data, we set the dislocations (represented by points) to be randomly and uniformly distributed within a 100 × 100 nm square and calculated the probability distribution of the dislocation spacing. It is evident that the dislocation spacing is mainly distributed to the right of the annihilation spacing (Fig. 3a). If we increase the number of dislocations in the square, the probability distribution of the dislocation spacing will shift significantly to the left and quickly cross the annihilation spacing threshold (Fig. 3b–d). Theoretically, when the number of dislocations in a unit area exceeds twice the current value, the average dislocation spacing falls below the annihilation threshold, and dislocations will be largely annihilated (Fig. 3c, d). Experimentally, we achieved in situ erasure of dislocations within the PMN-PT crystals by increasing the duration of secondary laser irradiation. When the secondary irradiation time exceeds twice the dislocation-induction time, the dislocation distribution significantly shortens from an anisotropic long stripe to an isotropic point at the focal center. Microscopically, the scanning electron microscopy (SEM) and HRTEM images of the re-irradiated zone show that dislocations have been nearly completely erased (Fig. 3e and Supplementary Fig. 10). Macroscopically, the intense stress birefringence caused by high-density dislocations is largely eliminated (Fig. 3f), which agrees well with theoretical predictions and results of the erasure experiments.

Our experiments indicate that thermal effects are also indispensable for dislocation erasure (Supplementary Fig. 11). This is foreseeable because thermal effects can enhance atomic diffusion and activate dislocation slip and climb, effectively overcoming the Peierls barrier for dislocation migration44,45. The resulting dislocation mobility, in synergy with ultrafast laser-induced point defects and external electric fields, significantly increases interaction probabilities among dislocations, creating favorable conditions for dislocation annihilation during the secondary laser irradiation (Supplementary Note 3).

The erasable and rewritable properties of ultrafast laser-induced dislocations are not affected by poling states, as evidenced by successful implementation in both unpoled and [010]-poled PMN-PT crystals (Supplementary Fig. 12). Furthermore, the developed strategy for high-density dislocation writing and erasing also exhibits exceptional cross-material universality, extending beyond ferroelectric systems to transparent dielectric crystals. Experimental validation has been achieved in magnesium oxide (MgO), zinc sulfide (ZnS), and lithium niobate (LiNbO3) single crystals (Supplementary Fig. 13), which may inspire more interesting discoveries and yield even superior materials for free-space dislocation engineering.

Compared with current non-mechanical stimuli for dislocation induction, the ultrafast laser approach offers more control parameters, such as pulse energy, pulse duration, and pulse number. We demonstrate that the shape and size of dislocation-formed zones can be further optimized by adjusting these laser parameters. As shown in Fig. 4a, under different pulse energies, the dislocation-formed area elongates with the incident pulse number and then converges to a limit and is difficult to extend further. While the increase in pulse energy and pulse duration can significantly lengthen the dislocation-formed zone (Fig. 4b). Currently, the maximum and minimum lengths of the anisotropic dislocation-formed zones in PMN-PT crystals are 30.2 μm and 2.7 μm, respectively (Supplementary Fig. 15). To ensure the regularity of dislocation-formed zones, we further determine the process windows for ultrafast laser-writing dislocations in the PMN-PT crystals (Fig. 4c), where the pulse energy and pulse duration suitable for dislocation writing are distributed around 1–1.8 μJ and 600–1000 fs, respectively (Window II). When the pulse duration is short (<500 fs), dislocation formation is difficult to activate under various pulse energies (Window I), agreeing well with the previous conclusion that the dislocation induction in PMN-PT crystals requires a certain degree of thermal effects. Excessive pulse energy and pulse duration would produce significant thermal ablation, leading to unpredictable cracks and defects and destroying the controllability of dislocation writing (Window III).

Fig. 4: Optical conditions for reversible writing of high-density dislocations.
figure 4

a Dependence of the length of a dislocation-formed zone on pulse number and pulse energy. Pulse duration is set to 885 fs. Inset: the top view of dislocation-formed zone. b Dependence of the length of a dislocation-formed zone on pulse energy and pulse duration. The pulse number is set to 150k. c Process windows for laser-writing dislocations. Pulse number is set to 150k. d Process windows for erasing dislocations. Dislocations are first written using optimal laser parameters in Window II, and then erased with laser parameters in Window A, B, and C. e 3D process windows with respect to pulse energy, pulse duration, and pulse number for dislocation writing and erasing in the PMN-PT crystal. More detailed 2D process windows see Supplementary Fig. 14. f Experimental results of multi-cycle dislocation erasing and rewriting. Red dots and blue dots correspond to the lengths of the dislocation-formed zone after writing and erasing, respectively. Source data are provided as a Source Data file.

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Based on the optimized dislocation writing, we massively produce dislocations with fine morphology and determine the process windows for dislocation erasing (Fig. 4d and Supplementary Fig. 16). The parameters for erasing dislocations are significantly different from those for dislocation writing, which generally require higher pulse energies (>2 μJ) and relatively shorter pulse durations (<800 fs). According to the criterion of completely eliminating the anisotropic dislocation-formed zone without producing additional ablation at the focal center, we determine that the pulse energy and pulse duration suitable for dislocation erasing are distributed around 2–4 μJ and 300–750 fs (Window B). As shown in Fig. 4e, comprehensive 3D process windows involving pulse energy, pulse duration, and pulse number have been built to advise the high-quality writing and erasing of dislocations in the PMN-PT crystal. By using the optimal parameters, multi-cycle dislocation erasing and rewriting at the same spatial location are successfully achieved (Fig. 4f).

There is no very clear limit on the dislocation rewriting cycles (i.e., a fixed threshold number). At the current stage, the maximum number of rewriting cycles is mainly limited by the repetitive positioning accuracy of the applied translation stage in our experiments. Specifically, during repetitive erase-rewrite cycling, positional deviations in laser targeting induce cumulative stress concentration through the pile-up of residual dislocations, potentially leading to microcracks (Supplementary Fig. 17). The reliable number of rewriting cycles can be further improved by applying a translation stage with higher repetitive positioning accuracy.

Unlike those in metals, the dislocation-formed zones in transparent dielectric crystals benefit from the matrix’s transparency, allowing for excellent visibility required by potential informatics applications. Due to the controllable dislocation writing and erasing properties in the PMN-PT crystal, the laser-irradiated zone inherently exhibits three basic states: dislocation erasure, 100-oriented dislocation distribution, and 010-oriented dislocation distribution (Fig. 5a, left), supporting multi-dimensional information integration (Supplementary Fig. 18). According to Shannon’s information theory, a ternary system offers optimal information recording and transmission efficiency among integer-based systems46, as it minimizes the number of data states required to express the same amount of information. Building on this, we demonstrated ternary-encoded four-dimensional information recording in PMN-PT crystals by multiplexing the polarization dependence of ultrafast laser-induced dislocations on the basis of 3D spatial coordinates (Fig. 5a, middle). The recorded data arrays can be captured by a camera in batches and identified frame by frame (Fig. 5a, right), eliminating the need for complicated optical measurements or point-by-point scanning typically employed in multidimensional information reading.

Fig. 5: Information recording and asymmetric physical encryption in 3D space based on controllable dislocation induction.
figure 5

a Ternary information recording by using the three basic states of dislocation-formed zones. Scale bars: 5 µm, 20 µm. b Information rewriting by using the reversibility of dislocation generation in the PMN-PT crystal. The dislocation-patterned letter “PT” was first erased and then rewritten as “HL”. Scale bars: 50 µm. c Concept of multi-layer asymmetric physical information encryption in 3D space. d Experimental results of dislocation-encoded asymmetric encryption and decryption in the PMN-PT crystal. The specific parameters for information encryption and decryption are detailed in the Methods section. Scale bars: 20 µm.

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Traditionally, erasing data points inscribed within an all-inorganic crystalline matrix poses a significant challenge due to the potential for irreversible lattice damage. In this study, we demonstrate that patterns consisting of a substantial number of dislocation points can be erased and rewritten with commendable repeatability (Fig. 5b). In the ternary-encoded information recording approach, the dislocation-erased zone itself functions as a data state. Consequently, numerous rewriting operations can be executed directly on the original data without necessitating a separate erasure process, thereby streamlining the rewriting procedure.

The process windows for dislocation writing and erasing in PMN-PT crystals exhibit both considerable breadth and significant distinction, providing a rich array of parameters for the engineering of reversible dislocation induction. Using this, we propose a dislocation-based physical encryption strategy in the crystal matrix (Fig. 5c). As previously confirmed, dislocations induced with identical writing parameters can be eliminated with multiple sets of erasing parameters. Hence, we can encrypt the original data points into ciphertext by erasing them with specified parameter combinations (i.e., a parameter lock). Then, by designing the ultrafast laser re-irradiation, we can decrypt the ciphertext with a set of rewriting parameters (i.e., a parameter key).

As a proof of concept, we experimentally demonstrate multi-layer information encryption and decryption in the PMN-PT crystal based on the international Morse code (Fig. 5d). Specifically, we use one set of laser parameters to write the original data (Fig. 5d, left). Then, we use different sets of parameters to erase the original data into ciphertext to achieve encryption (Fig. 5d, middle). Finally, we use another set of laser parameters to rewrite the ciphertext into plaintext to achieve decryption (Fig. 5d, right). To unlock the encrypted data, the erased points in the ciphertext must be restored to the points and lines consistent with those in the original data. Therefore, some of the erased points should not be rewritten into lines (cyan-circled points), which can be ensured by using different erasing parameters during the encryption process. In this configuration, although these erased data points appear the same (Fig. 5d, middle), the parameters required for their point-to-line rewriting differ, making only certain erased points (blue-circled points) able to be rewritten into lines during the decryption process.

The dislocation-based approach represents an advanced asymmetric information encryption scheme featuring a differentiated parameter lock and key, corresponding to the public and private keys. The rich parameters associated with ultrafast laser-induced dislocation writing and erasing allow for a significant enhancement of the complexity of the parameter lock and key. In theory, the combinations of parameter lock and key are infinite and can be arbitrarily expanded. Importantly, the parameter key is for one-time use. If a wrong parameter key is used, the plaintext will be automatically destroyed during the decryption process and cannot be restored (Supplementary Fig. 19), permanently blocking cracking attacks. These advantages facilitate the implementation of reliable 3D information encryption.

Discussion

In conventional concepts, the dislocation induction within ferroelectric crystals is characterized by low density, irreversibility, and challenges in achieving high precision and flexibility. In this study, we propose and demonstrate that single-beam ultrafast laser irradiation can create reversible and precisely controllable high-density dislocations in PMN-PT crystals. The dislocation distribution exhibits significant anisotropy, which can be synergistically manipulated through laser polarization and crystal poling, providing multi-degree-of-freedom controllability in 3D free space. We show that the induced high-density dislocation can be erased via in-situ secondary laser irradiation, a mechanism that reduces the average spacing of dislocations below the threshold for dislocation annihilation by supersaturating the dislocation density. Under optimal parameters, repeatable in-situ dislocation erasing and rewriting can be achieved. The excellent controllability and reversible writing capabilities of our method make it promising for advanced multi-dimensional information recording and asymmetric information encryption, while also being compatible with rapid data rewriting and readout.

These findings represent a breakthrough towards precise dislocation manipulation within ferroelectric crystals, opening up new perspectives for precise 3D material modulation and potentially assisting in understanding the formation, manipulation, and elimination mechanisms of high-density dislocations in transparent dielectrics. It would be exciting to fuse ultrafast laser-based dislocation control with advanced beam control technologies (e.g., spatial light modulation, diffractive optics, and galvanometer scanning), novel materials, and advanced characterization techniques to develop a highly efficient and versatile dislocation engineering strategy, thereby opening avenues for discovering novel dislocation-mediated functionalities and optimizing material performance through targeted defect architecture design.

Methods

Materials

The PMN-PT crystals used here were grown along <001> direction by using a modified vertical Bridgman method with a boule size of Φ100 × 130 mm3. The primary PMN-PT crystal samples were cut from the crystal boules and had the composition of 0.74 Pb(Mg1/3Nb2/3)O3-0.26 PbTiO3. They took the shape of a cube with a size of 10.3 × 10.3 × 2.3 mm3, and consisted of (100), (010), and (001) surfaces. For [001]-poled PMN-PT crystals, Ag electrodes were spread on their two (001) surfaces with a 10.2 × 10.2 mm2 size. Poling was carried out along [001]-direction at room temperature and under a direct current field of 7 kV/cm for 10 min. [010]-poled PMN-PT crystals were poled in the same way as [001]-poled PMN-PT crystals, with the Ag electrodes spreading on (010) surfaces. All surfaces of primary samples were then fine ground and polished to a size of 10 × 10 × 2 mm3 (Supplementary Fig. 20).

Ultrafast laser processing

An ultrafast laser direct writing system was employed to induce and erase dislocations in PMN-PT crystals (Supplementary Fig. 21). The light source was a mode-locked regeneratively amplified Yb:KGW-based ultrafast laser (PHAROS, Light Conversion Ltd.), operating at a wavelength of 1030 nm, with a repetition rate set to 150 kHz. The ultrafast laser could be focused at various depths within the PMN-PT crystals using an objective lens to achieve 3D dislocation induction. Typically, it was focused at a depth of 40 μm from the surface of the PMN-PT crystals by a 50 × 0.8 NA objective lens for direct writing dislocations, and the radius of laser spot after focusing is about 430 nm. The dislocations were generally written by using an ultrafast laser with a pulse energy of 1.2 µJ, a pulse duration of 885 fs, and a pulse number of 150k. To erase these dislocations, a 50 × 0.55 NA objective lens was used by focusing the incident laser at the same depth as dislocation writing. Generally, the pulse energy of the erasing laser was 2 µJ, the pulse duration was 503 fs, and the pulse number was 450k.

For asymmetric encryption shown in Fig. 5d, the first layer was at a depth of 25 µm, the second layer was at a depth of 45 µm, and the third layer was at a depth of 70 µm. The encoded data points within the green rectangular area were written using an ultrafast laser with a pulse energy of 1.2 µJ, a pulse duration of 885 fs, and a pulse number of 150k. For encoded data points in the green circular area, the pulse energy of the writing laser was 0.3 µJ, the pulse duration was 4 ps, and the pulse number was 50k. To generate the ciphertext consisting only of dots, the laser parameters in the cyan circular area were set to a pulse energy of 1 µJ, a pulse duration of 614 fs, and a pulse number of 30k. Additionally, 450k ultrafast laser pulses with 2 µJ pulse energy and 503 fs pulse duration were used to erase the 010-oriented dislocation and encrypted information in the blue circular area. Finally, the parameter key for decrypting the ciphertext in the red circular area was a pulse energy of 1.2 µJ, a pulse duration of 885 fs, and a pulse number of 150k. Currently, the maximum depth of dislocation writing in PMN-PT crystal is ~300 μm (Supplementary Fig. 22).

Structural characterization

For the transmission electron microscope (TEM) characterization in Fig. 1 and Fig. 3, the sample was first polished to expose part of the dislocation-formed zone on the surface (YZ-plane). Then, the FIB slicing was performed from the exposed dislocation-formed zone on the surface along the X-axis to obtain a slice that includes a cross-section of the dislocation-formed zone on the XY plane. Since the dislocation-formed zone is a sheet-like structure in 3D space, it appears as a narrow strip on the XY plane. The TEM characterization of dislocations was performed within the scope of the narrow strip (Supplementary Fig. 23). The TEM samples were prepared using the focused ion beam technique (Fei Helios Nanolab G3 UC). The sample was thinned with a gallium ion beam at 30 kV. Lower accelerating voltages of 5 kV and 1 kV with a beam current from 15 to 5 pA were used for further thinning to reduce the ion beam damage. Subsequently, a 0.5 kV ion beam was used for the final cleaning of specimens. TEM images were obtained by using an FEI Tecnai F20 microscope operated at 200 kV.

The PFM (MFP-3D origin, Asylum Research, Oxford Instruments) was used to observe the domain structure of PMN-PT crystal. For the PFM experiments, a conductive probe (HQ: NSC18/Pt, MikroMasch) was selected. The vertical PFM phase images were obtained by Dual AC Resonance Tracking (DART) technique.

Estimation of dislocation density

Dislocation density can be estimated by calculating the number of dislocations per unit area16:

$$\rho=\frac{{N}}{{A}}$$

where N is the number of dislocations, and A is the test area. The number of dislocations within a specific area can be counted by HRTEM imaging and fast Fourier transform analysis of the dislocation-formed zone (Supplementary Note 1).