Ferroelastic materials possess switchable spontaneous strain, making them suitable for diverse functional devices^[1-3]. Structural domains are inherently formed to minimize total free energy^[4-6] and act as functional building blocks whose geometry, orientation, and mobility strongly influence electromechanical coupling^[7-9]. In particular, domain wall structures govern nontrivial material responses, including polarization rotation^[10-12], local flexoelectric effects^[13,14], and switchable conduction^[15,16], which are not achievable in monodomain configurations. To exploit these functionalities, substantial efforts have been devoted to engineering domain structures via epitaxial strain, compositional tuning, and external fields^[17-21].

Lead-based tetragonal perovskites have emerged among ferroelastic materials as exemplary platforms for domain engineering^[22,23], comprising out-of-plane polarized c-domains and in-plane polarized a-domains. The formation of a-domains accommodates epitaxial strain but also introduces ferroelastic complexity^[24-27]. These domains are generally considered mechanically pinned due to elastic clamping and high domain wall energy, which limits their responsiveness to applied electric fields^[28,29]. This intrinsic difficulty in controlling a-domains constrains the design of domain-based functionality, particularly in devices that rely on spatially reconfigurable ferroelastic states^[26,30]. To address this challenge, recent studies have primarily demonstrated dynamic a-domain switching through tip-induced local stress^[31,32]. However, these approaches often depend on external mechanical forces and localized stress gradients to overcome pinning^[33,34], limiting their practical applicability in purely electric-field-driven devices. Moreover, switching was typically observed in fully developed or merged domains^[35], without addressing the possibility of selectively controlling partially nucleated ferroelastic states.

In this study, we propose that intrinsic structural inhomogeneities arising from local lattice strain enable the selective and reversible switching of a-domains under sub-coercive voltages. By targeting structurally perturbed regions within the c-domain matrix, discrete a-domain nucleation and annihilation can be achieved without mechanical bias or large electric fields. This approach shows that ferroelastic switching pathways can be finely tuned by engineering the local elastic energy landscape, granting access to metastable states that remain inaccessible under uniform strain conditions. Furthermore, thermodynamic modeling that incorporates elastic energy relaxation induced by local strain supports the experimental observations, revealing that partially developed a-domains exhibit lower switching barriers than fully stabilized domain configurations. This energetic perspective underscores the importance of local structural features in facilitating programmable ferroelastic behavior, moving beyond conventional views of a-domain dynamics as passive or secondary phenomena. Our findings demonstrate a novel approach for reversible and selective a-domain switching, providing a foundation for designing reconfigurable ferroelastic domain architectures through the controlled manipulation of intrinsic strain fields and low-energy electric stimuli.

The high-quality epitaxial PTO/SRO heterostructure grown on (001) STO substrates was confirmed by HR-XRD and ferroelectric P-E hysteresis measurements [Supplementary Figure 1A and B]. The thickness of the PTO film was measured to be ~200 nm, and the rocking curve^[38,39] and surface morphology results exhibit a clear a/c domain matrix [Supplementary Figures 1A and 2]. A HAADF-STEM image along the (100) plane reveals atomically flat, well-grown PTO/SRO layers at the nanoscale [Figure 1A]. To identify the two distinct orientations of a- and c-domains in PTO, DPC imaging was employed by analyzing the polarization orientation. DPC directly visualizes the internal electric field through beam deflection [Supplementary Figure 3], from which a polarization map was reconstructed by combining the x- and y-directional components of the field. The initial domain configuration of PTO showed that the polarization of the c-domain is oriented downward, forming 90° domain boundaries with neighboring a-domains [Figure 1B]. Upon switching the c-domain polarization upward by non-contact corona poling along the [001] direction, the a-domains were also reversed to prevent charge accumulation at the domain wall [Figure 1C]^[1].

Consistent with TEM results, the initial domain structure of thin line-shaped a-domains embedded in a crystallographic configuration between relatively large c-domains is also observed in the PFM amplitude mapping [Supplementary Figure 1C]. Moreover, bias-dependent PFM phase mapping under an applied voltage (V_a) exceeding the coercive voltage (V_c) reveals that the initial electric polarization is oriented downward toward the SRO electrode [Supplementary Figure 1D]. Considering the clear c-domain switching observed when |V_c| < |V_a|, the ferroelastic domain switching process was clarified through the following four steps: (1) identification of the initial domain structures; (2) application of a negative bias [V_a < 0 or V_a(-)] at the center of a large c-domain using a sweeping direct current (DC) bias combined with an alternating current (AC) voltage applied to the PFM tip [Supplementary Figure 1E]; (3) sweeping of a positive bias (0 < V_a or V_a(+)) over the same region; and (4) sweeping of negative or positive biases at different positions. During each bias application, PFM amplitude and phase loops were recorded, and the resulting domain structures were subsequently characterized by PFM mappings. The maximum V_a was determined by referencing the coercive voltage extracted from the switching of an adjacent, smaller c-domain and was assumed to be comparable in the tested region.

When a voltage higher than the coercive voltage (|V_c| < |V_a| = 7 V) was applied at position #1 [Figure 2A and B], reversal of the c-domain polarization was clearly observed, exhibiting a circular pattern at the edge of the reversed domain. An a-domain was newly formed during c-domain switching, even within the neighboring c-domain matrix [Figure 2B]. Once the a-domain was created, it remained even after the c-domain polarization was restored to its original downward state upon the application of V_a = +7 V [Figure 2C], indicating irreversible c- to a-domain switching. The switched domain is further evident in the PFM phase mapping [Supplementary Figure 4A-C], displaying a circular contrast in the reversed region as well as a 180° switched phase signal. After the initial formation of the a-domain, no additional a-domains were generated under similar bias-application procedures intended to induce c- to a -domain switching within the reduced c-domain matrix (#2 and #3 in Figure 2C). Because the formation of an a-domain during c-domain switching has been attributed to strain-energy relaxation, the restriction on further a-domain formation within the same volume can also be understood in terms of limited strain relaxation^[9,24,31,33].

The PFM amplitude and phase loops under the condition |V_c| < |V_a| are presented in Figure 2D and Supplementary Figure 4D, obtained throughout the domain switching procedure. The typical PFM amplitude signal (black dotted line in Figure 2D) proves clear c-domain switching at approximately 4~5 V, whereas the similar amplitude values at 0 V between the initial state and V_a(-) yield a pronounced contrast at the edges of domains with different electric polarizations. The P-E hysteresis curves [Supplementary Figure 1B] also support clear polarization switching at V_c < V_a. However, unlike the PFM results, the P-E loops exhibit a much lower coercive voltage (V_c ≈ 2 V), which can be attributed to the different measurement mechanisms and macroscopic contributions, such as charge transport, leakage current, interfacial effects, and experimental conditions.

A conventional PFM amplitude and phase loop was observed at position #1 under V_a(-), showing a significant change at V_c. Given the lower V_c compared to the other cases where |V_a| < |V_c|, and the absence of clear evidence for c- to a-domain switching at V < V_c, the localized reduction of the c-domain switching barrier causes it to closely merge with the c- to a-domain switching voltage in the PFM amplitude curve. This overlap makes a clear distinction between c-domain switching and a-domain formation difficult. In addition, once the a-domain is created, V_c for c-domain switching back to the initial state [V_c(+) = +3 V] is considerably lower than usual, probably due to the assistance of the a-domain in nucleating reversed c-domains^[1]. Meanwhile, slightly increased V_c values were observed at positions #2 and #3 compared to #1, i.e., c-domain switching accompanied by a-domain formation (#1) occurred at V_c = -5.0 V, whereas switching without a-domain formation (#2 and #3) occurred at V_c = -5.5~-6.0 V. These results suggest a correlation between c-domain switching and a-domain formation, indicating that the strain energy released by a-domain creation^[9,24,31,33] facilitates switching more readily than pure c-domain reversal.

To further investigate strain-related a-domain formation, a voltage lower than V_c (|V_a| = 4 V < |V_c|) was applied at position #4 [Figure 3A and B] to restrict c-domain switching. A clear a-domain was created in the middle of the c-domain and persisted even after subsequent application of positive voltages (at position #4 and #5 in Figure 3C). This phenomenon is more evident in the PFM phase mapping results in Supplementary Figure 5, showing a clear contrast from the created a-domain without observable c-domain switching, unlike the case of |V_c| < |V_a|. However, PFM amplitude measurements provide better insight into c- to a-domain switching, as the piezoelectric coefficient of a-domains (d₂₄ = 56 pm/V)^[36] is ~30% smaller than that of c-domains (d₃₃ = 79 pm/V)^[36]. This is also evident in the PFM amplitude mappings due to distinctly different PFM values at 0 V for c- and a-domains, represented by gray and black contrasts, respectively. In Figure 3D, an elliptical PFM amplitude loop (red dotted line) was observed in the c-domain region under V_a < V_c due to the unswitched c-domain polarization, whereas a typical PFM amplitude loop (black dotted line) were observed under V_c < V_a. At position #4, a pronounced drop in amplitude at V_a = -4.0 V (blue closed circles) supports c- to a-domain switching well below the threshold for polarization reversal from down (c^-) to up (c⁺) domains (V_c = -5.8 V). The reduced amplitude values did not recover to the initial values upon application of V_a = +4 V, instead showing another elliptical loop at lower PFM amplitude.

The created a-domain did not revert to c-domain even after applying V_c < V_a = 7 V at the position #5 (green triangles in Figure 3D), instead exhibiting a larger elliptical loop. According to the previous research^[30], the creation and annihilation of a-domains within a c-domain matrix depend on overcoming the energy barrier associated with the a/c domain boundary. However, the electrostatic and elastic energies induced by the applied bias, together with the a/c domain wall surface energy, are insufficient to fully explain the observed irreversible ferroelastic switching, as these mechanisms are generally limited to reversible processes. Recent studies^[40-42] have demonstrated that misfit dislocations and point defects introduce local strain fields that alter the domain wall dynamics and create additional energy pathways for domain motion. They suggested that the role of local strain is not a passive obstacle that hinders switching, but rather it acts as a key design variable that actively programs the switching path and reversibility by locally reconfiguring the energy landscape. Therefore, for a comprehensive understanding of ferroelastic switching in PTO thin films, the effects of local strain induced by structural deformations (e.g., defects and dislocations) should also be taken into account.

Considering the domain switching shown in Figures 2 and 3, a-domain formation initiates from specific positions where the voltage is applied. This suggests that partially generated, transient a-domain fragments at the biased positions within the c-domain act as nucleation sites for c- to a-domain switching and subsequently propagate along crystallographic directions to regions without applied voltage. Consequently, the interconnected a-domains represent a more energetically stable state compared to isolated partial a-domains within the c-domain. This observation is consistent with the PFM mapping results, in which a-domains are predominantly interconnected [Supplementary Figure 1C] and remain stable even under conditions of V_c < V_a (position #5 in Figure 3C). Conversely, this implies that if partial a-domains are generated under specific conditions, they have the potential to revert to c-domains upon application of bias voltage, enabling reversible c- to a-domain switching. To examine this possibility, the following procedure was performed: (1) obtaining the initial domain structures, (2) applying bipolar V_a, which involves first applying V_a(-) immediately followed by V_a(+) at the center of a c-domain to determine whether partial a-domain structures were formed, and (3) moving to the partial a-domains and applying V_a(+) to induce switching back from a-domain to c-domain.

In Figure 4A and B, a partial a-domain is formed without connection to other a-domains upon application of V_a = 6 V at position #6. The newly formed a-domain exhibits a discrete line structure, with the switched-back c-domain observed at the tip bias position. The remaining fragments of a-domains were also reverted to c-domains upon additional application of V_a(+) = +7 V, as shown in Figure 4C. To understand the piezo-response associated with reversible c- to a-domain switching, the bias-dependent PFM amplitude was plotted in Figure 4D, obtained during the DC sweeping process. A complete hysteresis loop is observed at position #6, with significant drops in amplitude at V_c→a = -4.2 V and recovered to the initial value at V_a→c = +3.5V. This domain switching does not include c^-- to c⁺-domain switching, as V_c(-) = -6.7 V, which is also evident in the PFM phase results in Supplementary Figure 6, showing no clear changes during c- to a-domain switching. Furthermore, application of V_a(+) also does not switch the c-domain at V_a = +6 V, even when it exceeds V_c(+) = +4.5 V, because the initial electric polarization of PTO is directed downward toward the SRO electrodes. Unlike the well-defined hysteresis observed in the PFM amplitude at position #6, the remaining fragments of a-domains (#7 and #8) exhibit gradual increases in amplitude during application of V_a(+) = +7 V to switch back to c-domains. These changes in PFM amplitude may be associated with the unstable states of the remaining a-domains, which could also relate to the relatively high and low PFM amplitude values at V_a = 0 V before and after bias application, respectively, compared to those observed at #6.

To understand the mechanisms underlying domain switching, a thermodynamic model was employed that considers the total free energy (ΔF_total) consisting of voltage-induced electrostatic ($$ \Delta U_{i}^{e s}(V) $$) and elastic ($$ \Delta U_{i}^{e l}(V) $$) energies for each domain type (i = a- or c-domains), along with the elastic energy ($$ \Delta U_{w}^{e l}\left(\varepsilon_{\mathrm{a}}\right) $$) associated with in-plane lattice strain (ε_a) and the surface energy (U_w) required for a-domain formation. Under an external voltage, the c-domain follows $$ \Delta F_{c}(V)=\Delta U_{c}^{e s}(V)+\Delta U_{c}^{e l}(V) $$ (blue line in Figure 5A), whereas the a-domain follows $$ \Delta F_{a}(V)=\Delta U_{a}^{e l}(V) $$ (red line in Figure 5A) because $$ \Delta U_{a}^{e s}(V)=0 $$. Forming an a-domain within the c-domain matrix requires additional energy to overcome the energy barrier of U_w associated with creating the a/c-domain wall. When ΔF_c (V) becomes comparable to U_w under an applied voltage, ΔF_total relaxes by reaching $$ \Delta F_{w}\left(\varepsilon_{\mathrm{a}}\right)=\Delta U_{w}^{e l}\left(\varepsilon_{\mathrm{a}}\right)+U_{w} $$ and adjusting the a-domain width to w_a [Figure 5B]. In this calculation, w_a is fixed at 20 nm based on DPC results [Figure 1], which is unattainable at ε_a = 0, where w_a exceeds 70 nm. Considering the misfit between SRO and PTO, a local ε_a of 0.39% is assumed to allows a-domain formation with w_a = 20 nm. U_w is treated as constant across different ε_a since w_a is fixed. From the PFM amplitude loops, the c-domain with downward polarization switches either to an upward-polarized c-domain at V_c→c ≈ +6 V or to an a-domain at V_c→a ≈ +4 V, corresponding to energy barriers of ΔF_c (V) = ΔF_c→c and ΔF_c (V) = ΔF_c→a = U_w, respectively.

From the PFM results, three types of domain switching were identified, which are further evidenced by the formation of various a-domains after area bias application at V_DC = -4 V [Supplementary Figure 7]: (i) non-switching, (ii) irreversible c- to a-domain switching, and (iii) reversible c- to a-domain switching. (i) Non-switching: The energy required to form an a-domain depends on the surface area of the a/c-domain wall [Figure 5B and C]. Therefore, creating a second a-domain within the same unit volume of the c-domain matrix requires twice the surface energy (ΔF_c→2a = 2U_w). However, the voltage needed to form this second a-domain exceeds V_c→c ≈ +6 V, causing c-domain switching to occur before the second a-domain can form [Figure 2C]. In addition, as the number of a-domains increases, the total free energy of the system also rises, energetically limiting the number of a-domains that can form within a given c-domain volume.

(ii) Irreversible c- to a-domain switching: A new a-domain can be created in a pristine c-domain matrix by overcoming the a/c-domain wall energy U_w and releasing strain energy to reach ΔF_w (ε_a) under |V_a| < |V_c|. To achieve a- to c-domain switching, ΔF_a (V) should become comparable to ΔF_c (V), similar to the c- to a-domain switching mechanism [Figure 5C]. This requires applying a positive voltage to PTO so that the energy state of the c-domain matches that of the a-domain. However, in most cases excessive release of strain energy makes it impossible to reach ΔF_c (V) without causing significant leakage currents or electrical breakdown. Our calculations indicate that a tip bias of +62 V would be required to switch an a-domain back to a c-domain, a level at which the thin film cannot be sustained due to excessive electric current. Therefore, enabling a- to c-domain switching without electrical damage requires modifying ΔF_w (ε_a) by tuning ε_a.

(iii) Reversible c- to a-domain switching: In PTO structures, strain is typically relaxed by forming a-domains due to the large misfit between the in-plane lattice parameters of SRO (b_SRO) and PTO (a_PTO). If a_PTO is locally increased by defects or dislocations, the formation of an a-domain within the c-domain matrix releases insufficient strain energy [Figure 6A and B], allowing the a-domain to switch back to the c-domain. To explain this ferroelastic domain switching using the thermodynamic model, the influence of local strain should be considered because both ΔF_w (ε_a) and ΔF_a→c depend on ε_a (inset of Figure 6B). Therefore, increasing ε_a lowers ΔF_a→c, enabling ferroelastic switching from the a- to the c-domain at lower positive voltages.

Consistent with this context, we experimentally confirmed the presence of local strain within the PTO film. Because this strain originates from the lattice misfit between the PTO and SRO layers, it is naturally associated with substrate-induced mismatch as well as growth-related defects that accumulate during epitaxy. Dark-field TEM (DF-TEM) imaging clearly visualizes contrast variations arising from threading dislocations along the vertical direction and from strain fields localized near the interface [Supplementary Figure 8]. To obtain more quantitative evidence of the interfacial strain, we performed lattice-parameter analysis using atomic-scale HAADF-STEM [Supplementary Figure 9]. The extracted tetragonality map of PTO film reveals distinct in-plane lattice strain confined to the interfacial region, which is fully consistent with the expected strain distribution in this heterostructure and corroborates our theoretical calculations. Therefore, the phenomenological results can be interpreted within the thermodynamic model as a function of ε_a.

Because ferroelastic switching is accompanied by structural deformation, the influence of defects with high energy states diminishes as they relax toward normal lattice configurations. Consequently, as the number of ferroelastic switching cycles (n) increases, newly formed a-domains release progressively more free energy [Figure 6A-C]. In contrast, V_c→a remains unchanged regardless of n, as c- to a-domain switching depends on U_w rather than ε_a. This leads to the asymmetric PFM amplitude-voltage hysteresis loops, where V_c→a stays constant while V_a→c increases with n, as shown for the nth loops in Figure 6C. To validate the ε_a-induced ferroelastic switching model, a tip contact force was applied to the a-domain at position #5 in Figure 2, where irreversible a- to c-domain switching was observed even at V_a = 7 V (black line in Figure 6D). Increasing the tip contact force reduces both the tetragonality (α) and lattice misfit (Φ), thereby lowering the relaxation energy in a manner similar to that of structurally defect-induced ε_a. Although PFM amplitude mapping under 500 nN tip force was not feasible for direct visualization of the ferroelastic transition, the bias-dependent PFM amplitude curves clearly reveal a- to c-domain switching [Figure 6D]. The amplitude exhibits an abrupt increase at +2 V, maintains the value throughout the voltage sweep, and returns to its original value at -4 V. This behavior closely resembles the ferroelastic switching observed in Figure 6C, where V_a→c varies with ε_a while V_c→a remains nearly constant during voltage cycling, with similar amplitude values observed during the a- to c-domain switching process. The retention and fatigue characteristics of the reversibly switched a-domains do not yet demonstrate the long-term stability required for practical applications. Repeated cycles of reversible c- to a-domain switching indicate that as n increases, V_a→c also increases, causing the switching behavior to gradually become more irreversible [Figure 6C and E]. These limitations in stability strongly suggest a path for future device optimization through precise strain engineering, e.g., tuning strain, defect density, and film thickness.

The fundamental mechanism of reversible c- to a-domain switching under sub-coercive fields is driven by local strain inhomogeneity. This mechanism is not exclusive to the PTO/SRO heterostructures but reflects a general ferroelastic switching principle. It is applicable across a broad range of ferroelectric systems containing unconventional domain switching, in which ferroelastic transitions follow low-energy elastic pathways activated by local strain gradients or structural disorder, regardless of material composition. For instance, Pb(Zr,Ti)O₃ films exhibit sub-coercive ferroelastic rotation at defect-rich or strain-perturbed regions^[31]. Similarly, BiFeO₃ shows dramatically enhanced mobility of its 71° and 109° ferroelastic boundaries where strain relaxation occurs^[28]. Comparable trends emerge in compositionally graded ferroelectrics^[33] and HfO₂-based systems^[43], reinforcing that the same strain-coupled mechanism governs accessible switching routes. Although the thermodynamic model presented here is specific to PTO, the governing physical terms (elastic energy, domain-wall energy, strain-dependent electrostatic contribution) are material-independent and establish a conceptual framework where local elastic inhomogeneity can be used to program domain switching across diverse ferroelastic materials.

In this study, we demonstrate that selective and reversible switching of a-domains can be achieved by exploiting intrinsic strain inhomogeneities under sub-coercive voltages. Localized structural perturbations associated with partially formed a-domains significantly reduce the elastic energy barriers and total free energy, thereby enabling reversible a- to c-domain transitions. By systematically comparing three distinct types of domain transitions (non-switching, irreversible switching, and reversible switching) we identified a strong correlation with variations in the local strain environment. That is, reversible switching occurs predominantly in strain-perturbed regions where metastable domain configurations are favored. Although mechanical loading experiments also altered the elastic energy landscape, they were less effective than intrinsic defects in sustaining reversible switching, highlighting the critical role of local structural inhomogeneity. While our findings establish the fundamental mechanism, the observed stability limitations emphasize that advanced strain engineering is the direct and most promising route to enhance the retention and cyclability for device applications. The ability to achieve sub-coercive switching is key for energy efficiency and scalability down to the nanoscale, offering excellent integration potential for reconfigurable logic gates and non-volatile memories. Our work establishes intrinsic strain control as a viable strategy for programmable ferroelastic switching and paves the way for designing reconfigurable ferroic devices through nanoscale elastic-field manipulation.