Observation of Micro-Scale Domain Structure Evolution under Electric Bias in Relaxor-Based PIN-PMN-PT Single Crystals

: Relaxor ferroelectrics play a vital role as functional components in electromechanical devices. The observation of micro -scale domain structure evolution under electric bias in relaxor fer-roelectrics has posed challenges due to their complex domain morphology characterized by small-sized domains. The present study aims to investigate the dielectric diﬀusion –relaxation characteristics, domain structure, and domain switching evolution under electric bias in high-performance single crystals of Pb(In 1/2 Nb 1/2 )O 3 -Pb(Mg 1/3 Nb 2/3 )O 3 - 33PbTiO 3 . The ﬁndings reveal the presence of strip - like domain patterns that interlock irregular small - sized nanodomains in PIN -PMN- 33PT single crystal s . Furthermore, the sample undergoes three distinct stages under electric bias, including the nucleation of new domains, the gradual forward expansion of domains, and the lateral expansion of domains. These observations provide valuable ins ights for understanding and exploring domain engineering techniques in relaxor ferroelectrics.

Since the discovery of relaxor-PT single crystals, various strategies have been developed for improving their piezoelectricity, including ion-doping modification, phase boundary construction, structural heterogeneity regulation, etc [17][18][19].For example, Li et al. achieved groundbreaking piezoelectricity with a piezoelectric coefficient of d33 ~ 4100 pC/N in Sm-doped PMN-PT single crystals by increasing the local structural heterogeneity and flatting the local free energy landscape [18].In Nd-doped PIN-PMN-PT single crystals, an excellent piezoelectric performance of d33 ~ 3500 pC/N has also been achieved [20].Moreover, acceptor doping has been widely demonstrated to improve the highpower characteristics of relaxor single crystals, such as in Mn-doped PIN-PMN-PT single crystals [21].In recent years, domain engineering technology has gained significant attention to improve the piezoelectricity in relaxor single crystals.Unlike traditional performance optimization methods, domain engineering technology is usually combined with the poling process and does not require an adjustment in the material composition or preparation process.Instead, domain engineering technology optimizes the piezoelectric performance by tailoring the domain structure and fully utilizing piezoelectric anisotropy.
The poling process is crucial in realizing piezoelectricity in ferroelectric ceramics and single crystals by breaking spatial-inversion symmetry to generate non-zero piezoelectric constants on a macroscopic scale.Typically, the poling process involves the application of a strong electric field to establish a well-organized crystalline orientation, which induces the reorientation of spontaneous polarizations within ferroelectric domains towards the applied field direction.The poling process is accompanied by domain evolution, involving domain wall motion and adjacent domains merging.Thus, delving into the domainswitching process under electric bias is essential for understanding and exploring domain engineering techniques in ferroelectrics.For instance, the recently emerging alternating current poling (ACP) method has achieved remarkable piezoelectric performance in relaxor-based single crystals by manipulating the domain evolution and customizing thedomain structure [22][23][24][25][26].However, observing the domain structure evolution at the micro-scale under electric bias in relaxor-based ferroelectrics is challenging due to their intricate domain morphology characterized by small-sized domains within these materials.
In addition to the traditional electromechanical applications, the artificial synapse devices based on ferroelectric materials, such as the ferroelectric tunneling junction (FTJ) and ferroelectric field effect transistor (FeFET), hold great promise for applications in neuromorphic computing and can help solve the bottleneck problem of traditional von Neumann architectures [27][28][29][30].The FeFET is a field effect transistor (FET) that uses ferroelectric material as a gate insulator, which has the advantages of non-destructive readout, low power consumption, and high operating speeds, are widely used in non-volatile storage.Principally, due to the Coulomb interaction between the carriers in the channel and the intrinsic electric polarization in ferroelectric, the carrier density can be modulated depending on the polarization orientation that is controlled by applying a gate voltage [31].This allows the modulation of threshold voltage and channel conductance to behave in a nonvolatile manner, where this non-volatility comes from the ferroelectric properties [32].Therefore, it is believed that the study of micro-domains and their electric field-induced polarization switching dynamic of ferroelectric materials is equally important for the design and development of artificial synapse devices based on ferroelectrics.
Piezoresponse force microscopy (PFM), as a high-resolution technique, has been proven to possess the capability to investigate the characteristics and nanoscale dynamics of ferroelectric domains.In this study, we systematically examined the static domain patterns, local polar disorder, and polarization switching dynamics of 27PIN-40PMN-33PT (PIN-PMN-33PT) single crystals, employing PFM.Consequently, we discovered unique strip-like domain patterns that interlock irregular small-sized nanodomains and clarified the micro-scale domain structure evolution process under electric bias.These observed distinctive ferroelectric domains and their dynamic switching behaviors contribute to tracing the source of the extraordinary piezoelectricity in relaxor-PT single crystals.

Experimental
The 27PIN-40PMN-33PT single crystal was grown using the modified Bridgman method in this study [11].Crystallographic orientations of the sample were determined using X-ray diffraction.The crystals were cut into some plates with directions of //[100]C//[010]C//[001]C to implement the measurements.Before the electric measurements, both (001)C surfaces were coated with gold electrodes by the sputtering procedure.The ferroelectric performances were characterized using a Premier II system (Radiant Technologies).The frequency-dependent permittivity-temperature spectra were measured employing a precision LCR meter (Agilent E4980A).The static ferroelectric domains and polarization switching dynamics were examined utilizing PFM imaging (Cypher ES, Asylum Research).

Results and Discussion
Figure 1 illustrates the X-ray diffraction (XRD) pattern of a powder form of PIN-PMN-33PT single crystal.The sample exhibits a pristine perovskite structure with no detectable impurities.A broad (200) diffraction peak without any splitting demonstrates that the prepared sample is located at the morphotropic phase boundary (MPB) while maintaining a rhombohedral (R) structure as its main body.It is well-known that, due to the symmetry constraint imposed by the crystal structure, the R-phase PIN-PMN-PT single crystals possess various types of domain configurations, including 180°-domain, 109°-domain, and 71°-domain.Figure 2a shows the permittivity-temperature spectra of PIN-PMN-33PT single crystals measured upon heating at 1 K/min with the measurement frequency from 100 Hz to 100 kHz.There exist two obvious dielectric anomalies at the temperature of TR-T (around 375 K) and Tm (around 471 K), which correspond to the phase transition temperatures of R-tetragonal (T) and T-cubic (C) transitions, and these two phase transition temperatures in the PIN-PMN-33PT single crystals are very close to the values (TR-T is 369 K, Tm is 470 K) that have been reported with similar compositions [14].Moreover, both phase transition temperatures in the PIN-PMN-33PT single crystals are higher than in the binary PMN-PT single crystals with similar PT compositions (the TR-T and Tm of PMN-33PT single crystals are 342 K and 422 K, respectively) and other comparable PT compositions, suggesting that the former possesses enhanced temperature stability [33][34][35][36].Furthermore, as depicted in Figure 2a, the permittivity-temperature spectrum exhibits typical diffuse phase transition (DPT) behavior, characterized by a diffused frequency-dependent dielectric peak around Tm, known as dielectric diffusion-relaxation characteristics.Generally, relaxor ferroelectrics exhibit similarities to a polar-glassy system at high temperatures.Consequently, the Vogel-Fulcher law, defined as Equation ( 1), was established to elucidate their Tm-frequency (f) relation [37,38].
Herein, f and k refer to the frequency and Boltzmann constant, respectively; activation energy and Debye frequency are represented by Ea and f0, respectively; and Tf denotes the static freezing temperature.In this case, the Ea discusses the polarization fluctuation in an isolated cluster above a static freezing temperature (Tf) induced by establishing a shortrange order between surrounding polar clusters.As the temperature decreases, reaching lower Tf values, the thermal activation behavior of the electric dipolar entities undergoes a freezing phenomenon.The inset in Figure 2a demonstrates a well-fitted Tm-f relation for the prepared sample using the V-F law.The fitting result gives a Tf value of 466.3 K, which is not only higher than that (Tf ~ 387 K) observed in the R-phase PMN-27PT single crystal but also higher than the Tf value (Tf ~ 432 K) obtained for the PIN-PMN-27PT single crystal with a lower PT composition [39].It suggests that augmenting the composition of PbTiO3 in the PIN-PMN-PT can enhance the static freezing temperature of the polarization fluctuation.To characterize the strength of dielectric diffusion for PIN-PMN-33PT single crystals, the modified Curie-Weiss law, defined as Equation ( 2), is proposed [40].
Here, ε represents the dielectric constant at various temperatures, εm denotes the permittivity at a temperature of Tm, and C refers to the Curie-like constant.Additionally, the parameter γ signifies the extent of dielectric diffusion, with values between 1 and 2. A larger γ value indicates stronger dielectric diffusion behavior.Figure 2b presents the fitting results for PIN-PMN-33PT single crystals.The fitting parameter γ is determined as 1.56 at a frequency of 100 kHz.Combining the fitting results of the Vogel-Fulcher law indicates that the PIN-PMN-33PT single crystals exhibit typical relaxor behavior.
To examine the performance temperature stability of PIN-PMN-33PT single crystals, Figure 3 gives the P-E loops at various temperatures and the relationship between the Pr and temperature.From Figure 3a,b, it is observed that the P-E loops maintain a rectangular shape from 298 K to 443 K, indicating the preservation of the macroscopic ferroelectricordered state within the sample at this temperature range.However, as illustrated in Figure 3b,d, the P-E loop exhibits a double-loop-like shape at 458 K, accompanied by a sharp drop in Pr.These observations suggest the disintegration of macroscopic long-range-ordered domains into disordered nanoscale domains, corresponding to the recovery of the thermal activation behavior of electric dipoles.Following the previous study on relaxorbased PMN systems, it is known that during the cooling process, the size of nanoscale domains significantly increases around the Tf, while the number of nanoscale domains reaches a maximum value [47][48][49][50].Applying an external electric field can prompt the formation of macro-domains and an ordered ferroelectric phase at temperatures below Tf.As a result, the P-E loop becomes rectangular.A powerful external electric field can also stimulate a transient long-range polar order within the temperature range of Tf to Tm.However, this transient state of order is unstable and deteriorates once the electric field is removed.This phenomenon is due to the thermally activated reorientation of dipoles in the nanoscale domains.Consequently, the polarization experiences a significant decline upon reducing the electric field.Thus, the double-like hysteresis loops can be observed around Tf accompanied by discontinuous drops in Pr.It is common knowledge that the ferroelectric domain structure and its domain switching dynamics significantly influence macroscopic electromechanical characteristics.In this study, before PFM measurements, the measured surface of the sample was polished, followed by annealing at 573 K to eliminate any mechanical stresses induced during crystal growth, cutting, and polishing processes.Figure 4a,b gives the PFM amplitude and phase images with the size of 10 × 10 µm 2 of the unpoled sample, respectively.Figure 4c presents a 3D morphology of the PFM phase image overlaid with the height image.The variations in the height of the 3D image correspond to surface roughness, which is approximately several nanometers, while the color-coded regions (orange and blue) indicate the orientation of vertical polarization vectors.Notably, the distribution of these orange and blue regions is independent of the crystal topography, indicating that the ferroelectric domains remain unaffected by the surface roughness.
Figure 4a,b shows that the PIN-PMN-33PT single crystals present a complicated domain structure.The presence of nanoscale domains is a characteristic feature of relaxorbased ferroelectrics.In Figure 4b, one can observe the coexistence of a large number of nanoscale domains (depicted as blue areas) within the domains on a micrometer scale (depicted as orange areas), and these domain structures are considered to be 109° and 71° ferroelastic domains.Additionally, it is worth noting that there is a higher proportion of large domains than small ones.Previous studies have established that this nanoscale domain structure is owing to the inhibition of polar nanoregions (PNRs) growth through the influence of quenched random electric fields (REFs) at high temperatures, which are induced by diversity chemical bonding and structural heterogeneity in perovskite ferroelectrics [48][49][50][51].To gain a more detailed understanding of the domain characteristics, Fig- ure 4d,e presents enlarged 5 × 5 µm 2 PFM amplitude and phase images drawn from Figure 4a,b, respectively.Figure 4f shows a 3D topography visualization of the phase image overlaid on the amplitude image, facilitating a better exploration of the polarization orientations of the ferroelectric domains.Analysis of the PFM mappings reveals that the phase difference between large and small domains is approximately 180°, indicating opposite polarization orientations.Furthermore, no clear interfaces are detectable within the large domains except for the domain walls that separate large and small domains.Although small domains segregate the large domains, these separated areas remain interconnected, likely contributing to the stability of the intrinsic ferroelectric domains.The average autocorrelation function can be employed in relaxor ferroelectrics to assess domain dimension and the associated short-range polar ordering quantitatively.The relationship is expressed as Equation (3) [52][53][54][55].
Wherein the parameter <ξ> represents the average domain size, reflecting the level of polarization disorder.A diminished <ξ> value implies a heightened local polar disorder.It suggests that the PIN-PMN-33PT single crystals own a small domain size and strong local polar disorder, which is consistent with the observed PFM amplitude and phase images as well as their typical relaxation behavior.
The domain evolution process of the PIN-PMN-33PT single crystal induced by the PFM probe tip bias (Vt) was captured and recorded using PFM techniques, as illustrated in Figure 5.The scanning area is 5 × 5 µm 2 within the (001) crystallographic plane, and the Vt is imposed in the [001]C orientation.It is essential to apply a significant electric driving force that surpasses the energy barrier to facilitate the switching of ferroelectric domains.At the microscopic level, the nucleation of a domain requires a critical dimension (rc), which is contingent upon the strength of the electrodynamic force [56,57].Specifically, if an electric field-induced geometrical dimension falls within the 0 < a < rc, the domain will revert to its original state after nullifying the electric field.Alternatively, if a > rc, the nucleated domain will exhibit stability and persist in its growth trajectory.At the applied tip bias of 0 V, the sample presents irregular small domains embedded within the larger domains, as depicted in Figure 5a.When the tip bias is raised to 3 V, significant changes are observed in the PFM mappings shown in Figure 5b.This lack of observable changes might be attributed to one of two reasons: (ⅰ) the electric driving force generated by the 3 V tip bias is insufficient to surmount the requisite energy barrier for domain switching, hence leading to the absence of domain switching, or (ⅱ) the geometrical dimension induced by the 3 V tip bias is smaller than the critical dimension required for domain nucleation, causing the nucleated domains to switch back to their original state.According to the report on the domain structure and its dynamical behavior of the [001]C-oriented PIN-49PMN-27PT single crystals with R-phase, we found that some new domains formed when a small tip bias of 0.5 V was applied to the sample [39].The results indicate that the PIN-PMN-33PT single crystals show better electric field stability than the PIN-PMN-27PT single crystals at the nanoscale, and this is consistent with the result that the former has a higher Ec [39].However, as the tip bias is further increased to 5 V, the small domains expand outward from the irregular nanodomain walls, which is similar to the PMN-27PT and PIN-PMN-27PT single crystals with R-phase.The reason may be that the irregular domain walls could enhance the local poling electric field at the tip apex, and such an enhanced electric field is substantially beneficial for the nucleation of the reverse domains [58].Moreover, the tip bias-induced domain expansion indicates that the initial polarization orientations within the larger domains oppose the direction of the tip bias.After applying the tip bias, the new domains begin nucleation and grow from the domain walls.In general, reducing the domain size leads to an increase in domain wall density.Moreover, the piezoelectric response of domain walls is inferior to that of the ferroelectric domains.Therefore, this suggests that small domains may negatively impact the piezoelectric response.However, examining the domain-switching characteristics of PIN-PMN-PT single crystals suggests that the domain walls promote polarization switching under electric drive.It contributes to a positive effect on the piezoelectric response.Hence, it can be inferred that small-sized ferroelectric domains have dual effects on piezoelectric properties.However, in the case of the PIN-PMN-33PT single crystals (which exhibit an ultrahigh d33 of 2556 pC/N), it is believed that small domain sizes or high domain wall densities are advantageous for achieving high piezoelectric properties.
By elevating the tip bias from 5 V to 7.5 V, the sizes of the small irregular domains experience significant growth due to polarization switching evoked by the electric field, as shown in Figure 5d,e.Consequently, the strip-like domains formed by these smaller domains become disrupted.When the PIN-PMN-33PT single crystal is subjected to a PFM tip bias of 8V, as exemplified in Figure 5f, the polarization switching of the crystal is essentially complete, but numerous spot-like nanodomains are observed in both the PFM amplitude and phase mappings.Moreover, as the tip bias reaches 9 V and 10 V, represented in Figure 5g,h, we can also find the small spot-like domains in the PFM images of the PIN-PMN-33PT single crystal.The reason for generating these small spot-like domains may be that the new domains induced by the PFM tip bias are partially flipped back to their original orientation owing to the depolarization behavior of the single crystal when the electric field is removed.Conducting direct observations of the domain-switching process has identified three distinct stages experienced by PIN-PMN-33PT single crystals under electric bias.These stages encompass (i) the nucleation of new domains, (ii) the gradual forward expansion of domains, and (iii) the lateral expansion of domains.This clarification of the domain-switching process in high-performance relaxor-based single crystals will provide important guidance in further domain engineering technology of ferroelectrics.

Conclusions
This study systematically investigated the macroscopic electrical characteristics, static ferroelectric domains, and PFM tip bias-induced polarization switching dynamic behaviors of the PIN-PMN-33PT single crystals.The samples exhibited outstanding piezoelectricity, with d33 ~ 2556 pC/N and d33 * ~ 2110 pm/V, and demonstrated good temperature stability, with Tm ~ 471 K. Notably, in the unpoled PIN-PMN-33PT single crystals, PFM imaging revealed the presence of unique strip-like domain patterns comprising irregular nanoscale domains, which likely contributes significantly to the ultrahigh piezoelectricity observed in the PIN-PMN-33PT single crystal.Furthermore, the PFM tip biasinduced polarization switching kinetics demonstrates the process of the nucleation and growth of new domains in PIN-PMN-33PT single crystal, which will provide important guidance in further engineering technology of relaxor ferroelectrics.

Figure 1 .
Figure 1.X-ray diffraction pattern of the powder form of the single crystal.

Figure 2 .
Figure 2. (a) Measured frequency-and temperature-dependent permittivity, (b) fitting results of the modified Curie-Weiss law (100 kHz), (c) measured P-E hysteresis loops at various electric field amplitudes, and (d) measured unipolar S-E curves at various electric field amplitudes.The inset of Figure (a) shows the Vogel-Fulcher fitting results.
Figure 4g,h displays the autocorrelation image for the PIN-PMN-33PT single crystal while giving the <C(r)> value.The PFM experimental data in PIN-PMN-33PT single crystals align well with the average autocorrelation function, resulting in a <ξ> value of 70.7 nm.