Enhancement of Piezoelectricity by Novel Poling Method of the Rare‐Earth Modified BiFeO3–BaTiO3 Lead‐Free Ceramics

In piezoceramics, the Curie temperature (TC) and piezoelectric coefficient (d33) are often inversely proportional, so it is very difficult to optimize high piezoelectricity and TC simultaneously. In addition, the high and temperature‐insensitive piezoelectric strain coefficient (d33*) with small hysteresis is also a longstanding obstacle in the development of lead‐free ceramics. In this work, a facile approach of donor doping strategy is adopted to replace Ba2+ with Yb3+, Y3+, Sm3+, and Nd3+ as a result, a high TC of 450 °C and outstanding d33 of 422–436 pC N−1 is achieved by a novel magnetic poling method. Thermally‐stable and outstanding piezoelectric strain performance (d33* ≈ 520–550 pm V−1 and ΔST ≈ 10%) with small strain hysteresis (H < 20%) results are highly encourageable in lead‐free ceramics. The main factors contributing to high piezoelectricity are the morphotropic phase boundary, suppression of defect charges by donor doping, thermal quenching, mesoscale nanodomain size, and novel poling method. The excellent piezoelectric performance and high TC of this work are superior to those of state‐of‐the‐art piezoceramics. The synergistic approaches of compositional design strategy and novel poling process in this work are highly beneficial for temperature‐insensitive piezoelectric sensor and actuator applications.

can improve their functional properties. However, lead-based ceramics are facing legislative restrictions and the functional properties of lead-free ceramics are inferior that cannot fulfill the requirements of practical applications. Hence, there is an urgent need to develop lead-free high-performance piezoceramics with a high T C by an easy synthesis method.
In piezoelectric materials, the four fundamental issues namely i) sustainability, ii) tunability, iii) reproducibility, and iv) reliability are the milestones for commercial applications. In this work, a simple scientific approach is adopted to resolve each issue, as briefly summarized hierarchically through a chart as shown in Figure 1. Among the other lead-free piezoceramics (1-x)BiFeO 3 -xBaTiO 3 exhibited good piezoelectricity near the morphotropic phase boundary (MPB) at x = 0.30-0.33, as well as a high T C > 400 °C. [13] For this work, the based composition was designed at the MPB where different phases manifest a flattened free energy profile that leads to high piezoelectricity. In addition during chemical composition weighing the 3 mol% Bi-excess powders were added for the compensation of Bi 2 O 3 evaporation. The outstanding piezoelectricity (d 33 ≈ 322 pC N −1 , d 33 * ≈ 360 pm V −1 ) with only 15% variation in d 33 * in the temperature 25-125 °C and a high T C ≈ 510 °C was achieved in the pure BFBT ceramics. In the current research work, thermal quenching and a novel magnetic poling method were adopted to tune and further improve their piezoelectric properties. The lead-free KNN-based ceramics have high piezoelectric properties (d 33 ≈ 300-400 pC N −1 and d 33 * ≈ 300-500 pm V −1 ) [14] but their multi-elements complex modification has the risk of poor reproducibility. In piezoceramics, the MPB and their physical properties are very sensitive to the exact composition but for mass production, fine composition control is very difficult in case of complex modification. [15] Here in this current work, multi-element complex modification is avoided and a singleelement doping strategy was adopted. For the reliability of a piezoelectric device, temperature stability and strain hysteresis are also very important parameters. [15] Chemical modification is a traditional and common method to customize the electromechanical properties of a material. However, the selection of chemical modifiers plays a pivotal role in the enhancement of piezoelectricity. [16] From the perspective of doping strategy, the donor and smaller-size dopants easily induce local heterogeneity and cause domain miniaturization without disturbing their MPB, leading to high piezoelectricity. [7,17] Moreover, donor doping reduces the defect charge concentration and induces a soft-ferroelectric effect, which is also beneficial for the improvement of piezoelectricity. Therefore, the defect engineering strategy was applied by using RE elements as donor dopants, and their effect as a function of ionic radii was studied systematically. Hence, such excellent piezoelectricity with a high T C of 454 °C in lead-free BFBT ceramics has tremendous potential for daily-life device applications.

Results and Discussions
It is generally believed that T C and d 33 are mostly inversely proportional so it is very hard to optimize both simultaneously in a single composition. The d 33 of piezoceramics can be improved by chemical modification but their T C is shifting toward the lower temperature. For real applications, the lower limit of piezoceramics is considered to be d 33 > 300 pC N −1 , d 33 * > 300 pm V −1 , and T C > 300 °C in a single composition. [8] Hence, the simultaneously enhanced piezoelectricity with a high T C is a bottleneck for the real application. The outstanding piezoelectric performance of our work exceeds those of BFBT and some of the PZT ceramics as shown in Figure 2a. The d 33 ≈ 436 pC N −1 of this work is above the PZT4 (d 33 ≈ 410 pC N −1 ) and close to the PZT-5A (d 33 ≈ 450 pC N −1 ) ceramics. Interestingly, the T C ≈ 454 °C of the RE-doped BFBT ceramics is much higher than the lead-based ceramics. The X-ray diffraction (XRD) patterns for the RE-modified BFBT ceramics are shown in Figure S1a, Supporting Information. All ceramics showed a single perovskite phase without indication of secondary phases. As the ionic radii of Yb 3+ (0.87 Å), Y 3+ (0.90 Å), Sm 3+ (1.24 Å), and Nd 3+ (1.27 Å) are smaller from Ba 2+ (1.61 Å) ion. From the close inspection, it was noticed that a slight shifting occurred in the (100) peak to the higher angles and also another peak (001) T appeared at 2θ ≈ 21°-22° as shown in Figure 2b. This shifting indicates the shrinkage of the lattice volume and implies that all RE elements go to the A-site and replace Ba 2+ atoms. For all compositions, the optimized concentration of RE-dopants is 1 mol%. To confirm it, 0.67Bi 1.03 FeO 3 -0.33Ba 1-x Sm x TiO 3 ceramics (with x = 0.00, 0.01, and 0.02) were synthesized and their crystal structure and piezoelectric properties were studied systematically. The enlarged view of (100) and (111) peaks in the 2θ range of 20°-23° and 2θ ≈ 37°-40° are shown in Figure S2a, Supporting Information. At first glance, a small peak appears on the left side of the (100) peak for x = 0.01 and again disappears for the x = 0.02 sample. Generally, the crystal structure lattice distortion for the tetragonal phase (tetragonality, c T /a T ) can be evaluated from the (001) T hump peak. For the investigation of crystal structure assemblage, the Rietveld refinement was carried out using a two-phase model (R3c + P4mm). The observed Figure 1. The structure chart addresses the four fundamental issues for real applications and a simple scientific approach to resolve each issue reported in this paper.

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and calculated patterns matched very well with each other as shown in Figure S1b-e, Supporting Information. Reasonable fitting parameters (such as χ 2 ≈ 2, R wp ≈ 10%, and R exp ≈ 8%) show the reliability of the applied model. From the refinement results, the estimated c T /a T ratio of pure BFBT increased from 1.01 to ≈1.02 for the BFBSmT (x = 0.01) sample. The crystal structure evaluation and lattice distortion with RE doping are represented by the schematic unit cells as shown in Figure 2c. However, for the higher order of Sm-content (i.e., x = 0.02) the c T /a T value again decreases and the crystal structure becomes close to the cubic-like phase. The ionic radius size difference creates local random stress and valence mismatch of the dopants induces a local random field. [7,17] These local structure distortions induce inhomogeneity and cause domain miniaturization as a result functional properties are improved. For the in-depth investigation of the local structure heterogeneity, Raman spectroscopy measurement was performed as shown in Figure S2b, Supporting Information. The whole spectrum of Raman from 100 to 800 cm −1 is divided into three subsections. Section I and II are associated with A-site and B-site atomic vibrations while section III is related to the BO 6 octahedral rotation. For x = 0.00 and 0.01 samples, the distinctive peaks were observed in the Raman spectra at 200, 400, and 600 cm −1 . These distinct peaks in the Raman modes show the coexistence of the R and T phases. However, for x = 0.02, a broadened spectral line suggests the high-level local structure heterogeneity due to A-site disorder in the BFBT matrix. The Raman spectroscopy measurements strongly support the argument for the local structure heterogeneity with Sm-modification. Previous investigations have proved that crystal structure MPB and maximum lattice distortion, as well as local structure heterogeneity, contribute to the improvement of piezoelectric performances. [8,[18][19][20] However, excessive doping concentration again destroys the functional properties due to the overcrossing of the final limit of local structure heterogeneity. Figure 3a-c shows the dielectric properties from room temperature to 600 °C for BFBSmT (x = 0.00, 0.01, and 0.02) at 1, 10, and 100 kHz. The ceramics with x = 0.00 and 0.01 shows a sharp transition peak in the dielectric constant and behave like a normal ferroelectric. However, for x = 0.02 the crystal structure transforms to the cubic-like phase and shows the frequency-dependent dispersed dielectric constant near and below T C (Figure 3c). Dielectric relaxation describes the exchanging energy of microparticles due to their interaction and then reacting to a stable distribution. [21] To describe the dielectric relaxation behavior for BFBSmT ceramics here, the Curie-Weiss law was applied as given by the following equation where ε, ε m , T, and T m are the dielectric constant, maximum dielectric constant, absolute temperature, and corresponding maximum dielectric constant temperature, respectively. The diffused factor (γ) can be calculated from the linear slope fitting where γ = 1 shows the normal ferroelectric material and γ = 2 indicates the ideal relaxor ferroelectric. [22] Figure 3d shows that the diffused factor values are increased from 1.43 to 1.81 with Sm incorporation which confirms the local structure heterogeneity and polar nanoregions (PNRs) are induced in the BFBT matrix. The compositional design strategy is very important for the improvement of certain properties at the expense of other properties. For example, a control level of chemical inhomogeneity by doping generates nano-scale domains which are beneficial for the improvement of piezoelectric performance and their  [8,63,64] b) the XRD diffraction patterns for BFBT and BFBRET ceramics at 2θ ≈ 20°-23° and 2θ ≈ 37°-40°, and c) schematic diagram for the increase in tetragonality (c T /a T ) with RE-doping.
www.advelectronicmat.de thermal stability. [18] However, the emergence of PNRs beyond a certain limit of the dopants again destroys piezoelectric properties. On the other hand, the high-level local structure heterogeneity and the appearance of local PNRs are favorable for giant energy storage properties. [17] During high-temperature measurements, these local PNRs fluctuate which causes frequency-dependent diffused phase transition. Figure 3e shows the dielectric constant versus temperature (ε r −T) curves for 0.67Bi 1.03 FeO 3 -0.33Ba 0.99 RE 0.01 TiO 3 (BFBRET) (with RE = Yb 3+ , Y 3+ , Nd 3+ , and Sm 3+ ) ceramics at 10 kHz. Among all other compositions, the highest dielectric constant (ε r ≈ 53 338 at the T C ) was noted for the BFBSmT ceramic. It can be seen that the dielectric loss (tanδ) of pure BFBT remains stable up to ≈265 °C and then abruptly increased above this temperature as shown in Figure 3f. This rapid increase in the dielectric loss at elevated temperatures is associated with electrical conductivity due to the long-range diffusion of the space charges. A small dielectric loss (tanδ ≈ 0.075) was noted for the pure BFBT sample at room temperature which further decrease to 0.036 at 140 °C and again increases at a higher temperature. Nevertheless, for the RE-doped BFBT ceramics, a noteworthy improvement occurred in temperature stability of the dielectric losses up to ≈365 °C. This increase in the temperature stability of tanδ is related to the suppression of defect charge concentration caused by donor doping. According to defect chemistry, due to the refractory nature of Bi 2 O 3 , the Bi-vacancies induced in BiFeO 3 can be compensated by the additional charge of the donor dopants (RE = Yb 3+ , Y 3+ Nd 3+ , Sm 3+ ) on Ba 2+ -site according to the following relations [23] This ionic charge defect compensation can suppress defect dipole and releases the latent polarization that favors the softferroelectric effect. The additional softening effect occurs from lowering the T C (≈510 °C) of the pure BFBT ceramic to ≈450 °C for the RE donor-doped ceramics. In general, soft-ferroelectric materials have a high dielectric loss at room temperature relative to hard-ferroelectrics. A slight increase occurred in the room temperature dielectric losses with RE element modifications but their stability is highly improved over a wide temperature range. The maximized temperature stability in dielectric losses leads to the highest piezoelectric performance as reported in the BFBT ceramics. [20] Figure 4 shows the ferroelectric polarization-electric field (P-E) hysteresis loops under the applied field of 50 kV cm −1 . For undoped BFBT ceramic, the room temperature remnant polarization (P r ≈ 19.6 µC cm −2 ) and saturation polarization (P s ≈ 26.4 µC cm −2 ) greatly increased to P r ≈ 38.5 µC cm −2 and P s ≈ 40.7 µC cm −2 at 100 °C as shown in Figure 4a1. However, their unsaturated P-E loop at 125 °C is due to the electrical leakage current from the thermal migration of space charges. The Bi 2 O 3 loss during sintering temperatures was controlled by adding 3 mol% Bi-excess powder. But still some charge defects

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P-E loops. Donor doping in BFBT ceramics suppresses the defect charge concentration as a result their functional properties are considerably improved. Therefore, for all RE-doped BFBT ceramics, well-saturated P-E loops with high electrical polarization can be observed over the given temperature spectrum (Figure 4b1-e1). The increase in the electrical polarization or decrease in the coercive field (E c ) with an increment of temperature is related to the thermally triggered domain switching. [24] The thermal improvement of domain switching is also evident from the increase in the intensity of current density-electric field (J-E) loops or decrease of maximum intensity peaks field as given in Figure S3a-f, Supporting Information. To investigate the domain evaluation with REdoping and the physical mechanism behind the improvement of functional properties, piezoelectric force microscopy (PFM) measurements were performed as shown in Figure 4 (subscript 2). For the undoped BFBT sample, the micro-size domains are observed as shown in Figure 4a2. On the other hand, for the RE-modified BFBT ceramics, the complex nanodomains can be suggested from their PFM response (Figure 4b2-e2). The ionic radius and valence mismatch of the Ba 2+ ion and RE elements creates local structure heterogeneity that suppresses the domain size. The switching of nanodomains is relatively easy under the external electric field and gives high functional properties. [14] Detailed information regarding the domain configuration and domain switching behavior under the DC-bias ±10 V is given in Figure S4, Supporting Information. One can see that relative to the pure BFBT, the RE-doped BFBT ceramics shows better domain switching under the positive and negative DC-bias field ( Figure S4a 2 -e 2 ,a 3 -e 3 , Supporting Information). It is because the donor doping suppresses defect charge concentrations and reduces the domain size, as a result, the domain switching becomes easy under the applied electric field. Figure 5 (subscript 1) shows the temperature-dependence bipolar strain-electric field (S-E) loops for BFBT and BFBRET ceramics at 25-125 °C under the applied electric field of 50 kV cm −1 . Their corresponding room temperature PFM amplitude response is given in Figure 5 (subscript 2). All ceramics showed typical butterfly S-E loops and their bipolar negative strain S neg bi increases with the increment of temperature. For undoped BFBT ceramics, the room temperature maximum bipolar strain ( S max bi ) was noted to be 0.181% (d 33 * ≈ 362 pm V −1 ) and gradually increased to 0.207% (d 33 * ≈ 414 pm V −1 ) at 125 °C as shown in Figure 5a1. However, the replacement of the Ba 2+ with RE elements in BFBT ceramics brings a noteworthy enhancement in their piezoelectric performance as evident from Figure 5b1-e1. The highest d 33 * values at 25 °C were noted to be 504, 511, 520, and 550 pm V −1 for BFBYT, BFBYbT, BFBNdT, and BFBSmT ceramics, respectively. The improvement of piezoelectric response with RE element modifications is also evident from their respective PFM amplitude response as shown in Figure 5a2-e2. It was interesting to note that the piezoelectric strain characteristics of this work are high enough from the soft PZT ceramics (PIC151, S max = 0.3% at 60 kV cm −1 and d 33 * = 500 pm V −1 ). [13] Generally, the excellent piezoelectric response is strongly correlated with the maximum lattice distortion or local structure inhomogeneity induced by chemical modification. This local lattice distortion comes from the ionic radius and valence difference of the dopant which creates local structure heterogeneity inside the unit cell and improves piezoelectric performance. [7,25] In the XII-coordination number, the ionic radii of Sm 3+ (1.24 Å) and Nd 3+ (1.27 Å) are smaller than Ba 2+ (1.61 Å) ion. [6] This ionic radius and valence mismatch causes chemical inhomogeneity and induces mesoscale nanodomains. Relative to large domains, the miniaturized domains respond more quickly to the external electric field or stress and thus improve their piezoelectric performance. [14] As www.advelectronicmat.de the ionic radius of Sm 3+ is smaller than Nd 3+ , therefore, the highest d 33 * ≈ 550 pm V −1 was observed for the Sm-doped BFBT ceramic. However, by further decreasing the ionic radius of the dopants such as Y 3+ (0.90 Å) and Yb 3+ (0.868 Å) the heterogeneity level crosses their final limit and a drastic decrease occurs in the domain size and probably generates some PNRs. Hence, the ionic radius and valence of a dopant have a critical role in the customization of functional properties. [7,17] As we observed that Sm-doped BFBT ceramics have high piezoelectric performance. Therefore, further investigation was carried out for this particular optimum composition to explore the origin of high piezoelectric performance. Figure 6a-c shows the PFM phase images of the Sm-modified BFBT (with x = 0.00. 0.01, and 0.02) for the virgin state. Now under the ±10 V, both upward and inverse domains can be observed for the pure BFBT sample as represented by arrows (Figure 6d,g). It is because micro-size domains are difficult to switch under this small electric field. [26] Figure 7a-f represents the PFM amplitude images and their corresponding schematic representation of the domain for the Sm-modified BFBT system. The small amplitude of the PFM response of the pure BFBT also suggests microdomains, where many defects charges have existed as shown in Figure 7a,d. On the other hand, the x = 0.02 ceramic exhibits different colors under the ±10 V DC-bias field as indicated by arrows (Figure 6f,i). These small pitch areas of different colors indicate the appearance of fine domains or PNRs that are unstable under the applied electric field. [26] However, the 1 mol% Sm-modified BFBT ceramic sample showed better domain switching under the ±10 V DC-bias field where non-switchable domains were not observed as evident from Figure 6e,h. It is because a small amount (x = 0.01) of Sm 3+ as a donor dopant on the Ba 2+ -site in BFBT suppresses the defect charges and induces local structure heterogeneity due to their ionic radius and valence mismatch. [7] Thus, judiciously chemical modification decreases the domain size and substantially improves their piezoelectric performance. The inhomogeneity induces extra interaction energies, such as electrostatic energy (induces random field) and elastic energy (generates random stress), which makes a flattened thermodynamic energy profile and eases polarization switching under external stimuli. [18] The random field and random stress are induced by the valence difference and ionic radius mismatch, respectively. [17] In addition, the donor dopants suppress the defect charge concentration and unlock the domains from their pinning center as a result their functional properties are improved. Interestingly, the highest amplitude can be observed from the PFM response as shown in Figure 7b. Therefore, the mesoscale complex nanodomains can be suggested for x = 0.01 ceramic as represented by Figure 7e. In the case of micro and nanodomains, the S neg bi values are increased with rising temperature due to the improvement of irreversible non-180° domain switching (Figure 7g,h). It was interesting to note that only 15% and 10% change occur in the magnitude of S max bi for x = 0.00 and 0.01 ceramics, respectively. For the higher order of Sm-content (x = 0.02), the heterogeneity crosses their final limit, and domain size further decreases and probably generates PNRs as represented by Figure 7f. These PNRs are unstable under the external stimulus and their fragmentation at elevated temperatures causes high variation in their piezoelectric strain (ΔS T ≈ 60%) as shown in Figure 7i. The decrease in S neg bi with rising temperature is another feature of the relaxor ferroelectric. In this work, the high piezoelectric performance is strongly supported by PFM measurements. Similar explanations have been reported for domain evolution and their response to the external electric field in BFBT ceramics. [26,27] TEM is one of the most powerful tools to probe the domain structure/morphology and have a close relationship with piezoelectricity. Therefore, the bright field TEM images were www.advelectronicmat.de measured for the Sm-doped BFBT system to uncover the underlying mechanism of the enhanced piezoelectricity in the present system as shown in Figure 8a-c. In the case of the undoped BFBT ceramics, tweed-like domains with submicron dimensions of 200-500 nm were observed as shown in the magnified view for a selected area (Figure 8a). Generally, the chemical compositional designing cause domain miniaturization that soars domain density and lowers domain wall energy. [28] As a result, the switching of domain becomes easy under the external applied electric field and leads to high piezoelectricity. Hence, with Sm-doping, the domain size decreased to the mesoscale nanodomains, and then finally PNRs appeared due to chemical heterogeneity. For the appropriate amount of Sm-content (x = 0.01), the mesoscale herringbone-like domain architectures are interlaced as displayed in Figure 8b. For the high order of Sm-content (x = 0.02), Moiré fringes nanodomains with a width of a few nanometers ≈10 nm size were observed (Figure 8c). The domains within this range are called PNRs. [14] Mostly, such domain structure shows relaxor-like behavior due to their short-range ferroelectric order. [26] The domain structure observed in the TEM images is consistent with PFM measurement and also with other electromechanical properties. Recently, Wang et al. observed a similar domain evolution in the Nd-modified BFBT ceramics. [29] For all samples, the unipolar S-E curves were measured under the applied electric field of 50 kV cm −1 as shown in Figure 9a-e. The temperature-insensitive piezoelectric strain is an important parameter for piezoelectric actuator application. For practical applications, not only the high d 33 * is required but also the temperature-insensitive piezoelectric strain, ΔS T = (d 33 * (T) − d 33 * (RT))/d 33 * (RT) are desired for the precise operation of a piezoelectric device. [30] Figure 9f presents the temperature-dependence variation of d 33 * values as a function of temperature (25-125 °C) where pure BFBT ceramic has a 15% variation in piezoelectric strain. However, the replacement of Ba 2+ by the RE elements considerably increased their piezoelectric response. The d 33 * ≈ 520 and 550 pm V −1 at 25 °C increased to 570 and 610 pm V −1 at 125 °C for BFBNdT, and BFBSmT ceramics, respectively. It was noticed that only a 10% variation occurred in the d 33 * values in the temperature
For piezoelectric transducers, simultaneously high d 33 , d 33 * , and T C are required in a single composition. [23] In piezoceramics, electrical poling is indispensable for d 33 measurement. Therefore, a novel poling method was adopted for the first to optimize the poling condition and obtain high d 33 values as shown through the experimental setup in Figure 10b (Figure 10d). These defects accumulate at the domain walls and create pinning centers for the switching of domains during electrical poling. [52] After the conventional poling, a few domain walls are moved under the external electric field and others are entangled with defect centers as shown in Figure 10e. The defects charge also causes aging in the properties of ceramic and the device gives up its functions with time. [53] However, the domain pinning effect could be relaxed by alternating current poling (ACP) as a result the d 33 values are improved. [54,55] Therefore, a bipolar triangular voltage was applied for 10 3 cycles at 1 Hz before the DC-bias poling. It was very interesting to note that a significant improvement occurred in the d 33 for all samples after AC-bias and DC-bias poling as shown in Figure 10c. It is because, under the AC-bias field cycling, the defect charges could be moved toward the grain boundary and unlock the domain from their pinning centers.

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After the AC-bias cycling maximum, domains will be aligned in the direction of the DC-bias field as represented by the schematic diagram in Figure 10f. The DC-poling and AC-cycling also have a substantial impact on P-E hysteresis loops of the normal ferroelectric ceramic and their influence becomes weak in the relaxor-ferroelectric. [20] Therefore, a significant increase can be observed in the P r after the conventional DC-poling and AC-cycling as shown in Figure S5, Supporting Information. Hence, the improvement of the d 33 value after AC cycling was also supported by ferroelectric properties measurement. Here, in this work, a new poling method was adopted for the first time where all ceramics were poled under the DC-bias field inside a strong magnetic field (DCPM). In a magnetic poling setup, two magnets of the opposite poles were adjusted on both sides of the sample during DC-bias poling. Interestingly, in the case of undoped BFBT ceramics, a noteworthy improvement occurred in d 33 from 268 to 322 pC N −1 by applying the magnetic poling process. Likewise, the d 33 increased to 422 and 436 pC N −1 for the Nd and Sm-doped BFBT ceramics, respectively. These results indicate that the ACP + DCPM poling is a new and smart method for the improvement of d 33 in the BFBT ceramics.
The physics behind the improvement in d 33 with the DCPM poling method could be explained by the additional parasitic polarization induced by an external magnetic field as discussed in Figure 11. As we know in classical electromagnetism, the four Maxwell equations state that varying electric and magnetic fields are coupled with each other. Therefore, electrical polarization and magnetization are also not independent of each other which can be mutually controlled. In multiferroic materials magnetic (electric) field induces polarization (magnetization). [56] BiFeO 3 is a well-known multiferroic material in which ferroelectricity is induced from the lone pair (6s 2 ) of Bi 3+ -ion and anti-ferromagnetism arises  [24,[31][32][33][34][35][36][37][38] and KNN-based [39][40][41][42][43][44][45] ceramics.

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from Fe 3+ ion. [57] The spin of the Fe ion is slightly canted away from its perfect direction by the lone pair Bi 3+ and creates the incommensurate long-range cycloidal spiral structure. [58] Figure 11a shows the schematic representation of the cycloidal spiral spin magnetic moment of Fe-ion in the BiFeO 3 unit cell. The magnetic field applied to this cycloidal spin induces parasitic polarization along the direction of the magnetic field. [56] Because under the applied magnetic field, the cycloidal spiral spin structure is changed into a conical spin structure as shown in Figure 11b. Hence, the redistribution of charges under the external magnetic field induces additional polarization which is called parasitic or local polarization (P local ). This P local can be calculated from the Dzyaloshinskii-Moriya (DM) interaction model and is proportional to the displacement (x) of oxygen ion, P local ∝ x ∝ e ij × (S i × S j ) (see Figure 11c). The DM interaction between the two magnetic moments m i and m j rises from the spin-orbit coupling and is responsible for magnetically driven ferroelectricity. [59] The electrostatic interaction of pre-existing polarization (P) and P local adding the magnetoelectric term to the total energy and the Hamiltonian of this effect is given by H DM = (P × e ij ) × (S i × S j ), where D ij = P × e ij vector is related to the oxygen octahedra rotation or cooperative shifting of oxygen ion. [57] Therefore, the magnetically driven ferroelectricity leads to the enhancement of the d 33 value after the magnetic poling.  Tables S2 and S3, Supporting Information. The outstanding piezoelectric performance (d 33 ≈ 422-436 pC N −1 and d 33 * ≈ 520-550 pm V −1 ) and high T C ≈ 454 °C of our work are best as compared to the other lead-free BFBT ceramics (Figure 12a,b). In addition, the temperature-insensitive piezoelectricity, ΔS T ≈ 10% and small H ≈ 18% of the current investigated work are superior to those of other lead-free ceramics. Importantly, the characteristics of this work are comparable with commercial lead-based ceramics such as PZT-5H (d 33 = 600 pC N −1 , d 33 * ≈ 500 pm V −1 , ΔS T ≈ 45%, H ≈ 10.2%, and T C ≈ 185 °C) and PZT-4 (d 33 ≈ 410 pC N −1 , d 33 * ≈700 pm V −1 , ΔS T ≈ 15%, H ≈ 18.5%, and T C ≈ 250 °C). [30,43,60] A giant and temperature-insensitive piezoelectric strain (d 33 * ≈ 520-550 pm V −1 and ΔS T ≈ 10%) with small strain hysteresis (H > 20%) was obtained in the Nd and Sm-doped BFBT ceramics. In previous literature, the high-temperature poling [61] and ACbias poling [62] methods have been applied for the improvement of d 33 values. In this work, the enhanced d 33 ≈ 422-436 pC N −1 was achieved by a novel magnetic poling method after AC-bias cycling/poling. The DM interaction from the spin-orbit coupling in BiFeO 3 successfully explains the magnetically driven ferroelectricity which leads to high piezoelectric performance. Hence, this work indicates that lead-free BFBT ceramics have a high potential to replace lead-based materials in real applications.

Conclusions
In this work, we used different RE elements (Yb 3+ , Y 3+ , Nd 3+ , and Sm 3+ ) to replace the Ba 2+ ion in BFBT ceramics. The ionic radius and valence difference of the RE dopants and Ba 2+ ion induced local structure heterogeneity or lattice distortion in BFBT ceramics which leads to enhancement of piezoelectricity. In addition, a novel method of poling in a strong magnetic field was applied where a 30% increase occurred in the d 33 value relative to the conventional DC-bias poled ceramics. In this work, the simultaneously enhanced d 33 ≈ 436 pC N −1 with a high T C ≈ 454 °C is comparable to those of state-of-the-art lead-based ceramics and superior to those of lead-free ceramics. A large d 33 * ≈ 550 pm V −1 with only a 10% variation in the temperature 25-125 °C and small strain hysteresis (H ≈ 18%) is a great achievement in lead-free ceramics. Such a high d 33 and d 33 * were mainly attributed to the crystal structure MPB, maximized local structure disorder, and mesoscale nanodomains. Furthermore, the domain engineering by donor doping and a novel magnetic poling method after AC-bias cycling significantly improved piezoelectricity. The Dzyaloshinskii-Moriya interaction theoretical model successfully explains that magnetically driven ferroelectricity that leads to the enhancement of the d 33 value. This research provides a new strategy and synergistic approach for the enhancement of piezoelectricity in lead-free ceramics. The outstanding piezoelectric performance with good thermal stability and high T C of current research work shows promising potential for elevated temperature applications.

Experimental Section
The BFBRET (RE = Yb 3+ , Y 3+ , Nd 3+ , and Sm 3+ ) ceramics were fabricated by a conventional solid-state reaction method. , during furnace cooling. All these secondary phases exhibited cubic crystal structure and that was why demolished the functional properties. For the first fundamental issue, 3 mol% Bi-excess powders were added during weighing and all pellets were buried in the same composition powder during their sintering. To resolve the second issue, all ceramics were quenched in water from their sintering temperature to control the non-ferroelectric secondary phases. The precursors were mixed with alcohol in nylon jars and ball-milled at 150 rotations per minute for 24 h by using yttrium-stabilized zirconia balls as a milling media. The wet slurries were dried at 120 °C and then calcined at 700 °C with a heating rate of 10 °C min −1 for 2 h. After the first calcination, the powders were hand-grinded with an agate mortar

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and pestle. Re-calcination for 2 h at 700 °C was carried out to further improve their chemical homogeneity. The 5 wt% polyvinyl alcohol (PVA) was added as a binding agent and dried at 120 °C for 6 h in the oven. The 10 mm diameter pellets were pressed by applying uniaxial pressure. The PVA was burnt at 300 °C for 1 h and finally sintered at 980 (BFBT) and 1000 °C (BFBRET) for 3 h with a heating rate of 10 °C min −1 . However, during cooling, all ceramics were thermally quenched in water to avoid the unstable temperature range for the formation of secondary phases. The crystal structure investigation was carried out by XRD (Bruker, D8 Advance) and dielectric properties were measured by an impedance analyzer (4294A, Agilent Technologies, USA). For electrical measurement, the 400 µm thick samples were coated with low-temperature silver (Ag) paste and backed at 120 °C to protect their quenching effect. Temperature-dependence ferroelectric and piezoelectric strain loops were measured by a ferroelectric analyzer (TF Analyzer 2000, AixACCT systems, Germany). PFM measurements were performed through a commercial microscope (AFM, NanoManTM VS, Veeco, USA) to observe the domain structures. For PFM measurement, the 200 µm thickness samples were polished by using diamond paste. One side of the sample was coated with low-temperature Ag paste and baked at 120 °C for 30 min. The domain morphology of the sample was investigated by a field emission transmission electron microscope (TEM, Nova NanoSEM230, FEI Co., USA). TEM samples were prepared by subsequent grinding, cutting, dimpling, and ion milling. Before the DC-bias poling, all samples were electrically poled for 10 3 cycles under a bipolar electric field of 50 kV cm −1 at 1 Hz for the purpose to relax the domains from the defect pinning sites. The DC-bias poling was performed under the applied electric field of 50 kV cm −1 at 80 °C together with a strong magnetic field of 1.4 T for 1 h. For magnetic poling, the two pieces of neodymium magnet coated with NiCuNi with dimensions of 40 mm diameter and 20 mm thickness were used. The quasi-static d 33 values were measured by a d 33 -meter (IACAS, ZJ-6B).

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