Nonlinear Dielectric Response of Relaxor Ferroelectric (1 − x)Pb(Mg1/3Nb2/3)O3 − xPbTiO3 Epitaxial Thin Films

Thin ferroelectric layers are capable of generating large dielectric and electromechanical responses at relatively low voltages, thus can be utilized in various applications including energy storage, energy harvesting, sensors, and actuators. Among ferroelectrics, relaxor ferroelectrics (1 − x)Pb(Mg1/3Nb2/3)O3 − xPbTiO3 are particularly interesting due to their superior dielectric and piezoelectric properties. However, dielectric and piezoelectric responses of the ferroelectric thin films are significantly suppressed relative to their bulk counterparts. The physical mechanism of the properties degradation still remains elusive, which greatly hinders their technological applications. Herein, this work systematically investigates the dielectric nonlinearity and the relationship between composition and intrinsic/extrinsic contributions of high‐quality (1 − x)Pb(Mg1/3Nb2/3)O3 − xPbTiO3 epitaxial thin films (x = 0, 0.1, 0.32) fabricated by pulsed laser deposition. Through the Rayleigh analysis, it is found that the suppression of domain wall motion by substrate clamping is the main cause of thin film performance degradation and is further confirmed by continuous application of background dc bias to extract the dielectric response's intrinsic and extrinsic contributions. This work will pave the way for practical applications of (1 − x)Pb(Mg1/3Nb2/3)O3 − xPbTiO3 thin films in energy storage and electromechanical devices.

][36] Previous studies found that the extrinsic contribution due to DW motion may account for 70% of the measured dielectric and piezoelectric properties in polycrystalline PbZr x Ti 1−x O 3 ceramics. [23,37,38]The Rayleigh analysis is typically used to separate the intrinsic and extrinsic contributions and to describe the dielectric nonlinearity of ferroelectrics. [5,39]he Rayleigh law applied to the dielectric nonlinearity can be expressed as [5,25,39,40]  =  init + E ac ( 1) where  is the measured dielectric constant under electric field, P(E) is the polarization, E is the electric field (E = E ac sin(t)), E ac is the amplitude of the applied ac field,  init and  are the reversible and irreversible Rayleigh coefficients, respectively.The reversible Rayleigh coefficient  init is due to contributions from the intrinsic lattice and reversible interface motion, while the irreversible Rayleigh coefficient  is due to the irreversible interface motion.In Equation (2), the signs "+" and "−" correspond to the decreasing and increasing electric field, respectively.To avoid domain nucleation and switching, E ac remains less than one third of coercive field (i.e., subswitching conditions).The Rayleigh law is no longer applicable over the subswitching fields, as the domain switching would occur and result in the field dependence becoming sub-or superlinear.To the best of our knowledge, the relationship between composition and intrinsic/extrinsic contributions in PMNPT epitaxial thin films has not been systematically studied.Thus, an investigation of the intrinsic and extrinsic dielectric responses in relaxor-based thin film systems as a function of the composition is essential to better understand the underlying mechanism of the reduced response observed in the films.
Here, we focus on PMNPT epitaxial thin films (x = 0, 0.1, 0.32, abbreviated as PMN, PMN-0.1PT, and PMN-0.32PT) to systematically study the electrical properties of the films and the relationship between composition and intrinsic/extrinsic contributions.Despite varying degrees of lattice tetragonality, Rayleigh analysis demonstrates that the irreversible Rayleigh coefficients of all films are negligible compared with bulk and single crystal, which demonstrates that the suppression of extrinsic contribution (i.e., DW motion) by substrate clamping could be the main cause of thin film performance degradation.Subsequent extraction of intrinsic and extrinsic contributions under background dc electric fields up to 740 kV cm −1 verifies this conjecture.As the composition approached the MPB, the extrinsic contribution increased because of the enhanced motion of domain walls.

Results and Discussion
≈130 nm thick PMNPT thin films are grown on Ba 0.5 Sr 0.5 RuO 3buffered SrTiO 3 (001) single crystal substrates by pulsed laser deposition (see the Experimental Section for details).The thickness of Ba 0.5 Sr 0.5 RuO 3 bottom electrodes and PMNPT epitaxial thin films are determined by the X-ray reflectivity (XRR) measurements (Figure S1, Supporting Information) and the crosssectional scanning electron microscopy (SEM) (Figure S2, Supporting Information).Figure 1a shows the results of X-ray diffraction (XRD) -2 measurements.Only the (00l) peaks from the substrate and the films are evident, indicating that all films are single-phase and epitaxially grown on the substrates.Atomic force microscopy (AFM) imaging reveals that the films are smooth with a root-mean-square roughness of only 600 pm (Figure 1b).To probe the lattice symmetry and strain state of the films, asymmetric synchrotron-based XRD reciprocal space mapping (RSM) studies about the 103-diffraction (Figure 1c-e) and 113-diffraction (Figure S3, Supporting Information) diffraction conditions were carried out.The absence of peak splitting suggest that the unit cell of the films appears to be tetragonal. [41]eanwhile, the PMNPT films and substrate reflection peaks are not at the same Qx, indicating that all the films are relaxed.[44][45][46] The tetragonal lattice shape of the films is further supported by RSMs measured at reflections with different  (0°, 90°, 180°, 270°) (Figure S4, Supporting Information). [47]For each composition, their Qx and Qz remain unchanged at different  angles, further confirming that the films exhibit a tetragonal lattice shape. [48]The broadening of the diffraction peaks is probably due to the nanotwinned domains. [49,50]o study the influence of the composition of the PMNPT films on the electric properties, the electrical responses including ferroelectric, dielectric and piezoelectric measurements are further performed at room temperature.Exceedingly low leakage current indicates high-quality of the films (the inset of Figure 2a) and also provides feasibility for subsequent ferroelectric hysteresis loops and dielectric studies under high dc bias fields.The observed asymmetrical I-V curves are probably due to the asymmetrical electrodes.The polarization versus electric field (P-E) loops are conducted at 1 kHz and shown in Figure 2a.All the P-E loops exhibit slim loops with a small coercive field and low remanent polarization, which are the typical characteristics for relaxors. [49]Consistent with that in the bulk, [16,51,52] as the solid solution composition approaches the MPB, the maximum polarization (P m ) and the remnant polarization (P r ) increase from 32.9 to 39.7C cm −2 and from 3.1 to 11.1 C cm −2 , respectively.This is due to the addition of PT with higher polarization. [53]igure 2d presents the electric field dependent dielectric constant (C-V) measured at 1 kHz.Typical butterfly-shaped C-V curves are shown and the dielectric loss tan  is below 0.06 for all films, further implying the high quality of the films.By increasing the PT content close to the MPB, the dielectric constant of PMNPT films also increases from PMN (831), PMN-0.1PT(944) to PMN-0.32PT (1020).]46] While similar reduced dielectric values had been reported previously in coherently strained PMN-0.32PTthin films grown on rare-earth scandate single crystal substrates, [54,55] which suggests that the suppression of dielectric response observed in thin-film version could be intrinsic rather than due to the extrinsic effect, such as passive interfacial layer.The piezoelectric properties of the PMNPT films were measured using a laser scanning vibrometer over an Au electrode pad with a diameter of 200 m. [56]Similar to the bulk PMNPT, electric field induced dilation of the films increased with increasing x (Figure 3a-c).The effective piezoelectric coefficient d 33 can be further determined based on the magnitude of the surface displacement.As shown in Figure 3d, the piezoelectric coefficient d 33 of the relaxed films gradually increases as the MPB is approached from PMN (d 33 = 20 pm V −1 ), PMN-0.1PT(d 33 = 23 pm V −1 ) to PMN-0.32PT (d 33 = 37 pm V −1 ), which is consistent with the increasing trend of dielectric responses mentioned above.][59] In order to analyze the mechanism responsible for the thin film performance degradation, we quantitatively extract the extrinsic and intrinsic contributions via two different methods: 1) Rayleigh analysis under increasing ac excitation field and 2) frequencydependent permittivity measurements under increasing background dc bias. [5,21,39,47,60]igure 4a-c shows the ac field dependent dielectric constant for the films.It can be seen that the dielectric constant exhibits a linear behavior as a function of the applied ac field amplitude, demonstrating that the dielectric response can be described using the Rayleigh law.According to Equation (1), the intercept from the y axis in Figure 4a-c represents  init and the slope of the line represents .The extracted  init and  values are found to increase with increasing x.The P-E loops calculated by the extracted  init and  values using Equation ( 2) are found to be good fit to the measured values (Figure 4d-f), further illustrating the applicability of Rayleigh law.In these PMNPT (x = 0-0.32)films, the irreversible Rayleigh coefficients  can be regarded as almost entirely contributed by irreversible DW motion because all the films are single phase via above XRD analysis, thus the impacts of phase boundaries can be ignored.Despite varying compositions, the irreversible Rayleigh coefficients  of all films are an order of magnitude smaller than those of bulk single crystals [61] or thick films, [5] while the reversible Rayleigh coefficients  init remain at the same order of magnitude (taking x = 0.32 as an example, the values of  init and  are ≈967 and 6.2 cm kV −1 for our thin films, while they are 2060 and 61.5 cm kV −1 for 1 m thick film, [5] respectively).This demonstrates that the suppression of extrinsic contribution (i.e., DW motion) because of substrate clamping should be the main cause of thin film performance degradation.At the same time, the significantly higher  values as the composition approaches the MPB (≈2.1, ≈3.2, and ≈6.2 cm kV −1 for x = 0, 0.1, and 0.32, respectively) is far more interesting, which suggest that the enhanced dielectric and piezoelectric responses may be the result of the promoted DW motion capacity.This is consistent with previous reports of significantly increased DW motions around MPB. [21,62] The Rayleigh studies are further confirmed by capacitance measurement as a function of the frequency at different applied background dc electric fields.Under high dc bias fields, the film would transform toward a single domain state, resulting a decrease in the number of DWs.Therefore, the extrinsic contribution is negligible at high dc electric fields and the intrinsic  contribution can be obtained subsequently.This is achieved by fitting the frequency dependence of the dielectric constant under bias fields to the equation  =  0 −  log and extracting the field dependence of the intercept ( 0 ) and slope (). [21,60]rom this data, one can extract the field at which extrinsic con-tributions are suppressed and the zero-field, intrinsic dielectric permittivity of a material.Figure 5a-c shows the frequency dependence (0.6-100 kHz) of permittivity under different bias fields (0-740 kV cm −1 ) for the PMNPT epitaxial thin films.As is shown, the dielectric constant and slope of the frequency response decrease with the increasing dc electric field as a result of "freezing" domain wall motion at high fields.At very high fields, the dielectric constant becomes frequency independent within the frequency range measured.Remarkably, the PMN-0.32PTfilm reveals ≈80% reduction in the dielectric constant with increasing applied dc bias.The intercept ( 0 ) as a function of the background dc bias for different PMNPT films are then plotted to visualize the intrinsic and extrinsic contributions (Figure 5d-f).It is obvious that the fitted curve can be divided into two regions, i.e., a lowand high-field regime, with a change in the trend around a field of magnitude ≈200 kV cm −1 .In the low-field region, the intercept  e reflects the combination of intrinsic and extrinsic contributions and the slope  e reveals the extrinsic tunability (which describes how the external dc bias suppresses the extrinsic response).In the high-field region, the DW motion is believed to be completely suppressed, and thus the intercept  i corresponds to the zero-field, intrinsic dielectric constant of the material and the slope  i reveals the intrinsic tunability (which describes how the external dc bias suppresses the intrinsic response).For all films, the low-field sloop  e is an order of magnitude larger than the high-field sloop  i , suggesting that the extrinsic response is much more susceptible to suppression with external fields.And the intercept of the high-field regime  i is only ≈1/3 of the intercept of the low-field regime  e .All told, the dominant role of extrinsic contribution is consequently confirmed.
The changes in the parameters associated with the intrinsic and extrinsic responses are fundamentally explained using theories of structural symmetry and polarization rotation.First of all, in the low-field region, absolute value of  e shows a growing trend with the increasement of the PT content (from ≈2.7 to ≈5.4 cm kV −1 ).This can be understood from two aspects: 1) as the PT content increases, the composition is gradually approaching the MPB, which leads to lower tetragonality (evidenced by lower c/a extracted from Figure 1 and Figure S3 in the Supporting Information).The DW displacement is promoted because of the lower internal stresses associated with the high spontaneous strain.In turn, it is easier to tune the domain structure by external stimulation. [5]2) The DW motion capacity is promoted with proximity to the MPB, which further promotes the proportion of extrinsic contribution originating from DW motion, causing the slope to rise.Second, the  e of PMN-0.32PT(≈1341) is apparently higher than PMN (≈885) and PMN-0.1PT(≈978) which is likely due to the higher density of DW that gives rise to a greatly enhanced extrinsic contribution to the permittivity.Finally, to the high-field region, absolute value of  i and  e also increases as the composition approaches the MPB composition.This can be explained by the theory of polarization rotation (intrinsic effect): as the composition close to MPB, the stability of tetragonal structure in PMNPT decreases as a result of the relatively low free energy difference between other phases which determines lower potential barrier, and the polar axis is prone to rotate under the action of the vertical electric field, resulting in the crystal symmetry changes. [63]Thus, the intrinsic contribution increases significantly.

Conclusion
In this work, high-quality PMNPT epitaxial thin films with different compositions (x = 0, 0.1, 0.32) were successfully synthe-sized by pulsed laser deposition.We delved into physical mechanisms of thin film performance degradation and how compositional changes affect domain wall motion and lattice distortion contributing to electrical responses.Through the Rayleigh analysis, we figure out that irreversible Rayleigh coefficients of all films are negligible compared with bulk and single crystal, which demonstrates that the suppression of domain wall motion by substrate clamping should be the main cause of PMNPT thin film performance degradation.A dc bias electric field up to 740 kV cm −1 is continuously applied to extract the intrinsic and extrinsic contributions to further confirm our conjecture.Moreover, it is verified that the extrinsic contribution increases as the composition approached MPB, which is related with the reduction of tetragonality leading to lower internal stress and superior domain wall motion capacity.The enhancement of intrinsic contribution approaching the MPB is rationally explained by polarization rotation theory combined with lattice distortion.Ultimately, our studies help to better understand the nonlinear dielectric response of PMNPT thin films and will benefit their practical applications in MEMS devices.

Experimental Section
≈130 nm PMNPT (x = 0, 0.1, 0.32)/≈50 nm Ba 0.5 Sr 0.5 RuO 3 (BSRO) heterostructures were grown on (001)-oriented SrTiO 3 single crystal substrates by pulsed laser deposition (Arrayed Materials RP-B).The BSRO bottom electrode was grown at a temperature of 700 °C in a dynamic oxygen pressure of 2.7 Pa with a laser fluence of 1.5 J cm −2 and a laser repetition rate of 3 Hz from a ceramic target of the same composition.The PMNPT growth was performed at a heater temperature of 525 °C in a dynamic oxygen pressure of 27 Pa with a laser fluence of 1.0 J cm −2 and a laser repetition rate of 5 Hz from a ceramic target of the same composition with 10% excess led to compensate for lead loss during growth.The Pt top electrode was deposited at room temperature by magnetron sputtering (Arrayed Materials RS-M) after photolithography.
The XRD 2- scans were taken using a high-resolution diffractometer with monochromated Cu K 1 source (Rigaku Smartlab 9 KW).Synchrotron reciprocal space mapping (RSM) studies were carried out at beamline BL02U2 of the Shanghai Synchrotron Radiation Facility (SSRF) ( = 0.6887 Å).Film thicknesses were measured using cross-sectional scanning electron microscopy (SEM) images.The surface morphologies of the PMN-PT films were scanned by a Bruker Multimode 8 AFM system.Polarizationelectric field (P-E) hysteresis loop measurements were performed with a TF 3000 analyzer (aixACCT), using a bipolar triangular pulse at a frequency of 1 kHz and varying amplitude.Dielectric permittivity and loss tangent measurements were carried out using an E4980A LCR meter (Agilent Technologies).The ferroelectric and dielectric properties measurements were performed using a Semishare high-precision probe station (Semishare E4).A laser scanning vibrometer (PolyTech GmbH) was used to measure the piezoelectric properties of the thin films.

Figure 3 .
Figure 3. Electric field induced strain for a) PMN, b) PMN-0.1PT, and c) PMN-0.32PTthin films.Inset shows the piezoelectric displacement of PMNPT thin films over the area of top electrode.d) Variation of the effective piezoelectric coefficient d 33 of the PMNPT thin films as a function of PT content.

Figure 5 .
Figure 5. Frequency dependence of the dielectric under a series of dc biases up to 740 kV cm −1 for a) PMN, b) PMN-0.1PT, and c) PMN-0.32PT.Intercept and slope extracted from the frequency dependence in (a)-(c) as a function of applied dc bias for d) PMN, e) PMN-0.1PT, and f) PMN-0.32PT.