Terahertz Probing Irreversible Phase Transitions Related to Polar Clusters in Bi0.5Na0.5TiO3‐Based Ferroelectric

Electric‐field‐induced phase transitions in Bi0.5Na0.5TiO3‐based relaxor ferroelectrics are essential to the control of their electrical properties and consequently in revolutionizing their dielectric and piezoelectric applications. However, fundamental understanding of these transitions is a long‐standing challenge due to their complex crystal structures. Given the structural inhomogeneity at the nanoscale or sub‐nanoscale in these materials, dielectric response characterization based on terahertz (THz) electromagnetic‐probe beam fields is intrinsically coordinated to lattice dynamics during DC‐biased poling cycles. The complex permittivity reveals the field‐induced phase transitions to be irreversible. This profoundly counters the claim of reversibility, the conventional support for which is based upon the peak that is manifest in each of four quadrants of the current–field curves. The mechanism of this irreversibility is solely attributed to polar clusters in the transformed lattices. These represent an extrinsic factor, which is quiescent in the THz spectral domain.

(I-E, P-E, or S-E, respectively). [9] It is now well established that, such phase transitions can be directly observed using a variety of in situ methods, such as X-ray diffraction (XRD), [10] neutron diffraction, [11] and transmission electron microscopy (TEM). [5] However, the local structural changes (below the nanometer scale), including chemical and displacement disorder, are normally too small for diffraction methods to detect. Consequently, dielectric measurement can be employed as a probe to sense electric field-induced phase transition. [8] In view of the complexity wrapped up in the dispersive polarizability, there is yet no detailed study of phase transition behavior of BNT from the intrinsic, atomic-level, dielectric property point of view. This makes THz dielectric spectroscopy a desirable method for probing polar materials, such as relaxor ferroelectrics. Hence the need for dielectrometry at THz energies.
Conventional dielectroscopy is typically deployed over a frequency domain spanning from 1 to 100 MHz. In this case, the dielectric response comprises of both the intrinsic (including lattice transformations), and extrinsic sources (including domain walls, grain boundaries, and point defects [12] ). Extrinsic factors contribute less to net dielectric response at the higher GHz to THz frequencies due to their long relaxation times, thereby allowing the contribution from intrinsic processes to be isolated and characterized. Furthermore, coherent THz spectroscopy enables simultaneous determination of the real (in-phase) and the complex (quadrature-response manifest as energy-loss by heat), polarization-response to the probe electric field. Understanding the individual contributions from microscopic intrinsic and extrinsic dielectric factors will enable an engineered and therefore accelerated development, and optimization of the aforementioned macroscopic advantages of these important materials.
In this work, BNT-based ceramics are biased by a DC electric field while being simultaneously probed with a coherent THz beam field. A new experimental methodology is therefore introduced for the study of phase transitions in ferroelectrics to reveal their intrinsic dielectric response. For the first time, the difference in the THz dielectric behavior of BNT-derived ferroelectrics, before and after the application of a DC electric field, has been observed using THz time-domain spectroscopy (THz-TDS). THz-TDS revealed that the applied DC electric fieldinduced change in the phase transitions of BNT-based ceramics is irreversible and can be ascribed to the crystal chemistry at the sub-nanometer scale.
The ferroelectric properties of Bi 0.35 Na 0.335 Li 0.015 Sr 0.3 TiO 3 (BNLST) were characterized at different maximum amplitudes of an external DC electric field in order to determine its polarization state and switching dynamics. Relaxor-like slim P-E loops with a large field-induced polarization and a negligible remnant polarization are observed (Figure 1a); additionally, four current peaks can be observed in the I-E curves (Figure 1b, show that the largest volume of polar switching and phase transitions takes place inside of the material. Such behavior is different from that of other classic relaxors and resembles more the features of antiferroelectrics (AFE). [13] From the literature, it appears that the original state of BNLST is more like a non-polar or weakpolar arrangement of electric dipoles. [8] There is no evidence for an AFE ordering in the BNLST ceramics, such as reported in other BNT systems. [14] In addition, the electric field-induced strain dependence (Figure 1c) indicates an electrostrictive-like behavior (linearity of the strain (S) versus square of the polarization (P 2 ) dependence [15] ), which is macroscopically coincident with the nonpolar symmetry. In this case, the strain, related to Adv. Electron. Mater. 2020, 6,1901373  the field-induced transitions, cannot be determined from the measured S-E loops. The existence of the four current-peaks in the I-E curves can be explained using field-induced phase transition theory: [8] the weak-polar state is transformed to the polar state at certain applied strengths of DC electric field (the peaks in the first and third quadrants), and then this polar state will relax to its original state upon removal of the coercive field (the peaks in the second and fourth quadrants). For this condition, it is generally accepted that the phase transitions in relaxors are reversible and the relaxor is in the "ergodic" state. However, to-date, there are no studies reporting whether the polar state goes "completely" or "partially" back to a weak-polar state after the applied electric field is switched off. The enclosed area of the ferroelectric hysteresis loops cannot be directly linked with the irreversibility of the phase transitions, but it can be related to the loss from friction due to the dipole rotations. Figure 2 shows the temperature-dependent dielectric permittivity and loss tangent of BNLST at six different frequencies (1, 10, 50, 100, and 500 kHz; and 1 MHz), as measured before and after poling. For the unpoled sample, the anomaly corresponding to the highest permittivity value (denoted as T m ), becomes more pronounced at lower frequencies and shifts to a higher temperature with increasing frequency (Figure 2a). The strong dispersion of the permittivity peak is generally accepted as a fingerprint of relaxor behavior, dominated by relaxation processes of the polar nano-regions (PNRs). [16] PNRs are nanometer-sized regions having a local polarization and existing in the vicinity of T m . [17] In order to investigate the effect of an external field on PNRs, dielectric measurements were carried out on the same sample after poling in a DC field at 6 kV mm −1 for 15 min, as shown in Figure 2b. By comparing the dielectric spectra in Figure 2a,b, it showed that the ferroelectric relaxor underwent an irreversible transition upon the application of the external electric field. Below T m , there is a significant increase in the values of the real part of the dielectric permittivity (ε′) and loss tangent (tanδ = ε″/ε′) of the poled sample due to the contribution of PNRs to the overall electrical response. It should be noted that the behavior of PNRs, as discussed here and following, is related to the arrangement of PNRs above the static freezing temperature (T f ). Below T f , the long-range polar order of these nanoregions is locked after poling. Here, the T f of PNRs in BNLST is below room temperature, as determined by the dielectric data fitted according to the Vogel-Fulcher law. [18] In addition, the dielectric dispersion completely vanished above T m after poling. Compared with tanδ before poling, the value of tanδ decreases sharply at high temperatures (especially above 300 °C) after poling. The decrease of tanδ can be a result of a permanent structure-change after the application of the bias DC electric field. As reported for pure BNT, the monoclinic (Cc) phase is suppressed after poling, which enables the rhombohedral (R3c) structure to be revealed on a global length scale. [19] Meanwhile, the dispersion of tanδ diminishes at high temperatures (over 300 °C) after poling, which is another evidence for the regulation of crystal structure with the help of an external DC electric field. However, no macroscopic phase transitions of BNLST can be directly detected from the dielectric spectrum. T m cannot be assigned as the critical phase transition point based on the XRD results of BNLST as shown in Figure S1, Supporting Information. On a detailed inspection, there is no change in cubic structure (space group Pm-3m), at room temperature.
Despite the difference in dielectric spectra before and after poling, it is still not possible to definitively claim that the fieldinduced phase transitions are irreversible at the lattice scale, mainly due to the multiple extrinsic contributions to dielectric behavior at sub-GHz frequencies. Since intrinsic, lattice-level processes are at the energetics of THz electromagnetic radiation, the phenomenon of reversible or irreversible field-induced phase transitions can be assessed using coherent THz spectroscopy. The BNLST sample has high permittivity and high dielectric losses in the THz spectral band, therefore, two tailored measurement methodologies were implemented: a reflection-based THz measurement configuration and conplane DC biasing. The schematical plot of the reflected THz-TDS set up is presented in Figure 3 and the technical details are presented in Experimental Section. A polished, plane-parallel wafer, with a diameter of 13 mm and a thickness of 500 µm, was measured by the THz-TDS systems. As shown in the inset of Figure 3, silver paste was applied on opposite edges of a given sample's same surface and served as electrodes, leaving the middle-area of the sample with a 5 mm-wide gap upon which the THz beam field-spot could fall. The electrodes were connected to a high voltage DC power supply and the poling was taking effect across the middle of the sample surface, where the effective area THz beam can probe due to the limited penetration depth. Prior to the THz-TDS measurement, the DC electric field was applied for 2 min. The THz beam field was propagated at normal incidence up to the sample-face (the sample-face being supported parallel to the plane of the optical table). This configuration was adopted to ensure simple kinematic reference of the sample-reflection with respect to the reference-mirror reflection (each resting under its own weight over a supporting rim); that is, a common optical path length was imposed ensuring that post-processing derivation of complex permittivity was not compromised by phase (path) error, to which THz-TDS is sensitive to. The difference between the sample's reflected signal before and after poling is used to derive the change in dielectric parameters, including permittivity and loss tangent, where the first differential of permittivity with respect to reflectance was implemented with respect to the following equation: [20] ε ω ε ω ε ω = ′ the reflectance, R, carries both amplitude and phase information and it is the ratio between the measured sample spectrum and the reference mirror spectrum; ω is angular frequency, ε′ and ε′′ are the real and imaginary parts of the permittivity, respectively. The detailed procedure of extracting the changes of dielectric parameters is presented in the Supporting Information ( Figure S2, Supporting Information). The real and imaginary parts of the dielectric permittivity of BNLST, as obtained by THz-TDS at 0.4 THz, are shown in Figure 4. The voltage was applied in the following cycle: (0, 0.2, 0, −0.2, 0…1, 0, −1, 0) kV. This cycle reproduces the electric field loading used in ferroelectric hysteresis tests. Herein, it should be noted that the coplane DC bias is unable to create homogeneous electric field distribution on the surface of 5 mm gap area, so the values of electric field are replaced by the real applied DC voltage in the following discussion. There is no change in the dielectric permittivity under ±0.8 kV, because the applied voltage is too low. When the voltage reached 1 kV, there is a distinct increase in both the real and imaginary parts of the relative dielectric permittivity. This can be explained by the field-induced transitions that take place at 1 kV, resulting in the enhanced ε′ and ε″ due to the intrinsically induced polarization. When the voltage returns to zero, ε′ and ε″ increase again because the dipoles are no longer locked by the bias field (freezing effect) and respond easily to the AC THz beam field. [21] After the application of the −1 kV voltage, the values of both ε′ and ε″ are slightly increased, when compared with those after poling at 1 kV. It is worth noting that ε′ further increases after the removal of the applied DC bias field. This is direct evidence that the original polar state of BNLST was changed after the half-cycle of the applied voltage. In other words, the so-called "reversible" field-induced phase transition is not "completely" reversible. In addition, the drop of Adv. Electron. Mater. 2020, 6,1901373  ε″ implies that less heat was dissipated due to the reduced friction among the external field-aligned dipoles.
Generally, there are four types of polarization process contributing to the overall dielectric response. They can be sub-divided into two main categories: i) resonance processes and ii) relaxation processes. [22] For resonance, electronic and atomic (ionic) polarizations are involved, whereas the dipolar (orientation) and interfacial (space charge) polarizations contribute to the relaxation. [23] Considering the resonance regime, electronic and atomic polarizations, respectively, result from the oscillatory displacement of the electron cloud and atoms (ions) in response to the probe AC THz beam field. Thus, both polarization mechanisms can exist at very high frequencies into the infrared (≈10 THz) and optical (≈1000 THz) spectral domains. On the other hand, the dipolar polarization is related to the rotation of the permanent dipoles under an external AC field and takes place below ≈1 GHz. [24] Similarly, the interfacial polarization involves the movement of limited free charge carriers at interfaces or grain boundaries, which respond to low frequency fields (≈10s of kHz). [22] Therefore, only the electronic and atomic polarization processes contribute to the dielectric response during THz spectroscopy, making it possible to investigate structural changes at the lattice scale. It has been demonstrated that atomic fluctuations contribute to the dielectric response of the THz spectral domain in dielectric systems. [25] The fluctuating atoms in PNRs can be treated as clusters of soft phonons, [26] the so-called polar clusters. The lattice-scale transformation in local polar clusters is suggested as the mechanism for the different THz dielectric response of BNLST ceramics before and after poling. The field-induced evolution of polar clusters inside PNRs is schematically presented in Figure 4. Before the poling process (position O), the whole system consists of the PNRs with random orientations of polarization in the non-polar regions. Each PNR is composed of polar clusters with different orientation of polarization at the lattice scale. In BNT-based materials, it is known that polar clusters originate from the localized in-phase octahedral tilt in the matrix phase. [27] They manifest the existence of the intrinsic lattice instabilities occurring in the ferroelectric due to the random occupancies of the Na + and Bi 3+ ions and the severe difference in the bonding characteristics of NaO and BiO. [28] Hence, it is reasonable to assume that the neighboring polar clusters do not share exactly the same orientation of polarization due to the lack of long coherence length. This assumption is in an agreement with the recent TEM studies on BNT. [29] Upon poling (Figure 4, position A), polarization of the polar clusters is re-aligned along the direction of the applied DC electric field. This means that the lattice instabilities can be theoretically removed under the electric field. It has been reported that the electric field helps to modify the crystal structure in terms of forcing all the ions to irreversibly take up positions compatible with the matrix phase. [19] Moreover, an increased number of activated polar clusters may emerge, which contributes to the enhanced ε′. After the poling process (position B), the polarization of most polar clusters flips back to the original orientation. However, a portion of polar clusters can be inhibited and their polarization deviates from that of the original position. These hindered clusters are believed to be responsible for the irreversible field-induced phase transitions, which intrinsically occur at the lattice scale. Unfortunately, the subtle changes at the PNR level cannot be detected by the THz-TDS because the whole PNR is unable to cohere with a THz field cycle. [30] In addition, the freezing effect from the bias DC electric field is suppressed at room and elevated temperatures, thus the dipoles can respond more freely to the probing AC field and contribute to further increasing of ε′. In addition, after another cycle of poling with a negative DC electric field, more polar clusters become hindered and lattice distortion is further "tuned", leading to an enhancement of the real part of the permittivity (position C).
Summing up the results from the THz-TDS measurements, in the THz spectral domain, there is a detectable change in the dielectric behavior of BNLST ceramics before and after poling ( Figure 5). The difference in the dielectric response can be directly linked with the intrinsic transformation of polar clusters at the atomic level. It was demonstrated that the BNT-based system undergoes field-induced phase transitions which are irreversible after the removal of the applied field. The origin Adv. Electron. Mater. 2020, 6,1901373  of the field-induced phase transitions is thought to be intrinsic (at the lattice level), coming from polar clusters within PNRs. Considering the correlation length limit of diffraction methods, THz-TDS spectroscopy is demonstrated to be a powerful probe for evaluation of phase transitions in ferroelectrics.
The irreversible, bias DC electric field-induced phase transitions were investigated in BNT-derived ceramics using THz-TDS. In contrast to THz dielectric spectroscopy, the conventional ferroelectric measurements of the P-E (I-E) hysteresis loops indicated, unconvincingly, that the phase transitions induced by an external electric field are reversible. The differences in the THz dielectric properties of the unpoled and poled samples as well as of the samples subjected to the reversepoling electric field, suggest the existence of a permanent fieldinduced lattice transformation, that is, local polar clusters. It is suggested that these polar clusters within the PNRs are responsible for the observed changes in the THz dielectric spectra. This work is essential in further understanding the intrinsic mechanisms underlying the phase transition behavior of the BNT-based materials. It provides an innovative approach of applying THz electromagnetic radiation to investigate the phase transition behavior in ferroelectric systems on the lattice scale.

Experimental Section
Sample Synthesis: The ceramic samples were prepared via the conventional solid-state method according to the chemical formula, Bi 0.35 Na 0.335 Li 0.015 Sr 0.3 TiO 3 . A stoichiometric batch of Bi 2 O 3 (99.9% Sigma-Aldrich), Na 2 CO 3 (99.5% Sigma-Aldrich), Li 2 CO 3 (99.0% Alfa Aesar), SrCO 3 (99.5% Alfa Aesar), and TiO 2 (99.8% Sigma-Aldrich) powders were weighed after drying at 200 °C overnight. The ingredients were ball-milled for 4 h. Calcination of the mixture was carried out in two steps: at 800 °C for 2 h followed by 900 °C for 4 h. The calcined powders were ball-milled for another 4 h and then uniaxially cold-pressed into pellets at 70 MPa. These green discs were finally sintered at 1150 °C for 3 h. The density of all pellets was measured by the Archimedes method and it reached values above 95% theoretical density.
Electrical Characterization: Electrical measurements were performed on the pellets with silver paste fired on both major sides. The temperature dependence of the real part (ε′) and imaginary part (ε″) of the dielectric permittivity was tested from room temperature up to 500 °C using an LCR meter (Agilent, 4284A, Hyogo, Japan) attached to a PC-controlled furnace. The I-E, P-E, and S-E loops were measured using a ferroelectric tester (NPL, Teddington, U.K.), at a frequency of 1 Hz and at room temperature.
Reflection Based THz-TDS Set-Up: A femtosecond Ti: sapphire amplifier system with a repetition rate of 1 kHz and a central wavelength of 800 nm was used as a light source. The optical beam was split into a pump beam and a probe beam by a polarizing beam splitter. The pump pulses passing through a chopper were used to generate THz radiation by a conventional electric-optic crystal of ZnTe. The THz beam was focused by a parabolic mirror and normally applied onto the broad face of the sample. Reflected THz pulses were then collected and steered by the parabolic mirrors, and focused onto a ZnTe crystal. The probe optical pulses passed through the same ZnTe detector crystal, a 1/4 wave plate, and a Wollaston prism, respectively. The elliptic polarization emerging from the 1/4 wave plate is analyzed by the prism into orthogonal component polarizations of electric vector that are angularly resolved and directed onto two balanced photodiodes, from which the magnitude and phase of the THz field is deduced.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.