# Revisiting phonons and the phase transition sequence in antiferroelectric Pb 0.98 La 0.02 (Zr 0.95 Ti 0.05 )O 3

Anirudh K R, Cosme Milesi-Brault, Přemysl Vaněk, Esther de Prado, Elena Buixaderas

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Anirudh K R, Cosme Milesi-Brault, Přemysl Vaněk, Esther de Prado, Elena Buixaderas. Revisiting phonons and the phase transition sequence in antiferroelectric Pb 0.98 La 0.02 (Zr 0.95 Ti 0.05 )O 3. Physica Scripta, 2025, 100 (7), pp.075908. 10.1088/1402-4896/addc4a. hal-05121061

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PAPER • OPEN ACCESS

Revisiting phonons and the phase transition
sequence in antiferroelectric
Pb<sub>0.98</sub>La<sub>0.02</sub>(Zr<sub>0.95</sub>Ti<sub>0.05</sub>)O<sub>3</sub>

To cite this article: Anirudh K R *et al* 2025 *Phys. Scr.* **100** 075908

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PAPER

# Revisiting phonons and the phase transition sequence in antiferroelectric Pb<sub>0.98</sub>La<sub>0.02</sub>(Zr<sub>0.95</sub>Ti<sub>0.05</sub>)O<sub>3</sub>

Anirudh K R¹, Cosme Milesi-Brault¹,², Přemysl Vaněk¹, Esther de Prado¹ and Elena Buixaderas¹

¹ Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 182 00 Prague 8, Czech Republic

² Université Paris-Saclay Centrale Supélec, Laboratoire SPMS, 91190 Gif-sur-Yvette, France

E-mail: buixader@fzu.cz

Keywords: Raman spectroscopy, phonons, antiferroelectric, calorimetry, phase transitions, XRD

## Abstract

The changes induced in Pb<sub>0.98</sub>La<sub>0.02</sub>(Zr<sub>0.95</sub>Ti<sub>0.05</sub>)O<sub>3</sub> (PLZT 2/95/5) by 2% of La substitution and its impact on the phase transition sequence were investigated by using Raman spectroscopy, differential scanning calorimetry, and x-ray diffraction to improve the understanding of the switching dynamics of antiferroelectric-ferroelectric systems. Comparison with Pb(Zr<sub>0.95</sub>Ti<sub>0.05</sub>)O<sub>3</sub> confirms that the La substitution alters the Pb dynamics and suppresses the polar order, stabilising the antipolar state already at high temperatures. On cooling from the cubic paraelectric phase, the calorimetric data revealed a small anomaly near T~500 K corresponding to a region where the material appears macroscopically cubic, but it is locally distorted. Then an antiferroelectric incommensurate phase appears below T<sub>C</sub> ~ 483 K, characterised by new Raman modes and three main soft modes: an antiferrodistortive soft mode, an antipolar soft mode, and a weaker soft mode at very low frequencies, related to the incommensurate positions of Pb, the amplitudon, which disappears when the material enters another antiferroelectric phase. The average symmetry of the intermediate incommensurate antiferroelectric phase is likely orthorhombic with the proposed *Imma* space group. The low temperature antiferroelectric phase shares the same space group (*Pbam*) and Raman modes with antiferroelectric PZT ceramics. Based on this combined approach, the proposed phase transition sequence on cooling is cubic paraelectric-cubic distorted paraelectric-incommensurate antiferroelectric *Imma*-orthorhombic antiferroelectric *Pbam*.

## 1. Introduction

Among antiferroelectric (AFE) materials, lead zirconate titanate Pb(Zr<sub>1-x</sub>Ti<sub>x</sub>)O<sub>3</sub> (PZT) is exceptional for its sequence of phase transitions in response to varying temperature, pressure, composition, and other factors, which are accompanied by changes in polarisation, strain, and other physical properties [1]. This material has been extensively investigated for the past decades due to its exceptional dielectric, ferroelectric, and piezoelectric properties, used in electrooptic, pyroelectric, and piezoelectric devices [2–5]. There is still an immense potential to explore how PZT might be adapted for targeted applications by specifically altering its composition, as this area has not yet been thoroughly studied. The phase transition sequence can be modified, and this can help to understand the fundamental principles behind the behaviour of antiferroelectric-ferroelectric (AFE-FE) systems and guide research toward other perovskite families suitable for energy storage applications.

The well-known PZT phase diagram includes two morphotropic phase boundaries where structures of various symmetries intersect [6]. PZT displays a rhombohedral structure at a high Zr concentration and a tetragonal structure at a high Ti level. Rather than the better studied rhombohedral-tetragonal morphotropic phase boundary, other PZT compositions, such as Pb(Zr<sub>0.95</sub>Ti<sub>0.05</sub>)O<sub>3</sub> (PZT 95/5), are close to the boundary between the antiferroelectric (AFE) and ferroelectric (FE) phases [7]. The delicate balance between these phases leads to interesting polarisation dynamics and electromechanical properties. An innovative method of phase
control close to room temperature was studied in PZT 95/5. This method could work as a three-state switch by controlling the temperature at around room temperature [8].

Introducing lanthanum in PZT influences the quality of the ceramics, inducing a decrease in grain size and porosity, and increasing their transparency and mechanical stability [9]. Viehland et al [10] illustrated a phase diagram showing the influence of La substitution (<9%) in PZT 95/5. The most characteristic features of Pb<sub>1-x</sub>La<sub>x</sub>(Zr<sub>0.95</sub>Ti<sub>0.05</sub>)O<sub>3</sub> (PLZT 100x/95/5) with less than 5% La are a strongly diffused AFE-FE phase transition and large thermal hysteresis [10–14]. The ABO<sub>3</sub> perovskite structure consists of ferroelectrically active BO<sub>6</sub> octahedra interconnected by A-site cations [15]. In PLZT, the aliovalent nature of La ions at the A-site disrupts these interactions, thereby changing the structural dynamics and phase sequence of the material. La replaces Pb, and it can create Pb vacancies in the crystal lattice. Here, La cations act as donors, whereas Pb vacancies act as acceptors. The La<sup>3+</sup>-Pb<sup>2+</sup> pairs can also be considered as dipoles, resulting in dipolar polarisation [16]. Several polar orderings, including polar clusters, tweed-like structures, and incommensurate (IC) structural modulations due to the competition between ferroelectric and antiferroelectric orderings, can be induced by La impurities [17]. The IC phase within the AFE state of PZT 95/5 caused by La substitution has been well illustrated by electron diffraction from the extra satellite reflection patterns at IC positions [13]. The dielectric response of AFE PLZT 2/95/5 indicated the breaking of the local cubic symmetry and the formation of polar nanoclusters in the paraelectric (PE) phase of PLZT 2/95/5 as in other relaxor PLZT ceramics [16, 18].

Lately the use of PLZT is undergoing a revival, because apart from its excellent piezoelectric properties, it shows a great potential to be used in energy storage [19–21], electrocaloric cooling [22], and pulse power energy converters [23]. Very recently its use in transparent electronic devices has been demonstrated [24]. Despite this, there is still a lack of understanding about the nature of the phase transitions in AFE PLZT and the symmetry of the intermediate phases, as no further fundamental studies have been done lately. The phase called slim loop FE has not been understood so far in PLZT x/95/5 or detected by other techniques. In addition, the older Raman studies [12, 14] showed only peaks below 200 cm<sup>-1</sup> or just below room temperature without mode assignment. Therefore, we wanted to revisit the subject in the light of the understanding gathered on PZT 95/5.

This paper aims to better understand the changes induced by 2% La substitution and its impact on the phase diagram using Raman spectroscopy, differential scanning calorimetry (DSC), and x-ray diffraction (XRD) experiments. By comparison with PZT 95/5, we have investigated the La influence on PLZT 2/95/5 and our studies revealed that La substitution suppresses the polar order and stabilises the antipolar order of the material. The accepted sequence of phase transitions is PE-SLFE-AFE<sub>IC</sub>-AFE, where SLFE stands for the Slim Loop FE phase and AFE<sub>IC</sub> for the IC AFE phase. Our outcomes are intended to improve the picture of the phase diagram of PLZT, especially with regard to the ‘diffuse’ AFE-AFE<sub>IC</sub> phase transition and the high-temperature intermediate phase with slim P-E hysteresis loops.

## 2. Materials and experimental methods

Ceramics were synthesised by conventional solid-state methods. For PLZT 2/95/5, fine particle powders were ball-milled and calcined at 850 °C twice before being cold-pressed into pellets and heated in a vacuum up to 700 °C, then in oxygen up to 1200 °C for 2 h. After cooling, the pellets were hot-pressed in an alumina mould in the air for 24 h at 1250 °C under the pressure of 15 MPa [25]. PZT 95/5 ceramics were synthesized like the ones used in [8]. Ceramics were cut into 8 mm discs and polished for the Raman experiments.

Differential Scanning calorimetry (DSC) measurements were carried out using a PerkinElmer Pyris Diamond DSC calorimeter. The samples were heated from room temperature to 600 K and cooled at the same rate after holding at that temperature for one minute, at rates of 1, 5, 10, and 20 K/min for PLZT and a rate of 10 K/min for PZT. Several measurements of the same ceramics were performed to check reproducibility. The calorimetric sample holder was purged with nitrogen at 20 mL/min. The Perkin-Elmer PYRIS software, version 13.1.1, was used for control and evaluation.

X-ray diffraction (XRD) measurements were performed by a SmartLab SE Multipurpose diffractometer (Rigaku Corp., Tokyo, Japan) with Cu Kα radiation and a HyPix-3000 2D detector. The patterns were collected using Bragg-Brentano geometry with the detector operating in 1D mode. The optics in the incident beam consisted of a 0.125° divergent slit, a 2.5° Soller slit, and a mask of 5 mm. For the diffracted beam, only a 2.5° Soller slit was employed. The diffractograms were processed by X'Pert HighScore Plus software with PDF-5 database to perform phase identification and subsequently by TOPAS V3 for the Rietveld refinement.

Raman scattering was recorded in back-scattering geometry using an RM-1000 Renishaw Raman microscope equipped with a double Bragg filter, allowing very good stray light rejection below 5 cm<sup>-1</sup> range. The Raman spectra were collected using the 514.5 nm line of an Ar laser at a power of about 25 mW (~4 mW on the sample). For temperature control of the samples a THMS-600 cell (LINKAM) was used on cooling from 600 K to 80 K. To obtain low-temperature spectra (300 K–80 K), samples were mounted in a continuous-flow He cryostat
(Oxford Instruments). A long-distance 20 × objective was mounted into a special angled arm attached to the microscope bearing for efficient optical coupling. The diameter of the laser spot on the sample surface amounted to ~10 µm. The spectral resolution was better than 1.5 cm⁻¹ with a 2400 l/mm grating. All Raman spectra were corrected from the Bose–Einstein thermal population factor.

## 3. Results

### 3.1. DSC results

We measured DSC at different heat flow rates (1, 5, 10, and 20 K min⁻¹) during the heating and cooling cycles. A sudden change in heat flow indicates a material phase transition at that temperature. According to the DSC measurements, PLZT undergoes three phase transitions. DSC curves of PLZT at rates of 5 K min⁻¹ and 20 K min⁻¹ are displayed in figure 1.

During heating and cooling at a rate of 20 K min⁻¹, the first peak appears at ~393 K and ~353 K, respectively. According to the known phase diagram [10], this transition ($T_{AFE}$) corresponds to the orthorhombic commensurate AFE phase to an IC AFE state. This phase transition has a diffusive character and displays a thermal hysteresis of approximately 40 K. The broadened peak in this transition, which can be considered as a weak first-order transition, also raises the question of phase coexistence in that temperature range. A second phase transition ($T_C$) with a smaller thermal hysteresis of ~5 K occurs at approximately 482 K and 477 K in the heating and cooling cycles, respectively. This transition behaves differently than the previous one; the peak is very sharp and with a higher change in the heat flow. At around 500 K there is a very small change in heat flow corresponding to the third phase transition ($T^*$) with a very weak peak. After this transition above 500 K, the sample reaches the PE phase.

Our DSC measurements on PLZT show that the phase transition sequence remains unchanged with heating and cooling, except for thermal hysteresis in the lower temperature range. Table 1 displays the PLZT transition temperatures obtained at different heat flow rates. For higher rates, the heat exchange is faster, and no thermalization effects are allowed, resulting in sharper peaks.

### 3.2. X-ray results

The XRD pattern of PLZT 2/95/5 measured in our ceramics at room temperature (black), together with the result from the refinement (in dotted red), is presented in figure 2. There are three insets, in linear, logarithmic, and linear scales, respectively, for better visualization of the overlapped peaks. Minor peaks formed by the overlapping of three or more peaks are not indexed. The peaks labelled by asterisks correspond to $K\alpha_2$ component of the x-ray radiation. It is possible to distinguish the splitting of many families of peaks, for instance, the splitting of the family {024} in 6 different peaks, which is characteristic of an orthorhombic structure. The peaks (024), (402), and (420) are not visible due to their extremely low structure factor. As a model for the Rietveld refinement, we use the phase PbZr$_{0.93}$Ti$_{0.05}$Nb$_{0.02}$O$_3$ (Pbam) (55) [26]. The peak positions perfectly matched the calculated ones meanwhile the intensities had a poorer matching. This can be attributed to various factors, including preferred orientations, which are common in ceramics, slight discrepancies between the atomic positions used in the model and the actual atomic arrangement, or the presence of defects and impurities. To verify this space group, we fixed the lattice parameters, and we used the Pawley model for the refinement. The process involved leaving the intensity as a free parameter to be refined rather than calculating its contribution from the atomic positions. As seen in figure 2, the difference between the experimental curve and the one obtained from the refinement is very small, confirming the Pbam space group. The refined lattice parameters are $a = 5.863$ Å, $b = 11.736$ Å, and $c = 8.214$ Å.

### 3.3. Raman results

In order to understand the changes in PLZT 2/95/5 with temperature and to identify the different phases we performed temperature-dependent Raman scattering and compared the results with the previously measured PZT 95/5 [8]. The temperature-dependent Raman spectra of PZT and PLZT corrected from the Bose–Einstein population factor in a cooling cycle are depicted in figure 3 from 600 K to 80 K, starting from the PE phases (red spectra in the lower part of the figure) to the AFE phases (blue spectra in the upper part). Raman experiments, in backscattering geometry, performed in both cross and parallel polarisations yielded similar results, indicating no specific assignment of mode symmetries in these two polarisation settings, and also averaged orientation within the probed volume (~200 µm³). The spectra depicted in figure 3 for both samples were taken at a cooling rate of 1 Kmin⁻¹ since PZT 95/5 shows a complex phase sequence depending on the experimental protocol followed like heating or cooling rates, and resting time [8].

Both PZT 95/5 and PLZT 2/95/5 show similar features at high temperatures typical for the cubic PE phase [27]. On cooling, PZT 95/5 develops a new phase which was identified as $FE_{HT}$ with a rhombohedral structure
<figure><img src="image_6.png" /><figcaption>**Figure 1.** DSC curves of PLZT 2/95/5 on heating and cooling at rates of 20 Kmin⁻¹ and 5 Kmin⁻¹.</figcaption></figure>

[8], because the Raman features of this sample were similar to those in the rhombohedral PZT 90/10 and PZT 80/20 ceramics [28, 29] with *R3m* space group. Near room temperature this phase transforms into another *FE*<sub>LT</sub> phase, from [28, 29], we can deduce that this is a transition into a tilted *R3c* phase, as confirmed in [8]. But in the case of PLZT, the sequence is different, it does not appear to have a FE phase as PZT. Instead, it evolves into another phase at ~482 K in the cooling cycle, whose Raman signal is significantly different from the two separate FE phases of PZT. In the heating cycle, this transition occurs at around 484 K. This phase was found to be IC modulated with electron diffraction [13], and temperature-dependent P-E investigations [13, 17] revealed that this intermediate state is antiferroelectric, confirming the absence of the FE state below ~483 K.

On further cooling, both PZT and PLZT develop a new phase identified as orthorhombic *Pbam* [30]. In PLZT, this transition into the AFE phase occurs at around 362 K. It also exhibits thermal hysteresis of approximately 30 K, as it occurs at 393 K in the heating cycle. Transition temperatures found for both ceramics by DSC and Raman experiments are displayed in table 2. Unlike PZT 95/5, PLZT did not exhibit noticeable modifications in the phase sequence or transition temperatures in response to rates of heating or cooling during the Raman experiment.

In figure 4 we compared the state of PZT and PLZT at selected temperatures, corresponding to different states in the phase diagram [10]. From figure 4(a), it is evident that at 80 K both materials are in the same state. The AFE phase is affected, by the inclusion of La in the system, mainly in shifting the frequency of some of the peaks and the shape of some modes in the intermediate regions. This is due to the change of bond lengths in the bending and stretching vibrations. At 300 K (b), PLZT remains in the AFE phase while PZT develops the tilted *FE*<sub>LT</sub> phase. The difference between the two individual phases is more visible in the intermediate region between 180 cm⁻¹ and 400 cm⁻¹ by the shape and number of modes. The intermediate *AFE*<sub>IC</sub> phase of PLZT and the *FE*<sub>HT</sub> phase of PZT are compared in figure 4(c). We confirm that these two phases are different due to the disparities in the positions and shapes of the modes, which are more pronounced in the lower frequency areas. In (b)–(d) the main indicators are the appearance of the modes near 420 cm⁻¹ and 680 cm⁻¹ in PZT. At 500 K (figure 4(d)), PLZT seems to be in the cubic phase (or on the SLFE phase) whereas PZT remained in the *FE*<sub>HT</sub> phase, which is supported by the distinguishing modes observed at 120 cm⁻¹, 420 cm⁻¹, and 680 cm⁻¹. By the comparisons of the phases of PZT with those of PLZT, it was obvious that the intermediate *AFE*<sub>IC</sub> has no similarity with any intermediate phase in PZT. Therefore, Raman results align with the hypothesis that this phase is AFE and likely IC orthorhombic like in PbHfO₃ and Sn-substituted PZT and PZO, with probable average space group *Imma* [31] or *Cmmm* [8] to be confirmed by further diffraction experiments at high temperatures.

To illustrate the phase transitions found by DSC and Raman experiments in PLZT 2/95/5 and PZT 95/5, we depicted in figure 5 an adapted version of the phase diagram of PLZT x/95/5 published by Xu *et al* [10] and the
<figure><img src="image_7.png" /><figcaption>**Figure 2.** XRD pattern of PLZT 2/95/5 ceramics at room temperature. Insets show in more detail some regions of interest. Asterisks denote $K\alpha_2$ components.</figcaption></figure>

<table><caption>**Table 1.** Transition temperatures obtained from DSC at different heating and cooling rates (in Kelvin).</caption><thead><tr><th rowspan="2">PLZT 2/95/5<br>Heat flow rate</th><th colspan="3">Heating (in K)</th><th colspan="3">Cooling (in K)</th></tr><tr><th>T<sub>AFE</sub></th><th>T<sub>C</sub></th><th>T<sup>*</sup></th><th>T<sup>*</sup></th><th>T<sub>C</sub></th><th>T<sub>AFE</sub></th></tr></thead><tbody><tr><td>1 K min<sup>-1</sup></td><td>390</td><td>480</td><td>501</td><td>500</td><td>480</td><td>358</td></tr><tr><td>5 K min<sup>-1</sup></td><td>391</td><td>481</td><td>501</td><td>500</td><td>479</td><td>356</td></tr><tr><td>10 K min<sup>-1</sup></td><td>392</td><td>481</td><td>502</td><td>499</td><td>478</td><td>355</td></tr><tr><td>20 K min<sup>-1</sup></td><td>393</td><td>482</td><td>502</td><td>498</td><td>477</td><td>353</td></tr></tbody></table>

transition temperatures found by our experiments on heating and cooling. Phase transition temperatures from the studies on the dielectric response of PLZT 2/95/5 were also added [18].

## 4. Discussion

Analysing the parameters of Raman modes is fundamental for a comprehensive understanding of the structural and dynamic behaviours of PLZT during phase transitions. The changes in the Raman spectra were evaluated by fitting the Raman spectra with damped harmonic oscillators.

At first glance, the AFE phases of both samples appeared to be comparable in terms of the number and behaviour of Raman modes. The frequencies of all modes agree with those reported previously [12, 14, 25, 32].

For PZT 95/5 we used a fit similar to the one explained in [8], and the orthorhombic AFE phase was fitted using 27 modes. $FE_{HT}$ and $FE_{LT}$ phases were fitted with 15 and 16 modes respectively.

For PLZT 2/95/5 the AFE phase was fitted using also 27 modes, although the fit shows some differences explained later. The intermediate $AFE_{IC}$ phase of PLZT consists of 16 modes like the one in PZT, however the shape of the lines indicates a different space group. In comparison to the low temperature AFE phase, one new mode emerged at ~25 cm⁻¹ in this phase, broader bands, instead of multiple peaks appear in regions near 350 cm⁻¹ and 500 cm⁻¹.

Because of the weak Raman signal activated due to cationic disorder in the PE phases of PZT and PLZT, it was fitted using 5 and 8 broad bands respectively, as in other PZT ceramics [33, 34]. The introduction of La strengthen the disorder and, apart from the main bands in PZT, three extra weaker bands had to be added.

In figure 6 we depict the deconvolution of the fits together with the experimental spectra of PLZT at selected temperatures in the three main phases (PE, $AFE_{IC}$, and AFE). Some of the peaks, marked with asterisks in this figure, can be taken as indicators of structural changes, as their intensity display abrupt changes on cooling throughout the phase transitions. The deconvoluted fit of PLZT was shown in [8].
<figure><img src="image_8.png" /><figcaption>**Figure 3.** Bose–Einstein reduced Raman spectra of (a) PLZT 2/95/5 and (b) PZT 95/5 on cooling from 600 K to 80 K.</figcaption></figure>

<table><caption>**Table 2.** Comparison of the transition temperatures obtained by DSC and Raman spectroscopy at the rate 1 K min⁻¹.</caption><thead><tr><th colspan="2"></th><th colspan="3">PLZT 2/95/5 (rate 1 K min<sup>-1</sup>)</th></tr><tr><th></th><th></th><th>T(K)</th><th>T<sub>AFE</sub></th><th>T<sub>C</sub></th><th>T°</th></tr></thead><tbody><tr><td rowspan="2">Heating</td><td>Raman</td><td>393</td><td>484</td><td>—</td><td rowspan="2">501</td></tr><tr><td>DSC</td><td>390</td><td>480</td><td>—</td></tr><tr><td rowspan="2">Cooling</td><td>Raman</td><td>362</td><td>482</td><td>—</td><td rowspan="2">500</td></tr><tr><td>DSC</td><td>358</td><td>480</td><td>—</td></tr></tbody></table>

The temperature dependences of the Raman modes frequencies for both the ceramics are presented in figure 7 along with the behaviour of the area of selected modes. In the frequencies (lower panels), each colour indicates a different phase, and the sudden appearance or disappearance of some modes makes the transition noticeable. The areas of the selected peaks depicted in the upper panels provide a clear visualization of the transition from one phase to another. A sudden change in the areas of the modes was visible in the transition region, especially in the modes at 121.5 cm⁻¹, 243.5 cm⁻¹, and 349.1 cm⁻¹.

The replacement of some Pb atoms by La in the A-site of the perovskite structure of PLZT can, in principle, induce extra external vibrations at low frequencies (below ~ 100 cm⁻¹), although this effect is dependent on the amount of La. On the other hand, La does not induce direct band splitting in the internal vibrations of the BO₆ octahedra, as it is not located at the B-site.

In the AFE phase, La substitution caused a significant hardening of all modes as evidenced by the upward shift in frequencies in the Raman spectra compared to PZT as clearly shown in figure 8, implying that the chemical bonds became stronger and stiffer. This frequency shift was more pronounced in the intermediate frequency range (180 cm⁻¹ to 580 cm⁻¹), corresponding internal modes of the octahedra. The external vibrations related to Pb and La, at lower frequencies (below ~ 100 cm⁻¹) were not much affected by the substitution, because the 2% amount of La is too small to induce new phonons.

A small peak present at 680 cm⁻¹ in PZT is absent in PLZT. This peak is relevant in identifying the FE rhombohedral phase in PZT [8], meaning that in PZT 95/5, there is a residual FE phase coexisting within the AFE phase. As there is no FE phase in PLZT, such a peak is not present in the Raman spectra. The extra mode at 360 cm⁻¹ in PLZT 2/95/5 is a new internal vibration of the oxygen octahedra. As PLZT is AFE, this requires a multiplication of the unit cell, and new modes from the Brillouin zone boundary became active.
<figure><img src="image_9.png" /><figcaption>**Figure 4.** Comparison of Bose–Einstein reduced Raman spectra between PLZT 2/95/5 and PZT 95/5 at selected temperatures. At low temperatures the same antiferroelectric phase is attained (a). At 300 K the tilted R3c ferroelectric phase of PZT 95/5 is not displayed by PLZT 2/95/5 (b). At 400 K the ferroelectric phase R3m of PZT 5/95/5 is not displayed by PLZT 2/95/5 (c).</figcaption></figure>

The analysis of the parameters of the low-frequency modes (below 150 cm⁻¹) shows that below $T_C$ when the AFE<sub>IC</sub> phase appears, most of the new modes harden on cooling. The most intense are those at ~30 cm⁻¹ and 100 cm⁻¹. Following the mode assignment in PbZrO₃ [35] the first one corresponds to the AFE soft mode related to the Pb/La antipolar displacements (Σ mode), and the second one to the antiferrodistortive (AFD) soft mode related to the oxygen octahedra tilt (R₂₅ mode).

An extra soft mode of lower frequency was found as a shoulder in the lowest frequency Raman band. Taking into account that this new phase is IC [13] and the low frequency of the mode, we can relate it with the Pb soft vibrations in this phase. According to the literature on IC crystals, on cooling, the nucleating IC phase should show two new soft modes called amplitudon (soft mode related to the amplitude of the IC waves), and a phason (soft mode related to the phase, i.e. the shift of the modulated wave) [36, 37]. By symmetry, the amplitudon is always Raman active, but the phason is out of the Brillouin zone centre, therefore not detectable by Raman scattering. From the new soft modes detected, the weaker and lowest-frequency one, with $\omega \sim 20$ cm⁻¹, also hardens on cooling and it may be related to the IC regions. Moreover, this range of frequency agrees well with amplitudons found in another IC ferroelectric materials as K2ZnCl4 [38] SrNb₂O₇ [39].

The space group of the AFE<sub>IC</sub> phase in this temperature range is still unknown, but its symmetry is probably orthorhombic, as in Sn-substituted PZT [40], Sn-substituted PZO [41], or PbHfO₃ [31]. Due to symmetry restrictions, it cannot have the same *Pbam* (n. 55) space group, therefore a higher space group is required, ruling out *Bmm*2 (n. 38) in favour of *Imma* (n.74) or *Cmmm* (n.65), with multiplied unit cell ($Z = 2$ or 4) due to the high number of new modes found. The symmetry analysis gives, as possible routes for this transition sequence: *Pm* $\overline{3}m \rightarrow *Imma* \rightarrow *Pbam*, or *Pm* $\overline{3}m \rightarrow *Cmmm* \rightarrow *Pbam*.

On further cooling, below $T_{AFE}$, the unit cell doubles again, $Z = 8$ and new Raman modes appear, corresponding to the new modes of the *Pbam* space group and also from the Brillouin zone boundary. The soft modes found are depicted in figure 9. Below 60 cm⁻¹ (left panel) there are two main modes in the AFE<sub>IC</sub> phase (purple symbols), corresponding to Pb/La vibrations against the oxygen octahedra network (external vibrations). Below $T_{AFE}$, the lowest one (with $\omega \sim 20$ cm⁻¹) hardens on cooling and disappears below $T_{AFE}$, and the other one ($\omega \sim 30$ cm⁻¹) also hardens on cooling, then displays a jump at $T_{AFE}$, and hardens further on cooling. These two modes are the two soft modes of the AFE<sub>IC</sub> phase (the amplitudon and the antipolar mode, resp.). Above 80 cm⁻¹ (right panel) in the AFE<sub>IC</sub> phase, the AFD mode has a frequency around 90 cm⁻¹ and
<figure><img src="image_10.png" /><figcaption>**Figure 5.** Temperature-La content phase diagram for PLZT 100x/95/5. Symbols for DSC and Raman data are from our measurements on heating and cooling. Thermal hysteresis was seen in the line between FE<sub>HT</sub> and FE<sub>LT</sub> phases in PZT 95/5 and in the line between the two AFE states in PLZT. Dielectric data are from [18].</figcaption></figure>

hardens on cooling, then it shows a sudden change in frequency (first-order like) at $T_{AFE}$, displaying similar behaviour as the reported AFD mode in PZO [35, 42]. Other weaker modes were necessary for the fit and are shown by open symbols.

In overall the temperature behaviour of the low-frequency phonons demonstrates that the phase transition from AFE<sub>IC</sub> towards the AFE phase of *Pbam* symmetry is of displacive type, driven by phonons out of the Brillouin zone. This phase transition is not lock-in transition, like in other IC ferroelectric crystals as K<sub>2</sub>SO<sub>4</sub>, where the shift of the IC satellites changes gradually with temperature until it freezes (locks) in a point of the reciprocal space belonging to a commensurate ferroelectric space-group. Here, and in other Pb-based AFE materials, the phase transition involves a further multiplication of the unit cell to attain another AFE state. This is due to the complex nature of the Pb-based perovskites, which have several competing soft instabilities.

One of the goals of the investigation was to understand what happens to the sample in the so-called SLFE phase according to the phase diagram (figure 5). Our DSC measurement revealed that there is a small anomaly at $T^* \sim 502$ K when the sample is heated or cooled at a high enough rate. In order to investigate this phase, we took the Raman spectra each 2 K from 525 K to 480 K, and carefully normalized and analysed the data. However, the analysis did not draw final conclusions about this, because the spectra between $T^*$ and $T_C$—we named this region distorted paraelectric (PE<sub>DIS</sub>) phase—and the actual PE phase look very similar, and the mode parameters do not display a convincing change to extract a phase transition temperature. A slight change in intensity is barely seen in the lower frequency bands but overall, the spectra below 500 K resemble those in the PE phase. As the structural distortion is so small, it is not well reflected in the Raman phonons. However, some traces of additional disorder were found by other techniques [13], and this agrees with the nucleation of polar regions, or at least polar fluctuations with larger correlation lengths, within the PE phase, with slightly distorted cubic symmetry (PE<sub>DIS</sub>), as claimed already from infrared and dielectric measurements [18], and also corresponds to the weak phase transition observed in our DSC measurements at $T^*$.

Our combined investigations concluded that the sequence of phase transitions for PLZT 2/95/5 on cooling is: PE-PE<sub>DIS</sub>-AFE<sub>IC</sub>-AFE. Raman spectra suggest that the PE and PE<sub>DIS</sub> phases are distorted from the cubic symmetry with different levels of disorder, the AFE<sub>IC</sub> is orthorhombic, on average probably *Imma* (or *Cmmm*), but no space group has been assigned so far, and the low-temperature AFE phase is orthorhombic with space group *Pbam*.

**5. Conclusions**

The comparison of PZT 95/5 with La substituted PLZT 2/95/5 by means of calorimetry and Raman spectroscopy revealed that both samples are antiferroelectric and orthorhombic at low temperatures with the
<figure><img src="image_11.png" /><figcaption>**Figure 6.** Deconvolution of the Raman fits at the three main phases of PLZT 2/95/5. Experimental spectra are marked by points, fits by blue lines. Asterisks denote modes strongly affected by the phase transitions. Raman spectra are reduced by the Bose–Einstein factor.</figcaption></figure>

same space group. However different intermediate states are displayed on heating to the paraelectric phase. PZT exhibits two distinct intermediate FE phases, a higher temperature one (FE<sub>HT</sub>) and a lower temperature one (FE<sub>LT</sub>). Raman spectra identified characteristic modes for each phase, facilitating the differentiation between the phases and determining the transition temperature. For PLZT, the transition takes place from a commensurate antiferroelectric (AFE) phase to another AFE phase which is incommensurate (AFE<sub>IC</sub>). Before fully transforming into the cubic paraelectric (PE) phase, PLZT goes through a distorted cubic phase (PE<sub>DIS</sub>). This transition from PE<sub>DIS</sub> to PE was not easily visible in Raman spectra, however it was detected in DSC as a very weak peak. On cooling, we found the same sequence with some thermal hysteresis mainly in the AFE<sub>IC</sub>–AFE transition. This behaviour resembles the phase transition sequence in other AFE Pb-based perovskites with Sn substitution [31, 41].

From the measurements, the effect of La on PZT 95/5 can be summarized like this:

- La substitution alters the Pb dynamics and suppresses the polar order stabilizing the AFE phase already at high temperatures. La does not promote FE behaviour, which only appears in the form of polar regions near T<sub>C</sub>, being suppressed on further cooling, unlike PZT 95/5, where ferroelectricity fully develops, and only below room temperature antiferroelectricity can be achieved.

- Below T<sub>C</sub> there is a temperature region where polar nanoclusters or polar fluctuations appear giving rise to a small calorimetric anomaly only visible at high cooling/heating rates and a small anomaly in the intensity of the Raman signal.
<figure><img src="image_12.png" /><figcaption>**Figure 7.** Temperature dependences of the frequencies of the Raman modes (lower panels) and the area of selected peaks (upper panels) in (a), (c) PLZT 2/95/5 and (c), (d) PZT 95/5. Hollow symbols refer to weaker modes.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 8.** Expanded comparison of frequencies of the Raman modes for PLZT 2/95/5 and PZT 95/5 in the AFE phase.</figcaption></figure>

- La enhances the IC positions of some atoms, therefore the AFE phase formed below $T_C$ is incommensurate. The averaged symmetry of this phase is still unresolved, but it is probably orthorhombic *Imma* (or *Cmmm*), Raman spectra proved that this phase is different from the FE phase appearing in PZT 95/5, and it is likely AFE due to the presence of new zone boundary modes and hardening of some of the modes on cooling. Our Raman experiment detected three main soft modes in the AFE<sub>IC</sub> phase: an antiferrodistortive mode, an antipolar mode, and a weaker amplitudon, which corroborates the IC nature of this phase.

- Finally, the low-temperature phase in PLZT is AFE and has the same space group *Pbam* as PbZrO<sub>3</sub>, supported by XRD measurements. La affects slightly the frequency of the Raman modes, shifting mainly up the frequency of the oxygen octahedra bending and stretching vibrations.
<figure><img src="image_14.png" /><figcaption>**Figure 9.** Temperature dependence of the Raman mode frequencies below 150 cm⁻¹ in PLZT 2/95/5. Three main soft modes are seen in the incommensurate phase, the AFD mode, the antipolar SM, and the amplitudon near 20 cm⁻¹. Weaker modes are presented with open symbols.</figcaption></figure>

## Acknowledgments

This work was partially financed by the Czech Science Foundation (GAČR) through a Lead Agency bilateral Czech-Slovenian project (no. 24-10699K).

## Data availability statement

The data cannot be made publicly available upon publication because the cost of preparing, depositing and hosting the data would be prohibitive within the terms of this research project. The data that support the findings of this study are available upon reasonable request from the authors.

## Disclosure statement

No potential conflict of interest was reported.

## ORCID iDs

Anirudh K R https://orcid.org/0009-0007-2311-5221

Cosme Milesi-Brault https://orcid.org/0000-0002-3431-3158

Přemysl Vaněk https://orcid.org/0000-0002-7607-3033

Esther de Prado https://orcid.org/0000-0003-1133-3161

Elena Buixaderas https://orcid.org/0000-0001-8540-1441

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