# Brillouin light scattering in niobium doped lead zirconate single crystal – Scientific Reports

Figure 1 shows examples of the Brillouin scattering spectra obtained at different temperatures in the cooling process and the frequency range of ± 75 GHz. In Fig. 1a, two modes are clearly visible. The stronger one is the longitudinal acoustic (LA) mode of PZO:Nb propagating along the [100] direction, while the weaker one stems from the glass plate, which holds the sample in the heating stage. The signal observed in the range of ± 10 GHz, which comes from the Rayleigh peak, was cut off. In Fig. 1b, only one Brillouin doublet of the LA mode coming from PZO:Nb can be observed down to about 227 °C. Below this temperature, a splitting of the LA mode appears and persists up to about 203 °C. A further decrease in temperature leads to the disappearance of the “high-temperature branch”. Unfortunately, no TA mode was observed in the whole temperature range. Most probably, it was connected with the experimental scattering geometry and the corresponding Brillouin selection rule23.

Figure 2 shows the LA mode frequency shift’s temperature changes and the full width at half-maximum (FWHM). Apparently, upon cooling softening of the LA mode takes place (Fig. 2a). This behaviour is similar to that observed in pure PZO (Fig. 2b)3, PbHfO324, PbHfO3 doped with tin12 and BaTiO33. The LA mode frequency (νB) changes in PZO:Nb follow those observed in PZO down to about 310 °C, while below that temperature the LA mode frequency is slightly higher for PZO:Nb.

A fascinating behaviour has been observed in the temperature range where phase transitions occur. All transition temperatures marked by vertical lines in Fig. 2a and c are taken from optical measurements presented in Fig. 310.

The phase transition from the paraelectric state (PE) to the first intermediate phase (IM1) occurs at about TC(= 237 °C). The next phase transition occurs from IM1 to the second intermediate phase (IM2) at about 230 °C, and then the coexistence of phases is observed10 between 227 and 220 °C. It is clearly visible from Fig. 3 that the domain structure changes between IM2 and IM1 phase and then between between IM1 and coexistence of phase below 227 °C and at the end the domain structure is not observed below 220 °C. However, from observing the central peak in Raman scattering experiments, the coexistence of phases persists down to 200 °C. Correlating the above temperatures with possible anomalies in LA modes frequency, it is evident that only a slight aberration is visible at Tc (where the permittivity exhibits a maximum10), and further softening occurs with decreasing temperature (Fig. 2a). Also, a minimal change in damping takes place (Fig. 2c). A similar case was observed from the Brillouin scattering study of PbHf0.7Sn0.3O312. In this crystal, the LA1 mode frequency did not show any minimum at the maximum permittivity temperature. The LA1 mode exhibits even further softening in the IM1 phase. It may suggest a lack of change in the crystal symmetry at TC, which stays in agreement with Raman scattering studies, in which no additional modes were observed10. Another slight anomaly is seen at IM1-IM2 phase transition (Fig. 2a), which is more pronounced in damping (Fig. 2c). Here, the LA1 mode frequency adopts a minimum value, and a splitting of this mode at 227 °C (Fig. 2a) occurs, which coincides with the IM2 macroscopic disappearance and the occurrence of the antiferroelectric state10. These peculiarities are associated with the increase in damping of the LA1 mode (Fig. 2c). Comparing these results with Raman scattering experiments suggests that the next acoustic LA2 mode is linked to the antiferroelectric state. At about 220 °C, an increase in damping in both LA1 and LA2 modes takes place together with a change in the Brillouin shift of the LA2 mode. This temperature corresponds to the disappearance of the IM2 phase as detected using a polarising microscope10 and Raman experiments of the Zr-O bending mode. With decreasing temperature, additional damping of the LA1 mode sets in, which is associated with relatively small frequency changes. At about 203 °C the LA1 mode disappears, which is consistent with the anomaly in Raman spectra.

Concerning undoped PZO (Fig. 2b and d), the two intermediate phases do not result from the antiferroelectric and paraelectric phase coexistence. However, a third intermediate phase (or post-transitional effects) emerges where two modes’ coexistence is apparent. In both cases, the softening of the LA1 mode frequency and the increase in damping in the paraelectric phase are observed, caused by the appearance of polar regions3 stemming from the mode–mode coupling of the transverse optic TO mode and the corresponding transverse acoustic TA one4,11. As already mentioned, this effect has been observed in many other perovskites3,11,24,25,26. According to Bussmann-Holder et al., polar-nano-regions are related to the oxygen ion’s nonlinear polarizability27. On the other hand, a kind of disorder in the oxygen octahedral tilts could be noted above TC27. Nb doping of PZO has a twofold effect. The transition metal ion is replaced by a higher valent one, and simultaneously the electrical misbalance is compensated by forming lead vacancies8,9,10,28. It is known that the lead-related vibrations are essential for the antiferrodistortive instability in PbHfO3 and PbZrO329. Therefore, it can be concluded that doping PZO with Nb has influenced the formation of polar regions in the paraelectric phase. It is consistent with the results shown in Fig. 2b and d, i.e. it causes slightly weaker damping of the LA1 mode and a slight increase in the frequency of this mode below 310 °C, as compared to PZO. The increase in frequency could stem from the coupling of acoustic vibrations and oxygen octahedral tilt vibrations, as observed in the Raman spectra10. The latter are massively influenced by Nb ions’ existence in the octahedral centre and the defects created in the lead sub-lattice10.

So that to relate better TC with the Brillouin light scattering results, the derivatives of frequency shift and damping for temperature have been assigned (Fig. 4). This approach has been used to obtain characteristic temperatures of relaxors and ferroelectrics30.

Indeed, the speed of changes in frequency and damping well corresponds to transition at TC. Also, an anomaly near 310 °C (marked with a slide line in Fig. 4) agrees with the temperature where polar nano regions, which come from defects, appear on cooling10. The next anomaly on cooling occurs at the Bussmann-Holder temperature TBH = 1.1 TC equal to about 288 °C (for calculations, temperatures TBH and TC have to be taken in Kelvins). This anomaly is due to the appearance of polar nanoregions (precursors). Interestingly, the temperature range between TBH and TC is divided into two regions (Fig. 4b). In the first one, a decrease in the speed of changes in damping could be observed down to about 255 °C, and in the second region, the rate of changes in damping increases when temperature decreases. Such a feature could also be observed in crystals obtained in different crystal growth procedures on their piezoelectric activity above TC9. The first derivative of frequency for temperature takes zero at the temperature at which the LA2 mode appears. Its minimum occurs at a temperature where the disappearance of transient effects using a polarising microscope was observed (Fig. 3). The minimum damping derivative occurs strictly at a temperature where the IM2 phase disappears. The two derivatives’ temperature changes also indicate that no extra heating of the sample is caused by laser light during measurements. Moreover, the minimum of LA1 mode and the LA2 mode’s appearance does not occur in TC. This unexpected result was not observed in pure PZO crystal.

It should be noted that, once polar clusters appear, they enable the coupling to the elastic waves via the electrostrictive effect, i.e. the coupling between the squared polarisation and the strain caused by the longitudinal acoustic mode18. However, if the polar clusters are long-lived, we can expect local piezoelectric coupling in the clusters, where the cubic symmetry is locally broken30. When a polarisation occurs due to the acoustic strain field’s action, it responds to and reacts to it18. This response is usually described as a relaxation process, and τLA is the relaxation time of this process. Since this process accompanies an energy exchange between the acoustic waves and the relaxational degree of freedom of the polar clusters, the energy dissipation is reflected in the damping of the LA mode, which is related to the phonon lifetime. This relaxation time can be derived from the abnormal changes in the frequency νB and the damping ΓB of a LA mode through the following equation31

$$\tau_{LA} = \frac{{\Gamma_{B} – \Gamma_{\infty } }}{{2\pi \left( {\nu_{\infty }^{2} – \upsilon_{B}^{2} } \right)}}$$

(1)

where $$\nu_{\infty }^{2}$$ is unrelaxed squared Brillouin shift in the high-frequency limit, $${\Gamma }_{\infty }$$ represents the high-frequency background damping which is not associated with the phase transition. Both quantities are derived from extrapolating toward the high-temperature region, where they exhibit nearly constant values.

Figure 5a shows the increase of relaxation time for LA1 mode with decreasing temperature for PZO and PZO:Nb. It signifies that the average volume of polar clusters increases and/or the interaction between the clusters is enhanced due to increased order parameter fluctuations near the phase transition temperature. Compared to pure PZO, doping with Nb ions causes a slight decrease in the relaxation time, suggesting a weakening in the interaction between polar nano regions or their smaller volume. It is consistent with the observation that the damping, represented by the half-width of the LA1 mode and is associated with the order-parameter fluctuations, becomes slightly smaller at temperatures below 310 °C compared to pure PZO. The overall changes in the mode frequency and damping in the PE phase are associated with polar clusters’ squared local polarisation18. As described above, the Nb doping disturbs the oxygen octahedra tilts, creates Pb vacancies and, thus, is expected to be responsible for more negligible polar activity in the PE phase.

The inverse of the relaxation time is shown in Fig. 5b. Linear behaviour could be observed just below 280 °C, while TBH = 288 °C for Nb-doped PZO. Such behaviour can be described using the following equation, which was initially suggested for the critical slowing down process in order–disorder systems25.

$$\frac{1}{{\pi \tau_{LA} }} = \frac{1}{{\pi \tau_{0} }}\frac{{T – T_{0} }}{{T_{0} }}$$

(2)

In this equation, T0 and τ0 are fitting parameters. The solid line in Fig. 5b denotes the best-fitted results, from which T0 = 168 °C and τ0 = 0.146 ps were confirmed. This kind of slowing-down behaviour was also observed in other systems, such as BaTiO325, Pb(Sc1/2Ta1/2)O332 and Ba2NaNb5O1533, which exhibit order–disorder behaviours, at least, partially.

The temperature dependence of the relaxation time and previous results of Raman scattering experiments10, i.e. the existence and behaviour of the central peak, lead to the conclusion that polar regions’ presence must be correlated with Pb vibrations. Moreover, it is independent of the dopant ions and the defects generated by them. It also demonstrates the critical role of the coupling of the optic and acoustic zone-center vibrations. The linear behaviour of the inverse relaxation time near TC is observed for perovskites, such as BaTiO3 and PbHfO325. Hence, we state that phase transition’s order–disorder nature also takes play in the PZO:Nb.

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