Fyzikální ústav Akademie věd ČR

BZT and NBT have become recently the most studied lead-free relaxor materials for their attractive piezoelectric and interesting physical properties. Our dielectric spectra of BZT of various compositions revealed that in addition to the lowest-frequency phonon mode near 1 THz, which is not much temperature dependent (no soft mode), there appear two relaxations in the spectra, the high-frequency one in the 10¹¹ Hz range (assigned to quasi-Debye losses) and the dominant low-frequency one, which obeys the common Arrhenius law for all the relaxor compositions below ~ 200 K (see Fig. 1) [1,2] and accounts for the permittivity vs. temperature maxima characteristic for the relaxor behaviour. Since from first-principles calculations as well as structural characterization it follows that the local Ti-O and Zr-O distances in BZT are independent of composition, the characteristic polar nanoregions (PNRs) should be localised within the chemical nanoclusters of BaTiO₃, where the Ti⁴⁺ ions are off-centred. Their simple Arrhenius thermal activation allowed us the assignment of the relaxations to local hopping of the Ti⁴⁺ ions among the off-centred positions within the Ti-O₆ octahedra. This picture was also confirmed by analysing the relaxation and phonon dynamics using first-principles calculations for the BaZr_1/2Ti_1/2O₃ composition in collaboration with the University of Arkansas, also separately for the Ti and Zr clusters [3]. This picture differs strikingly from the Vogel-Fulcher dynamics in lead-based relaxors, where there is no clear correlation between the PNRs and chemical clusters [4].

Fig. 1: Temperature dependence of the characteristic frequencies of the main excitations in BZT at the THz and lower-frequency range. The low-frequency relaxation follows the same Arrhenius law for all the compositions and is assigned to local Ti ions hopping within the Ti-O₆ octahedra in BaTiO₃ clusters.

In NBT the nature of the well-known dielectric anomaly near T_m ≈ 600 K was analysed for the first time [5], since its dielectric dispersion is not apparent below the standard MHz range. We have shown that the soft mode contributes only weakly to the permittivity, but it couples to two relaxations, from which the lower-frequency one is thermally activated and dominates the dielectric anomaly. At low temperatures only the soft mode contributes to the spectra. At higher temperatures it transfers part of its oscillator strength to both relaxations. Since T_m is specified by domination of the ferroelectric rhombohedral phase in the rhombohedral-tetragonal coexistence region, the permittivity maximum at T_m is caused by a smaller coupling of relaxation with the soft mode in the rhombohedral phase compared to that in the cubic and tetragonal phase. Some of the measured spectra and the analysed frequencies and dielectric strengths are shown in Fig. 2. The whole rather peculiar dynamics up to the soft mode in the THz range was assigned to highly anharmonic motion of the Bi³⁺ ions, which are known to be highly underbonded.

Fig. 2: (a) Selected measured and fitted spectra in NBT. (b) Evaluated characteristic frequencies and dielectric strengths of the three modes below ~ 100 cm^-1. Notice that the dominant relaxation is thermally activated and continues slowing down above, as well as below the permittivity maximum near 600 K.

[1] D. Nuzhnyy et al., Phys. Rev. B 86, 014106 (2012)
[2] J. Petzelt et al., Ferroelectrics 469, 14 (2014)
[3] D. Wang et al., Nature Communications 5, 5100 (2014)
[4] J. Petzelt et al., Phase Transitions 88, 320 (2015)
[5] J. Petzelt et al., Phase Transitions 87, 953 (2014)