Dynamics of the phase transitions in Bi-layered ferroelectrics with Aurivillius structure: Dielectric response in the terahertz spectral range

We have investigated the dielectric response in the terahertz (THz) spectral range of a series of Bi-layered ferroelectrics with Aurivillius structure involving ferroelectric compounds $({\mathrm{Bi}}_4{\mathrm{Ti}}_3{\mathrm{O}}_{12},\mathrm{Sr}{\mathrm{Bi}}_2{\mathrm{Ta}}_2{\mathrm{O}}_9,\mathrm{Sr}{\mathrm{Bi}}_2{\mathrm{Nb}}_2{\mathrm{O}}_9)$, a relaxor ferroelectric $\left(\mathrm{Ba}{\mathrm{Bi}}_2{\mathrm{Nb}}_2{\mathrm{O}}_9\right)$, and intermediate-type compound $\left({\mathrm{Sr}}_{0.5}{\mathrm{Ba}}_{0.5}{\mathrm{Bi}}_2{\mathrm{Ta}}_2{\mathrm{O}}_9\right)$. The lowest-frequency polar phonons were studied by means of the time-domain THz transmission spectroscopy in the frequency range $0.1–2\mathrm{THz}$ at temperatures $10–950\mathrm{K}$. Although previous structural studies suggested a displacive character of the structural phase transitions, no soft-mode anomalies were observed in our THz spectra near $T_c$ in any of the investigated compounds. A gradual and only partial softening of the lowest frequency polar phonon was revealed during heating. Dielectric anomalies near $T_c$ in all the compounds should be caused by slowing down of relaxations, directly observed in some cases below the polar phonon range. The ferroelectric transitions are therefore not classically displacive. In analogy to other relaxor ferroelectrics, existence of dynamic polar clusters is suggested to be in origin of such relaxations. Ferroelectric transitions in such cases are connected with an abrupt freezing and rise of these clusters into domains and the classical division of phase transitions into displacive and order-disorder is no more sufficient.

Figure 1

(Color online) Complex dielectric spectra ${\epsilon }_{ab}^{*}\left(\omega \right)$ of SBN single crystal at selected temperatures. Solid lines are results of the quasiharmonic oscillator fits [Eq. (1)]. Direction of rise of temperature is marked by an arrow. Splitting of the $E_u$ mode is most remarkably seen at 600 and $500\mathrm{K}$.

Figure 2

(Color online) Experimental complex dielectric spectra of BBN ceramic (points) together with their fits (solid lines).

Figure 3

(Color online) Experimental complex dielectric spectra of SBBT ceramic (points) together with their oscillator fits (solid lines).

Figure 4

(Color online) Experimental complex dielectric spectra ${\epsilon }_{ab}^{*}\left(\omega \right)$ of BiT single crystal (points) together with their oscillator fits (solid lines).

Figure 5

(Color online) Temperature dependencies of (a) the lowest phonon frequency ${\omega }_1$, (b) phonon damping ${\gamma }_1$ and (c) dielectric strength $\Delta {ϵ}_1$. The parameters of two lowest frequency phonons are shown for SBN crystal. Parameters of SBT are taken from Ref. 23. The lines are guides for the eyes.

Figure 6

(Color online) Temperature dependences of the real and imaginary part of complex permittivity of BBN ceramics at frequencies from $100\mathrm{Hz}$ up to $8.8\mathrm{GHz}$.

Figure 7

(Color online) Frequency dependences of the real and imaginary part of complex permittivity of BBN ceramics plotted at selected temperatures. Small discontinuities at $1\mathrm{MHz}$ are due to the different experimental techniques used.