Broadband dielectric spectroscopy of phonons and polar nanoclusters in ${\text{PbMg}}_{1/3}{\text{Nb}}_{2/3}{\text{O}}_3\text{−}35\%{\text{PbTiO}}_3$ ceramics: Grain size effects

The dielectric response of ${\text{PbMg}}_{1/3}{\text{Nb}}_{2/3}{\text{O}}_3\text{−}35\%{\text{PbTiO}}_3$ ceramics (close to the morphotropic phase boundary) from 100 Hz up to 100 THz was determined in a broad temperature range of 5–900 K. Two ceramics were studied and compared: coarse grain ceramics (CGC) (grain size $\sim 4\mu \text{m}$) and fine grain ceramics (FGC) (grain size $\sim 150\text{nm}$). Both ceramics showed similar polar-phonon response and the ferroelectric transition near $T_C=440\text{K}$ that was manifested by partial softening of the overdamped lowest-frequency phonon using the time-domain THz spectroscopy. However, the dielectric response was dominated by a complex relaxational dispersion in the microwave range due to relaxorlike dynamics of the polar nanoclusters, which strongly differed in both the ceramics. Whereas the CGC undergoes a well-defined ferroelectric transition such as a single crystal, FGC exhibits a relaxor behavior with substantially smaller permittivity showing partial clamping of the polar nanocluster dynamics by grain boundaries. The pronounced difference was also revealed in a second-harmonic generation showing much larger paraelectric signal in the FGC with a much smeared ferroelectric transition only. Due to contributions of both the soft phonon mode and dielectric relaxations into the dielectric constant near its maximum even in the paraelectric phase, the ferroelectric transition corresponds to a percolation threshold of the polar nanoclusters into macroscopic domains. Such a type of phase transition can be considered as a special case of crossover between the displacive and order-disorder types, where the ordering process concerns a mesoscopic range.

Figure 1

(Color online) Temperature dependences of (a) dielectric permittivity ${\epsilon }^{\prime }$ and (b) loss ${\epsilon }^{″}$ of the CGC for frequencies between 100 Hz and 250 GHz.

Figure 2

(Color online) Temperature dependences of (a) dielectric permittivity ${\epsilon }^{\prime }$ and (b) loss ${\epsilon }^{″}$ of the FGC at frequencies between 100 Hz and 250 GHz.

Figure 3

(Color online) Temperature dependences of the [(a), (c), and (e)] dielectric permittivity ${\epsilon }^{\prime }$ and [(b), (d), and (f)] loss ${\epsilon }^{″}$ of the CGC (solid lines) and FGC (dash lines) at [(a) and (b)] 100 Hz, [(c) and (d)] 300 MHz, and [(e) and (f)] 250 GHz.

Figure 4

(Color online) Frequency dependences of (a) dielectric permittivity ${\epsilon }^{\prime }$ and (b) loss ${\epsilon }^{″}$ of the CGC at temperatures between 100 and 480 K. Dash lines at $T\ge 300\text{K}$ are multicomponent Cole-Cole fits. $R1$ and $R2$ denote loss maxima of the two relaxational contributions (see the text).

Figure 5

(Color online) Frequency dependences of (a) dielectric permittivity ${\epsilon }^{\prime }$ and (b) loss ${\epsilon }^{″}$ of the FGC at temperatures between 100 and 450 K. $R$ denotes the asymmetric loss maximum by two overlapping relaxational contributions (see the text).

Figure 6

(Color online) IR and THz reflectivity spectra of (a) CGC and (b) FGC at temperatures between 5 and 800 K. THz reflectivities were calculated from the THz dielectric response.

Figure 7

(Color online) Complex dielectric response of CGC in the THz and IR ranges (solid lines) obtained by fitting of the IR reflectivity spectra together with THz experimental data (symbols) at temperatures below 450 K. TO1, TO2, and TO4 denote the loss maxima attributed to the three IR-active transverse optical phonons. $A_1\left(\text{TO}1\right)$ and $E\left(\text{TO}1\right)$ are components of the soft TO1 mode.

Figure 8

(Color online) The same as in Fig. 7 for temperatures above 600 K. $E\left(\text{TO}1\right)+\text{CM}$ denotes a joint contribution of the $E$ component and relaxational CM at the lowest frequencies.

Figure 9

(Color online) Complex dielectric response of the FGC in the THz and IR ranges (solid lines) obtained by fitting of the IR reflectivity spectra together with the THz experimental data (symbols) at temperatures below 450 K.

Figure 10

(Color online) The same as in Fig. 9 for temperatures above 500 K.

Figure 11

(Color online) Components of the soft TO1 phonon mode. Temperature dependences of the $A_1\left(\text{TO}1\right)$ and $E\left(\text{TO}1\right)$ frequencies in the CGC (solid lines and symbols) and FGC (dash lines and open symbols) obtained from the multioscillator fits of the IR reflectivity spectra together with the THz data.

Figure 12

(Color online) Soft and central modes in the CGC (solid lines and symbols) and FGC (dash lines and open symbols). Characteristic frequencies of the relaxational central mode components $\left(R1,R2,R\right)$ and soft $E\left(\text{TO}1\right)$ mode correspond to the maxima in the dielectric loss spectra. Symbols denote the experimental points, lines $R1$, $R2$, and $R$ are fits of their temperature dependences (see details in the text).

Figure 13

(Color online) Temperature dependence of the SHG signal in CGC (solid lines) and FGC (dashed lines).