Aging and slow dynamics in ${\mathrm{Sr}}_x{\mathrm{Ba}}_{1-x}{\mathrm{Nb}}_2{\mathrm{O}}_6$

The uniaxial “relaxor” ferroelectric ${\mathrm{Sr}}_x{\mathrm{Ba}}_{1-x}{\mathrm{Nb}}_2{\mathrm{O}}_6$ (SBN) is found to crossover from holelike to cumulative aging as it is cooled into the frozen relaxor regime. The cumulative aging contrasts sharply with the behavior of cubic relaxors, supporting ideas that the spin-glasslike aging in cubic relaxors is connected with polarization components orthogonal to the net ferropolarization. In the relaxor regime, small dc fields are found to suppress much of the dissipative response, similar to long-time aging. Pyroelectric currents are measured, along with limits on pyroelectric noise, allowing limits to be set on dynamically coherent domain sizes. Large nonlinear susceptibilities are found near the freezing transition.

Figure 1

(Color online) The complex dielectric coefficients (${\epsilon }^{\prime }$ and ${\epsilon }^{″}$) for the two samples are shown as a function of $T$ at $f=100\mathrm{Hz}$. Data were taken on cooling at about $4\mathrm{K}∕\min$ (SBN) and about $2\mathrm{K}∕\min (\mathrm{SBN}:\mathrm{La})$ and at rms fields of $13\mathrm{V}∕\mathrm{cm}$ (SBN) and $0.7\mathrm{V}∕\mathrm{cm}(\mathrm{SBN}:\mathrm{La})$.

Figure 2

(Color online) Temperature dependence of ${\epsilon }^{″}∕{\epsilon }^{\prime }$ is shown for a range of frequencies, including both at $T_{\mathrm{P}}$ and at the lower-$T$ kinetic freeze-out.

Figure 3

(Color online) $T$ dependences of the frequency for which ${\epsilon }^{″}∕{\epsilon }^{\prime }$ is maximized are shown in an Arrhenius plot.

Figure 4

(Color online) Aging behavior of ${\epsilon }^{″}∕{\epsilon }^{\prime }$ is shown for a range of $T_{\mathrm{A}}$. All $T$ sweeps were made at roughly $3\mathrm{K}∕\min$. $\epsilon$ was measured with an rms field of $0.7\mathrm{V}∕\mathrm{cm}$ at 50 Hz for $\mathrm{SBN}:\mathrm{La}$ and with $13\mathrm{V}∕\mathrm{cm}$ rms at 100 Hz for SBN. In panels (a) through (c) curve 1 is taken on cooling from 350 K to $T_{\mathrm{A}}$, at which $T$ was fixed for 16 h. Curve 2 was taken cooling to a lower $T_{\mathrm{B}}$, with immediate reheating to 350 K along curve 3. Curves 4 and 5 are reference heating and cooling curves. For panel (d) the starting $T$ was 300 K and the aging time 17.6 h. $T_{\mathrm{B}}$’s were 180, 180, 140, and 120 K, respectively. For panels (e) and (f), the initial annealing $T$ was 450 K, aging at $T_{\mathrm{A}}$ lasted for 5 h, and $T_{\mathrm{B}}$ was 150 K.

Figure 5

(Color online) Comparison of the aging of ${\epsilon }^{″}$ in SBN at different measurement frequencies is shown. The starting time for $t_{\mathrm{W}}$ was taken to be when $T$ first reached 290 K. We find no regime with $\omega \tau$ scaling, i.e., both $\omega$ and $\tau$ matter, not just the product.

Figure 6

(Color online) Dependence of ${\epsilon }^{″}∕{\epsilon }^{\prime }$ on the electric field in which the SBN sample is cooled is shown. The measurement frequency was 100 Hz and the rms ac field was $27\mathrm{V}∕\mathrm{cm}$.

Figure 7

Transient effect of a temporarily applied electric field on the aging of ${\epsilon }^{″}∕{\epsilon }^{\prime }$ is illustrated. The initial oscillations come from oscillations of $T$.

Figure 8

(Color online) Plots of ${\epsilon }^{″}∕{\epsilon }^{\prime }$ versus aging time (starting from when $E$ is turned on) at different $T$ and $E$ show clear characteristic aging times ${\tau }_{\mathrm{C}}$ at which $d({\epsilon }^{″}∕{\epsilon }^{\prime })∕d\ln \left(\tau \right)$ is maximal.

Figure 9

Characteristic aging times, as seen in Fig. 8, are shown in an Arrhenius plot and versus electric field at fixed $T$.

Figure 10

(Color online) Net polarization versus $T$, as measured from integrated pyroelectric current, is shown for the SBN sample. Current was measured on warming at rates of roughly $30\mathrm{K}∕\min$ in zero field after cooling in several different fields.