Two-step phase changes in cubic relaxor ferroelectrics

The field-driven conversion between the zero-field-cooled frozen relaxor state and a ferroelectric state of several cubic relaxors is found to occur in at least two distinct steps, after a period of creep, as a function of time. The relaxation of this state back to a relaxor state under warming in zero field also occurs via two or more sharp steps, in contrast to a one-step relaxation of the ferroelectric state formed by field cooling. An intermediate state can be trapped by interrupting the polarization. Giant pyroelectric noise appears in some of the non-equilibrium regimes. It is suggested that two coupled types of order, one ferroelectric and the other glassy, may be required to account for these data.

Figure 1

The standard empirical history-dependent phase diagram (Refs. 15, 16, 17) is shown for PMN. Sharp crossovers are shown with arrows to indicate the conditions (warming, cooling, increasing $E$) under which they were found. “FE” represents a ferroelectric state, “PE” a paraelectric state with nanodomains, and “RXF” a glassy relaxor state.

Figure 2

${\epsilon }^{\prime }\left(t\right),{\epsilon }^{″}\left(t\right)$, and $I_P\left(t\right)$ after applying a field of $3.7\mathrm{kV}∕\mathrm{cm}$ (at $t=0$) at 175 K after zero-field cooling.

Figure 3

$d{\epsilon }^{\prime }\left(t\right)∕dt$ and the polarization current are shown as a function of time $t$ after switching on a field of $2.5\mathrm{kV}∕\mathrm{cm}$ for the [001] PMN-6%PT sample.

Figure 4

Part (a) shows $d{\epsilon }^{\prime }\left(t\right)∕dt$ (solid line) and $I_P\left(t\right)$ (dashed line) after switching on $E=0.55\mathrm{kV}∕\mathrm{cm}$ at $T=250\mathrm{K}$ for the [111] PMN-12%PT sample. Part (b) shows $I_P\left(T\right)$ (solid line) on warming at $E=0$ the ZFC-F2 state, with the corresponding data (dashed line) for a simple FC prepared state. (The FC data were taken at half the sweep rate and then rescaled to approximately compensate.)

Figure 5

The two-step pulses in $I_P\left(t\right)$ are shown for different $E$ at 177 K. The curves have been offset for clarity. Curve (1) was taken at $3.17\mathrm{kV}∕\mathrm{cm}$, curve (2) at $2.91\mathrm{kV}∕\mathrm{cm}$ (with $I_P$ scaled $\times 2$), and curve (3) at $2.67\mathrm{kV}∕\mathrm{cm}$ (with $I_P$ scaled $\times 5$). The inset shows the $E$ dependences of the times.

Figure 6

Arrhenius plots of the $T$ dependences of the two times are shown at $E=3.17\mathrm{kV}∕\mathrm{cm}$. The fits give activation energies of 6700 K and 7600 K with nominal attempt rates of $5\times {10}^{13}{\mathrm{s}}^{-1}$ and $8\times {10}^{15}{\mathrm{s}}^{-1}$, respectively.

Figure 7

(a) ${\epsilon }^{\prime }\left(T\right)$ is shown on zero-field warming after different $E\text{−}T$ histories: (1) FC at $3.74\mathrm{kV}∕\mathrm{cm}$, (2) ZFC-F2 prepared at $3.74\mathrm{kV}∕\mathrm{cm}$ and 175 K, (3) as in (2) but ZFC-F1, interrupted after the first step, and (4) ZF, simple zero-field cycling. (b) $I_P\left(T\right)$ is shown for procedures (1) and (2). The inset shows a blow up of curve (2), in which the large noise is evident. Curve (1) is not perceptibly noisy on this scale.

Figure 8

$I_P\left(T\right)$ on zero-field warming is shown in detail for (a) ZFC-F2 and (b) ZFC-F1, illustrating both that the approximate reproducibility of the large current noise of ZFC-F2 in the previous figure and the larger noise from ZFC-F1. This ZFC-F1 warming curve was taken after 17 h of aging at $E=0$ and $T=174\mathrm{K}$, illustrating the stability of this state. Another curve taken after very brief aging looks very similar.