Disrupting long-range polar order with an electric field

Electric fields are known to favor long-range polar order through the aligning of electric dipoles in relation to Coulomb's force. Therefore, it would be surprising to observe a disordered polar state induced from an ordered state by electric fields. Here we show such an unusual phenomenon in a polycrystalline oxide where electric fields induce a ferroelectric-to-relaxor phase transition. The nonergodic relaxor phase with disordered dipoles appears as an intermediate state under electric fields during polarization reversal of the ferroelectric phase. Using the phenomenological theory, the underlying mechanism for this unexpected behavior can be attributed to the slow kinetics of the ferroelectric-to-relaxor phase transition, as well as its competition against domain switching during electric reversal. The demonstrated material could also serve as a model system to study the transient stages in first-order phase transitions; the slow kinetics does not require the use of sophisticated ultrafast tools.

Figure 1

The relaxor-to-ferroelectric transition during electric poling in BNT-2La demonstrated by dielectric behavior and in situ TEM observations. (a) Temperature-dependent dielectric constant and loss tangent for a virgin bulk sample. (b) Bright-field micrograph of a grain along its [112] zone axis, and (c) the corresponding electron diffraction pattern prior to poling. (d) Temperature-dependent dielectric properties of the same bulk sample as in (a) after poling. (e) Bright-field micrograph and (f) electron diffraction pattern of the same grain as in (b) after poling. The apparent depolarization temperature $T_{\mathrm{d}}$ is marked in (d). The nominal direction of the poling field in the in situ TEM experiment is indicated by the bright arrow in (e). The $\frac{1}{2}${ooo} and $\frac{1}{2}${ooe} superlattice diffraction spots are highlighted by a bright circle and a bright arrow, respectively, in (c).

Figure 2

Development and disruption of long-range polar order in BNT-2La. (a) Polarization, $P$, and longitudinal strain, $x_{33}$, developed under applied field of a bulk sample. The point pairs on the polarization and strain curves marked as $Z_0-Z_8$ indicate the fields where corresponding in situ TEM observations were recorded. (b–i) The corresponding in situ TEM results on a [112]-aligned grain. The positive direction of applied fields in the TEM experiment is indicated by the bright arrow in (e). The $\frac{1}{2}${ooo} and $\frac{1}{2}${ooe} superlattice diffraction spots are highlighted by a bright circle and a bright arrow, respectively, in (c).

Figure 3

In situ TEM observations on another [112]-aligned grain in the same TEM specimen as in Fig. 2. The positive direction of the applied field is indicated by the bright arrow in (c) and $Z_0,Z_2,Z_4,Z_5,Z_6,Z_7,Z_8$ mark the corresponding fields indicated in Fig. 2. The $\frac{1}{2}${ooo} and $\frac{1}{2}${ooe} superlattice diffraction spots are highlighted by a bright circle and a bright arrow, respectively, in (b).

Figure 4

Disrupting long-range polar order by electric field demonstrated in a bulk BNT-2La polycrystalline sample. (a) Polarization, $P$, vs electric field, $E$, hysteresis loop during the second cycle of the bipolar electric field. The corresponding polarization current density, $J$, curve reveals two anomalies in both the first and the third quarter cycle. (b) Evolution of the $\frac{1}{2}$(311) superlattice diffraction peak monitored by x-ray diffraction on a disk sample first poled at 60 kV/cm for 20 min (marked as “poled”), and then subjected to a dc field of −12 kV/cm [corresponding to the condition marked as “R” in (a)] for various times. The reductions in $d_{33}$ of a poled BNT-2La sample under a series of reverse dc electric fields are shown in (c) for electric fields of −9, −10, and −11 kV/cm, and (d) for electric fields of −12, −15, and −18 kV/cm. Experimentally measured $d_{33}$’s after each time period are shown as discrete points, while the dashed lines are fitting curves derived using the KWW relationship. Error bars for $d_{33}$ are of the order of the size of symbols and not shown. (e) Correlation of the characteristic time τ with the amplitude of the reverse dc field.

Figure 5

Rationalization of the electric field–induced ferroelectric-to-relaxor transition in polycrystalline BNT-2La with the phenomenological model. (a) The free-energy density profile of the ferroelectric phase (red) and the relaxor phase (blue) of BNT-2La at room temperature. The phase transition path marked by the arrows shows a lower energy barrier than polarization reversal and corresponds to the $J_3$ and $J_4$ peaks in Fig. 4. (b) The change in the volume fractions of various phases during polarization reversal in the third quarter cycle of electric field: $f_{\mathrm{R}}$, the volume fraction of the relaxor phase; $f_{+}$ and $f_{-}$, the volume fraction of the ferroelectric phase in the positive and the negative polar state, respectively. (c) Calculated $P$ vs $E$ hysteresis loop with mixed phases (black curve), plotted together with the constituent ferroelectric (red) and relaxor (blue) phases. FE and RE stand for ferroelectric and relaxor, respectively.