Barkhausen noise probe of the ferroelectric transition in the relaxor $\mathrm{PbM}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}{\mathrm{O}}_3\text{−}12\%\mathrm{PbTi}{\mathrm{O}}_3$

Barkhausen current noise is used to probe the slow field-driven conversion of the glassy relaxor ferroelectric state to an ordered ferroelectric state. The frequent presence of distinct micron-scale Barkhausen events well before the polarization current starts to speed up shows that the process is not a conventional nucleation-limited one. The prevalence of reverse switching events near the onset of the rapid part of the transition strongly indicates that electric dipole interactions play a key role. The combination of Barkhausen noise changes and changes in the complex dielectric response indicate that the process consists of an initial mixed-alignment domain formation stage followed by growth of the domains aligned with the applied field.

Figure 1

The empirical phase diagram of a ${\mathrm{PMNPT}}_{12}$ sample from the same batch as those used for the noise studies shows the equilibrium paraelectric phase (PE), separated by a frequency-dependent crossover from the nonequilibrium relaxor state (RXF). The RXF is separated from the FE state by a nearly rate-independent melting line and a somewhat rate-dependent freezing line. The large gap between the melting and freezing temperatures at low $E$ gives the large hysteretic regime. Path 1 shows a ZFC process, and path 2 shows an FC process.

Figure 2

The block diagram of the circuit for measuring the LF and HF components of the polarization current, $I_P\left(t\right)$. The key component is the initial current-to-voltage converting op-amp AD549, with very low current noise, which is followed by instrumentation amp INA128, whose gain is set to 5 via an external resistor. The sample, located at the AD549 input, is shown as a slab with shaded contact plates.

Figure 3

A typical example of the LF $I_P\left(t\right)$ along with the changes in ε′ and ${\varepsilon }^{\prime \prime }$ on a ZFC protocol.

Figure 4

The key features of the HF noise on a typical ZFC protocol are illustrated in Fig. 4, which shows LF $I_P\left(t\right)$ along with HF $I_P\left(t\right)$.

Figure 5

Expanded views of individual spikes at various stages of the process: (a) creep stage, (b) creep stage, (c) late creep stage, (d) after FE transition, (e) after setting $E=0$, before melting, and (f) after main melting. The ringing seen most clearly in (b) is the response of the antialias filter to a brief pulse. Longer pulses, e.g., (c), smooth out the ringing. Pulse (e) appears to come from a mixed pair of positive and negative pulses.

Figure 6

Illustration that Barkhausen spikes in the reverse direction of the net polarization are typically found in the early stages of the main $\mathrm{RXF}\to \mathrm{FE}$ conversion event.

Figure 7

A spectrum taken from the regime of continuous Barkhausen noise. The squares are the bare spectrum. The circles show the same data after detrending and subtracting the spectrum of a detrended background taken just after the Barkhausen noise largely subsided. The shaded areas indicate regions in which the uncertainty in the time-dependent background subtraction prevents reliable estimates of the Barkhausen spectrum.

Figure 8

HF noise and ${\varepsilon }^{\prime \prime }\left(t\right)$, aligned via the LF $I_P\left(t\right)$ data. The solid $I_{LF}\left(t\right)$ goes with ${\varepsilon }^{\prime \prime }\left(t\right)$ data and the dotted $I_{LF}\left(t\right)$ goes with $I_{HF}\left(t\right)$.