Local Probe Comparison of Ferroelectric Switching Event Statistics in the Creep and Depinning Regimes in $\mathrm{Pb}({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}){\mathrm{O}}_3$ Thin Films

Ferroelectric materials provide a useful model system to explore the jerky, highly nonlinear dynamics of elastic interfaces in disordered media. The distribution of nanoscale switching event sizes is studied in two $\mathrm{Pb}({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}){\mathrm{O}}_3$ thin films with different disorder landscapes using piezoresponse force microscopy. While the switching event statistics show the expected power-law scaling, significant variations in the value of the scaling exponent $\tau$ are seen, possibly as a consequence of the different intrinsic disorder landscapes in the samples and of further alterations under high tip bias applied during domain writing. Importantly, higher exponent values (1.98–2.87) are observed when crackling statistics are acquired only for events occurring in the creep regime. The exponents are systematically lowered when all events across both creep and depinning regimes are considered—the first time such a distinction is made in studies of ferroelectric materials. These results show that distinguishing the two regimes is of crucial importance, significantly affecting the exponent value and potentially leading to incorrect assignment of universality class.

Figure 1

(a) PFM phase images of down-polarized domains (bright contrast) with different roughness, written with 8 V in PZT-Nuc (left) and 10 V in PZT-Mot (right). (b)–(e) Local polarization switching bias maps for (b),(c) PZT-Nuc and (d),(e) PZT-Mot, acquired at negative (b),(d) and positive (c),(e) tip bias, corresponding to switching from pre-polarized down domains and from as-grown up domains, respectively.

Figure 2

Average domain displacement at each switching scan. (a) PZT-Nuc, ${\mathrm{V}}_{\mathrm{tip}}<0$, (b) PZT-Nuc, ${\mathrm{V}}_{\mathrm{tip}}>0$, (c) PZT-Mot, ${\mathrm{V}}_{\mathrm{tip}}<0$, (d) PZT-Mot, ${\mathrm{V}}_{\text{tip}}>0$. The shaded blocks show data in the creep regime included in the power law fitting.

Figure 3

(a) Probability distribution $P(s=S)$ of switching event sizes of surface $S$. Event size distributions and power-law fit for PZT-Nuc ${\mathrm{V}}_{\mathrm{tip}}>0$, ${\mathrm{V}}_{\mathrm{tip}}<0$ and PZT-Mot, ${\mathrm{V}}_{\mathrm{tip}}>0$ in the creep regime. PZT-Nuc and PZT-Mot for $V_{\text{tip}}>0$ are shifted vertically for clarity by a factor of 10 and 0.1 respectively. (b) Fitted exponents for box widths of 60–310 nm, clustering around $\tau =2.57$ and histogram of exponent values.

Figure 4

Equivalent disc radii of domains nucleated and expanding under constant dc scanning tip bias. (a) At $-3.5\mathrm{V}$, domains grow logarithmically with time. (b) At $-5.0\mathrm{V}$, domains grow linearly with time, indicating a depinned domain wall motion.