are observed throughout the interface length. However, significantly more statistics would be necessary to confirm this observation, which we hope to address in further investigations.

Figure 5.22:Left: Map of switching events along a moving domain wall in PZT-Nuc when the positive DC tip bias during switching scans is incrementally increased at each scan. Right: Map of the position of switched pixels along the vertical axis in the left panel as a function of the applied tip bias. The colour code represents the depth (along the horizontal axis) of the switching event at that scan line. The map shows spatial correlation of events at low bias which breaks down as the switching bias is increased.

5.9 Conclusions

We observe markedly different switching dynamics in Pb(Zr0.2Ti0.8)O3 films with different defect landscapes established during sample growth, and discriminate between creep and depinning regimes as a function of the applied tip bias. While the switching event statistics all show power law scaling summarised in table5.1, we find significant variations in the value of the scaling exponentτ. The exponents range from 1.98±0.05 to 2.87±0.12 in the creep regime when considering only switching events occurring at driving fields below the depinning threshold. Lower values ranging from 1.81±0.05 to 2.56±0.1 are found when the distribution of events is not restricted to the creep regime, and switching events occurring during the entire driving field window are included.

The dynamics of individual growing domains was also investigated at a constant tip bias of -3.5 V and -5.0 V. Analysis of the resulting domain wall nucleation and motion suggest that in these measurements, a tip bias of -3.5 V induces creep motion of the written domain walls and newly nucleated domains while at -5.0 V, the applied force exceeds the critical barrier and allows depinning and more rapid dynamics. The characteristic size exponents were also fitted with the tip bias kept constant, in both of these measurements. While at -3.5V, the fitted exponent of 3.36±0.16 is

less reliable due to the overall range of accessed switching event sizes, the elevated value nonetheless highlights the importance of very small events at low driving forces. At -5.0V, the fitted exponent is found to be 2.1±0.05.

Overall, the exponents extracted in this study are significantly higher than the ones predicted by an elastic model, which suggests that deviations from this model could potentially occur or that more statistics and a broader range of scales need to be accessed in order to measure the size exponents more accurately. Questions remain as to whether the polarisation reversal through a scanning tip rather than a field applied homogeneously throughout the probed volume of material could lead to deviations from the expected power law exponents. Although studies of switching dynamics in BiFeO3

suggest that the overall dynamics is the same in both cases [166], this question deserves more careful study and theoretical support.

These results also show the importance of distinguishing between creep and depinning regimes in experimental measurements of characteristic ex-ponents linked to crackling. Furthermore, larger switching event sizes need to be made accessible in order to probe a larger range of sizes and increase the confidence that the distribution of event sizes follows a power law. As-suming that the distribution of events does follow a given universality class, reaching event sizes large enough to access the upper cutoff to the power law distribution might further allow particular models within that universality class to be distinguished.

Direct comparison of switching event sizes and currents could be allowed by acquiring the switching currents during the switching scans, which could allow independent extraction of size and energy exponents as defined in [92] and direct spatially-resolved comparison with the resulting domain configurations.

Further information could also be acquired by depositing arrays of micrometer-scaled electrodes on the surface of the films and performing similar measurements as in this work but with the driving force applied through these electrodes instead of through the tip. This setup could offer significant advantages. First, the electric fields applied through the sample

Table 5.1:Table of size exponentsτ measured in two samples with different defect landscapes.

Measurement No tip bias cutoffs With tip bias cutoffs PZT-Nuc Vtip >0 1.81±0.05 1.98±0.09

5.9 Conclusions

would in this case be much more homogeneous than through a tip and resem-ble the field applied in theoretical models much more closely, and the time during which the field is applied would be controlled much more accurately.

Second, applying the electric field through electrodes should in principle remove questions related to the effective tip field, ever-present in scanning probe measurements. This would also allow measurements to be performed on multiple electrodes and the acquired data to be pooled into a single distribution, significantly increasing the available statistics. Interestingly, the switching currents could be acquired simultaneously and potentially allow simultaneous extraction of the size exponent defined as the measured sizes of individual domains or defined as the integrated current above noise threshold as is done in [92]. Although this setup would have the drawback of lower spatial resolution as the PFM scanning would have to be performed through the electrode, it could provide a very powerful tool for direct measurement of critical exponents in ferroelectric with spatial resolution.

CHAPTER 6

Correlations between domain wall currents and distortions

6.1 Motivation

As discussed in chapter 2.4, in Pb(Zr0.2Ti0.8)O3, one mechanism for the appearance of conduction at ferroelectric domain wall involves the accumu-lation of charged defects such as oxygen vacancies at the domain boundaries, providing a conducting pathway. In materials where the domain wall con-duction is provided by such defects, the currents at the walls are therefore expected to scale with the concentration of defects. Such a relationship has indeed been observed in studies of thin films of La-doped BiFeO3, where oxygen vacancies introduced by lowering the oxygen partial pressure during the post-growth cooling phase were shown to modulate the magnitude of the domain wall currents [43] by increasing the Fermi energy at the walls [42]. Doping has also been shown to increase the conductivity of domain walls in Ti-doped ErMnO3[49]. In the particular case of conduction at 180 domain walls in Pb(Zr0.2Ti0.8)O3 thin films, the conduction was attributed to domain wall tilting, leading to locally charged domain walls screened by charged defects such as oxygen vacancies.

Independently, considering domain walls as elastic interfaces in disordered media, fluctuations in the density of defects lead to variations in the disorder potential energy landscape. These fluctuations act as pinning sites and promote wandering, resulting in a characteristic self-affine roughness at equilibrium. Bearing these both in mind, one might therefore ask whether

the functional properties of the domain walls (in this case their increased electrical conductivity) can be linked directly to their geometric properties in terms of their distortions from a straight, elastically optimal configuration.

Measurements carried out on freshly written nano-domains in Pb(Zr0.2Ti0.8)O3

thin films showed strongly conductive domain walls with respect to the ferroelectric phase itself, with a metallic conductance character. However, in this case the nanodomains had both a high curvature as seen from the top surface as well as tilts along the polarisation axis, either of which could influence the conduction [52]. Subsequent theoretical studies suggested that tilts in face play an important role [167], but did not address the question of curvature. Thus, disentangling the effects of local domain wall curvature and tilt and how they affect the domain wall conduction could prove to be an interesting study.

In this chapter we therefore present preliminary work exploring whether a connection can be established between the local domain wall deformations and magnitude of the currents in Pb(Zr0.2Ti0.8)O3 thin films.

Dans le document Scanning probe studies of structural and functional properties of ferroelectric domains and domain walls in Pb(Zr0.2Ti0.8)O3 thin films (Page 90-95)