6.4 Preliminary results
The approach followed here is to extract the domain wall distortions, to-pographical curvature and domain wall currents at each point along the domain walls. However, because the distortion correction algorithm does not always perfectly correct distortions, a window around the wall has to be used in order to make sure that the domain wall currents and the correct topographical curvature are captured. To this effect, a window 5 pixels (40 nm) wide, with 2 pixels on each side of the domain wall position, and 1 pixel (8 nm) high was used. The dimensions of the window were chosen based on the observation that in this measurement series, most of the uncorrected distortions occur on the horizontal axis and the typical distortions remaining after application of the distortion correction algorithm are of the order of 2 pixels. The full width at half maximum of the current peak is typically of∼ 6-8 pixels (45-50 nm).
Figure 6.8:Wall 1 position with colour coding corresponding, from left to right, to the domain wall curvature, displacement from average, topographical curvature and domain wall current.
In this selected window, the sum of the c-AFM currents is calculated in order to integrate through the conducting channel and increase the signal.
This sum of currents is assigned as the current at the domain wall position in the window centre. The topographical curvature assigned to that same domain wall position is the maximum curvature over the 5 pixel window, based on the hypothesis that the highest curvature will lead to the highest contact area and measured current.
The resulting maps of the local domain wall curvature, displacement from the average position, maximum topographical curvature and current
Figure 6.9:Wall 2 maps of curvature, displacement from average, topographical curvature and domain wall current.
sum are shown for each wall in figures6.8-6.11. The currents shown in these figures were acquired at a tip bias of -1.375 V. At this tip bias, neither domain wall motion, nor hysteresis between the forwards and backwards branches of I-V ramps were observed and we therefore conclude that the currents are conduction rather than displacement currents. The domain wall positions were extracted from the PFM scan preceding the c-AFM scan at Vtip = -1.375 V.
Figure 6.10:Wall 3 maps of curvature, displacement from average, topographical curvature and domain wall current.
6.4 Preliminary results
A visual inspection of figures6.8-6.11suggests an absence of strong direct correlation between the extracted metrics of domain wall distortion and tip-sample contact and domain wall current magnitude. Wall 1, which is the roughest of the walls studied does have regions where both the local domain wall and topography curvatures match corresponding regions of higher domain wall current. However, other similarly highly curved regions in the domain wall and topography do not exhibit higher currents.
Figure 6.11: Wall 4 maps of curvature, displacement from average, topographical curvature and domain wall current.
This can further be seen by plotting the current as a function of the domain wall and topography curvatures and domain wall displacement.
Panels (a,c,e) of figure 6.12 show these plots for all domain wall points, while panels (b,d,e) show the distribution of the curvatures and domain wall displacement. As can be seen by comparing each plot with its corresponding histogram, the regions of higher currents in the plot also correspond to the regions of higher prevalence of the curvatures and displacement. This suggests that the higher values of the currents observed for lower domain wall radius might simply be an effect of the larger statistical sample in this range of radii. The same observation can be made regarding the domain wall displacements and topographical radius of curvature.
These correlations, or lack thereof, need to be analysed in further detail using specialised statistical techniques for skewed distributions such as calculating rank-based correlation coefficients, which will be the focus of further work.
Another possibility that needs to be considered is whether the distortions in the domain wall positions are due to topographical features affecting
Figure 6.12:Domain wall currents plotted as a function of (a,c,e) domain wall radius, topographical curvature and domain wall displacement. (b,d,f) Corresponding histograms of domain wall and topographical radii, and domain wall displacement respectively.
the writing process, rather than varying concentrations of defects. Figure 6.13shows the topography of the written structure, while the corresponding domain wall positions are shown by black lines. The large overhanging features observed in wall 1 seem to propagate within topographical valleys, while the top section of wall 4 seems to skirt along the edges of islands in the film surface. A more detailed analysis of such correlations is therefore required as well.
It is also possible that the curvature in the sample surface plane is a poor proxy for the distortions of the wall along the polar axis, which would be energetically much more costly and require screening for instance by defects [99]. Such distortions of the domain wall along the polar axis have been imaged both at the scale of a few unit cells [28] in Pb(Zr0.2Ti0.8)O3and at the order of 10-100 nm by Cherenkov SHG microscopy in LiNbO3 [168], and shown to induce higher conductivity.
Refinements of the preliminary analysis shown here are the subject of ongoing work.