Nanoscale studies of domain wall motion in epitaxial ferroelectric thin films Available to Purchase

We note that during AFM writing, the exact magnitude of the effective field is difficult to quantify because of a possible gap between the film surface and the tip (Ref. 8), and variations in tip shape. Local piezoelectric hysteresis measurements on $120–800Å$ thick films show that the minimum switching field is $∼6–16$ times larger than the bulk coercive field, an effect that is not observed with macroscopic electrodes on similar films. The effective field $E$ in the experiments is therefore presumably ∼ one order of magnitude smaller that that calculated as $E(r)$ in this study. This has no effect on the exponent $μ$ governing the exponential velocity dependence. Unless otherwise noted, the values reported are the directly calculated ones, with no further corrections.

In the absence of a depolarization field the nucleus is isotropic. Taking into account the depolarization changes the shape of the nucleus, but does not affect in an essential way the physics leading to the creep process.

This value is computed for $PbTiO3$⁠. The presence of Zr in PZT would lead to local variations of this energy density.

There are constants of order one, dependent on the dimension $d$⁠, which have been omitted from each term in the energy. These constants will not affect the creep exponent $μ$⁠.

Note that in order to take into account the depolarization effects lengths along the vertical axis have to be scaled by a factor $(σp∕σw)1∕2$⁠, as in (4). Here $L$ denotes lengths perpendicular to the polarization direction.

In this simplified description we assume that the temperature is small enough to neglect thermal effects.

Above $Lc$⁠, the domain wall can also remain locally pinned on individual strong pinning sites, but in the present discussion, only weak collective pinning is considered.

For the random bond case, long range dipolar forces would push in the two-dimensional case the exponent to $μ∼0.66$ (Ref. 34).

We now denote simply by $ξ$ the $max(ξ,rf)$⁠.

As before the length here is the length perpendicular to the polarization direction.

In the thinnest films, longer writing times resulted in unstable and destructive interactions between the tip and the sample. Therefore the larger domains obtained for long writing times were only measured in the thicker films.

We note that the studies referred to were carried out in thick (over $1μm$⁠) ceramic and sol-gel films, where the presence of multiple grain boundaries and differently oriented domain walls provides a much more complex disorder landscape compared to the epitaxially grown films used for this study.