  Using multiscaling analysis, we compare the characteristic roughening of
ferroelectric domain walls in PZT thin films with numerical simulations of
weakly pinned one-dimensional interfaces. Although at length scales up to a
length scale greater or equal to 5 microns the ferroelectric domain walls
behave similarly to the numerical interfaces, showing a simple mono-affine
scaling (with a well-defined roughness exponent), we demonstrate more complex
scaling at higher length scales, making the walls globally multi-affine
(varying roughness exponent at different observation length scales). The
dominant contributions to this multi-affine scaling appear to be very localized
variations in the disorder potential, possibly related to dislocation defects
present in the substrate.
