  Using the model system of ferroelectric domain walls, we explore the effects
of long-range dipolar interactions and periodic ordering on the behavior of
pinned elastic interfaces. In piezoresponse force microscopy studies of the
characteristic roughening of intrinsic 71{\deg} stripe domains in BiFeO$_3$
thin films, we find unexpectedly high values of the roughness exponent {\zeta}
= 0.74 $\pm$ 0.10, significantly different from those obtained for artificially
written domain walls in this and other ferroelectric materials. The large value
of the exponent suggests that a random field-dominated pinning, combined with
stronger disorder and strain effects due to the step-bunching morphology of the
samples, could be the dominant source of pinning in the system.
