%0 Journal Article %T Domain Wall Roughness in Stripe Phase BiFeO$_3$ Thin Films %A B. Ziegler %A K. Martens %A T. Giamarchi %A P. Paruch %J Physics %D 2014 %I arXiv %R 10.1103/PhysRevLett.111.247604 %X 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. %U http://arxiv.org/abs/1402.3919v1