X-ray diffraction studies of stripelike ferroelectric domains in thin films of BiFeO3

We have used x-ray diffraction to study the structure of strained, epitaxial ${\text{BiFeO}}_3$ (BFO) films, which exhibit ordered arrays of stripelike ferroelectric domains, in which the polarization vector P alternates by either 109${}^{\circ }$ or 71${}^{\circ }$. Diffraction maps exhibit an intricate satellite structure that arises from coherent, gratinglike diffraction from the domain structure. In the case of the 109${}^{\circ }$ arrays, the domain structure was found to exert a strain modulation on the ${\text{DyScO}}_3$ substrate, with the same periodicity, indicating that domains in BFO can have an influence on the substrate structure. In the case of the 71${}^{\circ }$ arrays, in which there is no contrast between neighboring domains and coherent scattering is not expected, weak scattering is nonetheless observed, which we interpret as evidence for previously unobserved, internal strains in these domain walls. To understand the x-ray data, we introduce a simple, single-scattering model that incorporates Gaussian disorder and fits the diffraction maps, providing domain periods and surface “puckering” angles that are in good agreement with atomic force microscopy and piezoresponse force microscopy measurements. Our study demonstrates a simple, computationally inexpensive technique for semiquantitatively interpreting coherent domain scattering in ferroelectric films, and suggests that tuning domain structures is a potential route to engineering the near-surface properties of perovskite oxides.