  We describe the directional growth of ferroelectric domains in a multiferroic
BiFeO3 thin film, which was grown epitaxially on a vicinal (001) SrTiO3
substrate. A detailed structural analysis of the film shows that a strain
gradient, which can create a symmetry breaking in a ferroelectric double well
potential, causes ferroelectric domains to grow with preferred directionality
under the influence of an electric field. Our results suggest the possibility
of controlling the direction of domain growth with an electric field by
imposing constraints on ferroelectric films, such as a strain gradient.
