The strong coupling between antiferromagnetism and ferroelectricity at room temperature found in BiFeO₃ generates high expectations for the design and development of technological devices with novel functionalities. However, the multi-domain nature of the material tends to nullify the properties of interest and complicates the thorough understanding of the mechanisms that are responsible for those properties. Here we report the realization of a BiFeO₃ material in thin film form with single-domain behaviour in both its magnetism and ferroelectricity: the entire film shows its antiferromagnetic axis aligned along the crystallographic b axis and its ferroelectric polarization along the c axis. With this we are able to reveal that the canted ferromagnetic moment due to the Dzyaloshinskii–Moriya interaction is parallel to the a axis. Furthermore, by fabricating a Co/BiFeO₃ heterostructure, we demonstrate that the ferromagnetic moment of the Co film does couple directly to the canted moment of BiFeO₃.