Progress in nanotechnology requires new approaches to materials synthesis that make it possible to control material functionality down to the smallest scales. An objective of materials research is to achieve enhanced control over the physical properties of materials such as ferromagnets, ferroelectrics and superconductors. In this context, complex oxides and inorganic perovskites are attractive because slight adjustments of their atomic structures can produce large physical responses and result in multiple functionalities. In addition, these materials often contain ferroelastic domains. The intrinsic symmetry breaking that takes place at the domain walls can induce properties absent from the domains themselves, such as magnetic or ferroelectric order and other functionalities, as well as coupling between them. Moreover, large domain wall densities create intense strain gradients, which can also affect the material's properties. Here we show that, owing to large local stresses, domain walls can promote the formation of unusual phases. In this sense, the domain walls can function as nanoscale chemical reactors. We synthesize a two-dimensional ferromagnetic phase at the domain walls of the orthorhombic perovskite terbium manganite (TbMnO₃), which was grown in thin layers under epitaxial strain on strontium titanate (SrTiO₃) substrates. This phase is yet to be created by standard chemical routes. The density of the two-dimensional sheets can be tuned by changing the film thickness or the substrate lattice parameter (that is, the epitaxial strain), and the distance between sheets can be made as small as 5 nanometres in ultrathin films, such that the new phase at domain walls represents up to 25 per cent of the film volume. The general concept of using domain walls of epitaxial oxides to promote the formation of unusual phases may be applicable to other materials systems, thus giving access to new classes of nanoscale materials for applications in nanoelectronics and spintronics.