Synchrotron and lab-scale x-ray diffraction shows that tetragonal-like T'-BiFeO 3 films on miscut LaAlO 3 substrates ( < 5) exhibit (00l)-planes tilted away from those of the substrate as predicted by the "Nagai model" (except for miscut <0.2). Tilts as large as 1 are achieved even in 100 nm thick films, strikingly larger than those observed in other perovskites. We attribute this to the large c/a ratio and the high crystalline coherency of the T'-BiFeO 3 /LaAlO 3 interface. This coherency is possible through an observed "diagonal-on-diagonal" alignment. Interestingly, the substrate miscut does not influence the relative population of monoclinic domains.
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Main textStrain engineering, i.e. the intentional modification of crystal structure, microstructure, and morphology of epitaxial thin films via the mismatch between the film's and the substrate's lattice parameter and symmetry, is a powerful tool to tune functional properties of materials. [1][2][3] Similarly, the presence of step edges on the substrate surface resulting from substrate miscut can also have a large impact on the microstructure of thin films, for example by breaking the four-fold surface symmetry of a (001)-oriented cubic substrate. Thus, for a film consisting of unit cells having a non-square in-plane lattice, the degeneracy between different in-plane film-substrate alignments may be lifted in an approach referred to as domain engineering. 4,5 Furthermore, a surface step locally results in a three-dimensional clamping of the film material instead of the biaxial stress experienced elsewhere. As a consequence of the resulting non-uniform strain in the out-of-plane direction, the (00l) planes of the film may become tilted with respect to those of the substrate. For the case of Ga x In 1-x As on GaAs, Nagai demonstrated 6 that simple geometrical arguments explain the observed tilting of the film planes by an angle when grown on a substrate having a miscut angle , as shown in Fig. 1. In this simple model, the film out-of-plane lattice parameter is constrained to match the substrate at each step edge and then gradually relaxes to its unstrained value across the flat surface terrace. In fact, with out-of-plane lattice parameters for the film and substrate, c F and c S respectively, one expects tan / tan = (c F -c S )/c S , and thus a negative (positive) tilt if c F > c S (c F < c S ).Observing a tilt corresponding to this "Nagai model" is possible only in a system where the clamping in three dimensions is strong, i.e. where the film/substrate interface shows a low defect density, and only if competing mechanisms, such as misfit dislocations with inclined Burgers vectors, 7 do not dominate. Quantitative verification of the Nagai model has therefore remained elusive in oxide heteroepitaxy except for very thin films having a lattice parameter similar to that of the substrate (for example, 8 15 nm of SrRuO 3 on 4-miscut SrTiO 3 , resulting in a tilt of ~0.06). A much larger film/substrate tilt should be observed in a system with c F >> ...