Strain engineering enables modification of the properties of thin films using the stress from the substrates on which they are grown. Strain may be relaxed, however, and this can also modify the properties thanks to the coupling between strain gradient and polarization known as flexoelectricity. Here we have studied the strain distribution inside epitaxial films of the archetypal ferroelectric PbTiO(3), where the mismatch with the substrate is relaxed through the formation of domains (twins). Synchrotron X-ray diffraction and high-resolution scanning transmission electron microscopy reveal an intricate strain distribution, with gradients in both the vertical and, unexpectedly, the horizontal direction. These gradients generate a horizontal flexoelectricity that forces the spontaneous polarization to rotate away from the normal. Polar rotations are a characteristic of compositionally engineered morphotropic phase boundary ferroelectrics with high piezoelectricity; flexoelectricity provides an alternative route for generating such rotations in standard ferroelectrics using purely physical means.

Thin films of PbTiO3, a classical ferroelectric, have been grown under tensile strain on single-crystal substrates of DyScO3. The films, of only 5 nm thickness, grow fully coherent with the substrate, as evidenced by synchrotron x-ray diffraction. A mapping of the reciprocal space reveals intensity modulations (satellites) due to regularly spaced polar domains in which the polarization appears rotated away from the substrate normal, characterizing a low-symmetry phase not observed in the bulk material. This could have important practical implications since these phases are known to be responsible for ultrahigh piezoelectric responses in complex systems.

With shrinking device sizes, controlling domain formation in nanoferroelectrics becomes crucial. Periodic nanodomains that self-organize into so-called 'superdomains' have been recently observed, mainly at crystal edges or in laterally confined nanoobjects. Here we show that in extended, strain-engineered thin films, superdomains with purely in-plane polarization form to mimic the single-domain ground state, a new insight that allows a priori design of these hierarchical domain architectures. Importantly, superdomains behave like strain-neutral entities whose resultant polarization can be reversibly switched by 90°, offering promising perspectives for novel device geometries.

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