Flexoelectric rotation of polarization in ferroelectric thin films


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 PbTiO3, 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.

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Figure 1: Piezo-response force microscopy image of a twinned ferroelectric film.
Figure 2: X-ray diffraction data revealing a correlated distribution of tetragonality and twin angles.
Figure 3: Direct imaging of strain gradients.
Figure 4: Sketch of stresses, strain gradients and polar vectors in the twinned film.
Figure 5: Direct observation of polarization rotations.


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W. Caliebe is gratefully acknowledged for his help at the W1 beamline. This work is part of research programme 04PR2359 of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO). G.C., A.H.G.V. and B.N. also acknowledge financial support from the NWO-Vidi grant 700.54.426, and from the Explora grant MAT2010-10067-E (G.C.). A.L. and E.S. acknowledge financial support from the European Union under the Framework 6 program under a contract for an Integrated Infrastructure Initiative. Reference 026019 ESTEEM.

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G.C. and B.N. have devised, designed and organized the work; A.H.G.V. and A.J. have grown the films under the supervision of G.R. and D.H.A.B.; A.H.G.V., G.C., G.R. and B.N. have carried out the X-ray experiments and analysed the X-ray data; A.L., E.S. and C.M. have designed, carried out and organized the electron microscopy experiments and analysed the data. All the authors have contributed to the discussions.

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Correspondence to G. Catalan or B. Noheda.

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Catalan, G., Lubk, A., Vlooswijk, A. et al. Flexoelectric rotation of polarization in ferroelectric thin films. Nature Mater 10, 963–967 (2011). https://doi.org/10.1038/nmat3141

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