Flexoelectricity, incommensurate phases and the Lifshitz point
Journal of Physics: Condensed Matter
Institue of Physics
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Pöttker, H., & Salje, E. (2016). Flexoelectricity, incommensurate phases and the Lifshitz point. Journal of Physics: Condensed Matter, 28 (075902)https://doi.org/10.1088/0953-8984/28/7/075902
The solutions for the minimizers of the energy density f(q, p) = Aq² + Bq⁴ + p² + g_A,B + β(q'p — p'q) + |q'|² + κ|p'|² describe the flexoelectric effect with a flexoelectric coupling coeffcient β. The order parameters q and p can be visualized as strain and polarisation, respectively. The parameter κ denotes the ratio of intrinsic length scales for q and p. We show that the structural ground-states include 3 phases, namely the paraelastic state q = p = 0, the ferroelastic state where polarization exists inside and near twin boundaries, and the incommensurate (modulated) phases with a very rich array of structural modulations ranging from nearly pure sine waves to kink arrays and ripple states. The phases coincide in the multicritical Lifshitz point. Linear flexoelectricity p ~ q' is encountered only approximately inside the ferroelastic phase and near the phase boundary between the paraelastic phase and the incommensurate phase. The relationship between the polarisation and the strain gradient is highly non-linear in all other states. The spatial profiles and energy distributions are discussed in detail.
HP is supported by the German Research Foundation (DFG) via SFB 1060 – The Mathematics of Emergent Effects. EKHS thanks the EPSRC (EP/K009702/1) for financial support.
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External DOI: https://doi.org/10.1088/0953-8984/28/7/075902
This record's URL: https://www.repository.cam.ac.uk/handle/1810/252411
Licence URL: http://creativecommons.org/licenses/by/2.0/uk/Attribution 2.0 UK: England & Wales