Apr 12, 2010

The flexoelectricity of barium and strontium titanates from first principles

Bend it like barium titanate

Ab initio sheds light on how much polarization can be extracted from flexoelectricity in deformed crystals.

Supercell and strain profile

Strain gradients can induce polarization in insulators due to the mechanism known as flexoelectricity. Strain gradients by themselves break symmetry (the gradient introduces a difference in lattice shape between two ends of a crystal), so flexoelectric polarization can be induced in any dielectric, including those that are centrosymmetric and in which polarization mechanisms such as piezoelectricity or ferroelectricity would be forbidden. Although flexoelectricity is a more general mechanism than piezoelectricity, it tends to be smaller. However, gradients are large at the nanoscale, because the relaxation length scale is short. Also, flexoelectricity is proportional to permittivity. Therefore, small structures of high permittivity materials can have flexoelectric polarizations comparable to those achievable through piezoelectricity. Recognition of this has led to a recent surge of interest: flexoelectric sensors have been devised, the flexoelectricity of important oxides has been measured, and the effect of flexoelectricity on the properties of thin films and nanowires has been described.

However, there remain several unresolved problems. The bending experiments that are usually performed to measure flexoelectricity cannot yield all the flexoelectric tensor coefficients. Moreover, materials that on first sight appear similar, such as BaTiO₃ and SrTiO₃, are experimentally found to have flexoelectric coefficients that differ by orders of magnitude. This situation could benefit from the use of ab initio calculations, as these would allow accessing the intrinsic values of all the individual flexoelectric coefficients.

Such calculations have so far been precluded by their requirement of periodic supercells, which runs counter to the breaking of periodicity introduced by the gradients. In order to resolve this, the authors have designed a supercell where the strain gradient is itself periodic: one that looks like an accordion, stretched at one end, compressed in the middle, and stretched again at the other end. Calculations for this supercell show good agreement with the experimental flexoelectricity of SrTiO₃, but a considerable difference with experimental results for BaTiO₃. Hong et al suggest that experimental flexoelectric measurements of BaTiO₃ may have extrinsic contributions such as surface piezoelectricity. Testing this hypothesis will be the next stage of their research.

The authors

 Gustau Catalan has been involved in the field of flexoelectricity since his identification of the key contribution of this phenomenon to the properties of ferroelectric thin films. He has had the good fortune of meeting Emilio Artacho, an ab initio expert and co-author of the SIESTA code, who was persuaded, without the need for any bribes, to become interested in the problem. Jiawang Hong, from Tsinghua University in Beijing, spent one year in the Earth Science Department, at the University of Cambridge, where he did the calculations (as well as many other things!) as part of his PhD project, guided by Gustau, Emilio and Jim Scott, the latter an old hand and a household name in ferroelectrics, as full of brilliant insights as he is of references to obscure papers from a bygone era. Gustau Catalan is now an ICREA Research Professor at CIN2, in Barcelona, where he intends to continue his research in flexoelectricity and other size-dependent phenomena in electronic oxides.

+ Journal of Physics: Condensed Matter