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Based on a first-principles based multiscale approach, we study the polarity P of ferroelastic twin walls in SrTiO_{3}. In addition to flexoelectricity, which was pointed out before, we identify two new mechanisms that crucially contribute to P: a direct "rotopolar" coupling to the gradients of the antiferrodistortive oxygen tilts, and a trilinear coupling that is mediated by the antiferroelectric displacement of the Ti atoms. Remarkably, the rotopolar coupling presents a strong analogy to the mechanism that generates a spontaneous polarization in cycloidal magnets. We show how this similarity allows for a breakdown of macroscopic inversion symmetry (and therefore a macroscopic polarization) in a periodic sequence of parallel twins. These results open new avenues towards engineering pyroelectricity or piezoelectricity in nominally nonpolar ferroic materials.

Within the framework of density functional perturbation theory (DFPT), we implement and test a novel "metric wave" response-function approach. It consists in the reformulation of an acoustic phonon perturbation in the curvilinear frame that is comoving with the atoms. This means that all the perturbation effects are encoded in the first-order variation of the real-space metric, while the atomic positions remain fixed. This approach can be regarded as the generalization of the uniform strain perturbation of Hamann et al. [D. R. Hamann, X. Wu, K. M. Rabe, and D. Vanderbilt, Phys. Rev. B 71, 035117 (2005)] to the case of inhomogeneous deformations, and greatly facilitates the calculation of advanced electromechanical couplings such as the flexoelectric tensor. We demonstrate the accuracy of our approach with extensive tests on model systems and on bulk crystals of Si and SrTiO3.arXiv:1811.12893v1 [cond-mat.mtrl-sci] 30 Nov 2018

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