Piezoelectricity of SrTiO<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>3</mml:mn></mml:msub></mml:math>: An<i>ab initio</i>description

The complete piezoelectric tensor of ferroelectric SrTiO${}_{3}$ at low temperature is computed by ab initio theoretical simulations. Both direct and converse---coupled with elastic compliance---piezoelectricity are computed and interpreted in terms of electronic and nuclear contributions. The role of the ferroelectric soft phonon mode on this property is found to be dramatic thus leading to a possible giant piezoelectric response at very low temperature. Two possible space groups are considered for the ferroelectric phase of SrTiO${}_{3}$, both compatible with the available experimental data: a tetragonal $I4cm$ and an orthorhombic $Ima2$ one. The piezoelectric response of the two symmetries is predicted to be rather different and could be experimentally detected to clarify the (still unknown) structure of the ferroelectric phase of SrTiO${}_{3}$.

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