This research is funded by the Latvian Council of Science, project No. lzp-2018/1-0147. The computer resources were provided
by Stuttgart Supercomputing Center (project DEFTD 12939) and Latvian Super Cluster (LASC). Many thanks to R. Dovesi, A. Erba,
and M. Rérat for numerous stimulating discussions.We present the results of a detailed first principles study of the piezoelectric properties of the (SrTiO3)m/(BaTiO3)M−m heterostructure using the 3D STOm/BTOM−m superlattice model. The atomic basis set, hybrid functionals and slabs with different numbers of STO and BTO layers were used. The interplay between ferroelectric (FEz) and antiferrodistortive (AFDz) displacements is carefully analyzed. Based on the experimental data and group theoretical analysis, we deduce two possible space groups of tetragonal symmetry which allow us to reproduce the experimentally known pure STO and BTO bulk phases in the limiting cases, and to model the corresponding intermediate superlattices. The characteristic feature of the space group P4mm (#99) model is atomic displacements in the [001] direction, which allows us to simulate the FEz displacements, whereas the P4 (#75) model besides FEz displacements permits oxygen octahedra antiphase rotations around the [001] direction and thus AFDz displacements. Our calculations demonstrate that for m/M ≤ 0.75 layer ratios both models show similar geometries and piezoelectric constants. Moreover, both models predict an approximately 6-fold increase of the piezoelectric constant e33 compared to the BaTiO3 bulk value, albeit at slightly different layer ratios. The obtained results clearly demonstrate that piezoelectricity arises due to the coordinated collective FEz displacements of atoms in both STO and BTO slabs and interfaces and reaches its maximum when the superlattice approaches the point where the tetragonal phase becomes unstable and transforms to a pseudo-cubic phase. We demonstrate that even a single or double layer of BTO is sufficient to trigger FEz displacements in the STO slab, in P4mm and P4 models, respectively.Latvian Council of Science, project No. lzp-2018/1-0147; Stuttgart Supercomputing Center project DEFTD 12939; Latvian Super Cluster LASC; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART
