Ferroelectricity of stress-free and strained pure SrTiO3 revealed by ab initio calculations with hybrid and density functionals

Abstract

The properties of stress-free and biaxially strained stoichiometric $\mathrm{SrTi}{\mathrm{O}}_{3}$ in the absence and presence of antiferrodistortive (AFD) distortion were calculated ab initio. To obtain reliable results, multiple exchange correlation (XC) functionals, including the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, were used. HSE was the primary XC functional, while another functional provided a good lower bound of ferroelectricity (FE). The reliability of the calculations was further reinforced by the calculations of the strain and AFD dependence. In contrast with previous works, we show that the ferroelectric phase (${C}_{4\mathrm{v}}^{1}$, ${C}_{4\mathrm{v}}^{10}$) is more stable in the absence of quantum and thermal fluctuations than the paraelectric phase (${O}_{\mathrm{h}}^{1}$, ${D}_{4\mathrm{h}}^{18}$), even for the stress-free case, and clarify the properties of these FE phases. The energy gain of stress-free FE, in comparison with the thermal and quantum fluctuation energy, indicates that a paraelectric phase emerges at room temperature by thermal fluctuations, but is near 0 K marginally close to the FE phase, which aligns with the experimental incipient FE. This implies that the paraelectricity of stress-free $\mathrm{SrTi}{\mathrm{O}}_{3}$ in experiments contains incoherent atomic-scale FE regions. These results are consistent with the FE microregions (FMR), signatures of polar disorders, and the emergence of FE in $\mathrm{SrTi}{\mathrm{O}}_{3}$ due to impurities and defects. The value of spontaneous polarization ${P}_{\mathrm{S}}$ could reach $10\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{C}/\mathrm{c}{\mathrm{m}}^{2}$ in the absence of fluctuations, even for the stress-free case. In view of the earlier theory of the carrier layer at polar discontinuities, the present results may explain the conduction at the interfaces of the $\mathrm{LaAl}{\mathrm{O}}_{3}/\mathrm{SrTi}{\mathrm{O}}_{3}$. In addition, an ``enhancement of FE due to symmetry constriction'' is proposed as an additional mechanism to the strain-enhanced FE in the epitaxial effect. For large compressive strain, e.g., 2%, the Perdew-Burke-Ernzerhof density functional for solids (PBEsol) yielded properties with ${P}_{\mathrm{S}}g20\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{C}/\mathrm{c}{\mathrm{m}}^{2}$, agreeing with HSE, and therefore is usable as a practical substitute of HSE for $\mathrm{SrTi}{\mathrm{O}}_{3}$.