Stabilization of small polarons in BaTiO3 by local distortions

Abstract

Small polarons and point defects in ${\mathrm{BaTiO}}_{3}$ are investigated using hybrid functional calculations. Based on the experimentally-confirmed order-disorder-type phase transitions, Ti displacements along $\ensuremath{\langle}111\ensuremath{\rangle}$ directions are included in the cubic model. We reveal that the self-trapped electrons at Ti sites are stable in both rhombohedral and cubic ${\mathrm{BaTiO}}_{3}$ and the Ti off-centering, which introduces antibonding hybridization between lowest-lying $\mathrm{Ti}\text{\ensuremath{-}}3d$ and $\mathrm{O}\text{\ensuremath{-}}2p$ orbitals at the conduction band minimum, is essential for stabilizing the self-trapped electrons. Our calculations are in contrast to previous theoretical studies, even qualitatively, but reasonably consistent with the long-standing experimentally-observed small polarons in ${\mathrm{BaTiO}}_{3}$. This finding may explain why self-trapped electrons are not stable in ${\mathrm{SrTiO}}_{3}$ but are in ${\mathrm{BaTiO}}_{3}$ from the symmetry viewpoint.