First-principles investigation of small polarons in rhombohedral NaNbO$_{3}$

Abstract

Sodium niobate (NaNbO$_{3}$) is a perovskite oxide and a key component of emerging lead-free antiferroelectric capacitors for high-energy-density applications. However, its performance can be hindered by irreversible phase transitions and leakage currents associated with low electrical resistivity. Defect and doping engineering offers a potential way to overcome these problems, but its use requires a detailed understanding of electronic, ionic, and polaron charge-compensation mechanisms, where the role of polarons remains largely unexplored. Here, we investigate the stability of small hole and electron polarons in rhombohedral NaNbO$_{3}$, which is a structurally well-defined model system that avoids lattice-dynamical instabilities. Trapping energies are calculated using density-functional theory corrected by a Hubbard $U$, using the enforced-piecewise-linearity approach including finite-size scaling. For the small hole-polaron centered on O-2$p$ orbital, we find a trapping energy of $-$0.65 (eV) and an adiabatic migration barrier of 0.32 (eV) determined by nudged-elastic-band calculations. In contrast, we show that excess electrons do not self-trap on Nb-4$d$ orbitals, reflecting weak electron-phonon coupling in the conduction band manifold. These results identify oxygen as an intrinsic hole trap in NaNbO$_{3}$ and highlight the importance of including hole polarons in defect models of NaNbO$_{3}$-based electroceramics.