Hole polarons in LaFeO3 and La1−xSrxFeO3−δ : Stability, trapping, mobility, effect of Sr concentration, and oxygen vacancies

Abstract

The stability, trapping, and mobility of electron holes are investigated in lanthanum ferrite ${\mathrm{LaFeO}}_{3}$, and in ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{FeO}}_{3\ensuremath{-}\ensuremath{\delta}}$ ($x\ensuremath{\approx}0.1$, 0.4, and 0.6) by hybrid-density-functional and density-functional-$\mathrm{theory}+U$ calculations. In pure ${\mathrm{LaFeO}}_{3}$, the electron hole is more stable under a localized (polaronic) form than under a delocalized form, the energy difference (self-trapping energy) lies between $\ensuremath{\approx}\ensuremath{-}0.3$ and $\ensuremath{-}0.4$ eV. This self-trapped hole polaron is not strictly localized on a single Fe atom: instead, it occupies a quantum state made of a $3d$ orbital of a Fe atom, strongly hybridized with $2p$ orbitals of four neighboring oxygens. The hole polaron is thus localized on five atoms (among which one single Fe), which can be described as the ${\mathrm{Fe}}^{3+}$ oxidation into ${\mathrm{Fe}}^{4+}$. Electron hole transport results from the combination of onsite reorientations and hoppings, with energy barriers estimated at $\ensuremath{\approx}0.01--0.20$ eV and $0.3--0.4$ eV, respectively. The aliovalent substitution of lanthanum by strontium in ${\mathrm{LaFeO}}_{3}$ induces the presence of localized electron holes, preserving the insulating character of ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{FeO}}_{3}$, regardless of the studied Sr concentration. The formation energy of the oxygen vacancy in ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{FeO}}_{3}$ ($x\ensuremath{\approx}0.1$ and 0.4) is estimated at $\ensuremath{\approx}+0.8$ eV. This value is here successfully used to quantify the evolution of defect concentration as a function of the oxygen partial pressure.