Insights on the relevance of DFT+U formalism for strongly correlated Ta d electrons probing the nanoscale in oxides: Combined time-differential perturbed γ-γ angular correlation spectroscopy and ab initio study in Hf 181 (→181Ta)-implanted α- Al2 O3 single crystal

Abstract

This work presents a combined experimental and ab initio study investigating the relevance of applying the density-functional theory plus U (DFT+U) formalism to correctly describe strongly correlated electrons of diluted probe atoms useful to sense the nanoscale in any material, in particular, 5d orbitals of 181Ta probe atoms doping insulating and semiconducting oxides. Experimentally, we applied the time differential perturbed γ -γ angular correlation (TDPAC) spectroscopy using ion-implanted 181Hf(→181Ta) tracers in parts per million concentration in an α-Al2O3 single crystal, measuring the hyperfine interactions (HFIs) for a complete key set of crystal orientations, achieving the observation of the desired axially symmetric electric-field gradient tensor(EFG) sensed by substitutional 181Ta atoms at Al sites free of defects. This goal allowed a direct comparison of a known physical situation with the correct first-principles modeling. The all-electron ab initio electronic structure calculations were performed in the framework of DFT and DFT+U formalisms. A complete defect-formation energy study for different charge states of the doped systems was essential to determine the correct ionization degree of the Ta impurity, which is likely to be double ionized already at room temperature, showing also the necessity to apply the Hubbard U parameter to correctly describe the electron density and electronic structure of the strongly localized Ta-5d states as 181Ta acts as an isolated probe impurity in α-Al2O3. This combined study also permitted to assign the second observed HFI to 181Ta atoms at substitutional Al sites with structural disorder in their distant neighborhood.We show that the inclusion of the U parameter does not produce significant changes in the equilibrium atomic positions, indicating that all the changes produced in the EFG come from the electron density recombination, showing the extraordinary capability of the EFG to detect subtle changes in the electronic structure. We also show that the Ta-d contribution to the EFG is dominant over the p one, decreasing as the impurity level becomes ionized. When this level is empty, the Ta-p contribution is the dominant one, leading to the experimentally observed EFG. The necessity to apply the DFT+U formalism at Ta probe atoms in semiconductors and insulators to correctly describe the EFG tensor is discussed, proposing that the use of DFT+U becomes relevant only when the probe´s impurity level is strongly localized.