Electronic structure of interstitial hydrogen in lutetium oxide from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>DFT</mml:mtext><mml:mo>+</mml:mo><mml:mi>U</mml:mi></mml:math>calculations and comparison study with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>μ</mml:mi><mml:mi>SR</mml:mi></mml:mrow></mml:math>spectroscopy

The electronic structure of hydrogen impurity in ${\mathrm{Lu}}_{2}{\mathrm{O}}_{3}$ was studied by first-principles calculations and muonium spectroscopy. The computational scheme was based on two methods which are well suited to treat defect calculations in $f$-electron systems: first, a semilocal functional of conventional density-functional theory (DFT) and secondly a $\text{DFT}+U$ approach which accounts for the on-site correlation of the $4f$ electrons via an effective Hubbard-type interaction. Three different types of stable configurations were found for hydrogen depending upon its charge state. In its negatively charged and neutral states, hydrogen favors interstitial configurations residing either at the unoccupied sites of the oxygen sublattice or at the empty cube centers surrounded by the lanthanide ions. In contrast, the positively charged state stabilized only as a bond configuration, where hydrogen binds to oxygen ions. Overall, the results between the two methods agree in the ordering of the formation energies of the different impurity configurations, though within $\text{DFT}+U$ the charge-transition (electrical) levels are found at Fermi-level positions with higher energies. Both methods predict that hydrogen is an amphoteric defect in ${\mathrm{Lu}}_{2}{\mathrm{O}}_{3}$ if the lowest-energy configurations are used to obtain the charge-transition, thermodynamic levels. The calculations of hyperfine constants for the neutral interstitial configurations show a predominantly isotropic hyperfine interaction with two distinct values of 926 MHz and 1061 MHz for the Fermi-contact term originating from the two corresponding interstitial positions of hydrogen in the lattice. These high values are consistent with the muonium spectroscopy measurements which also reveal a strongly isotropic hyperfine signature for the neutral muonium fraction with a magnitude slightly larger (1130 MHz) from the ab initio results (after scaling with the magnetic moments of the respective nuclei).

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