First-principles calculation of oxygen K-electron energy loss near edge structure of HfO₂

Oxygen K-electron energy loss near edge structures (ELNES) of monoclinic, tetragonal, and cubicHfO₂ were calculated by the first-principles full-potential augmented plane wave plus local orbitals (APW+lo) method. By considering the relativistic effect as well as the core-hole effect in the calculation, the experimental oxygen K ELNES was successfully reproduced. The first, second, third, and fourth peaks originate from oxygen p components hybridized with Hf d-e_g, d-t_2g, s, and p components, respectively. It was found that the spectral differences among the polymorphs are mainly caused by the local structure of the Hf in the crystal.