Orientations of oxygen hole states and ionicity of bismuth atoms in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$

We report a study of the x-ray-absorption near-edge structure of the Bi ${\mathit{L}}_3$ and O K edges in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$. A comparison with the Bi ${\mathit{L}}_3$ edges of ${\mathrm{Bi}}_2$ ${\mathrm{O}}_3$ and ${\mathrm{KBiO}}_3$ indicates that the Bi atoms are in a state close to a formal valency of +3 in the superconducting compound. We attribute the peaks below 529 eV in the O K-edge spectra of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ to holes on the O sites. We investigate the symmetries of these holes by using polarized x rays. By comparing the experimental spectra with simulations based on self-consistent electronic-structure calculations, we determine that the hole states at the O sites in the Cu-O and Bi-O planes do indeed lie in these planes, while those associated with the apical O atoms of the O pyramids in the structure are aligned along the c axis.