Several sum rules for x-ray-absorption (XAS) dichroism have been recently derived. Here we discuss the particular case of linear polarization, relevant to cuprate oxides. We apply this analysis to the ${\mathit{L}}_2$ and ${\mathit{L}}_3$ edges of ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ in order to obtain quantitative, model-independent information about the out-of-plane character of 3d holes. A Cu 3${\mathit{d}}_{3\mathit{z}}^2$-${\mathit{r}}^2$ to 3${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ ratio of 3% is found for an insulating and two superconducting samples, and of 7% for the overdoped one. The interest of measuring both the ${\mathit{L}}_3$ and ${\mathit{L}}_2$ edges to perform similar XAS sum-rule analysis in higher-${\mathit{T}}_{\mathit{c}}$ cuprates is discussed.

• Received 22 June 1994

DOI:https://doi.org/10.1103/PhysRevB.51.629