Ca 3d unoccupied states in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ investigated by Ca ${\mathit{L}}_{2,3}$ x-ray-absorption near-edge structure

The high-resolution Ca ${\mathit{L}}_{2,3}$ x-ray-absorption near-edge-structure (XANES) spectrum of a ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ single crystal has been measured by use of a magnetic-projection x-ray microscope probing a surface area of 200×200 μ${\mathrm{m}}^2$. The Ca ${\mathit{L}}_{2,3}$ XANES spectrum is analyzed by performing a multiple-scattering XANES calculation in real space and comparing the results with the spectrum of ${\mathrm{CaF}}_2$. Good agreement between the calculated and experimental crystal-field splitting ${\mathrm{\Delta }}_{\mathit{f}}$ of the Ca 3d final states is found and the splitting is shown to be smaller by 0.5 eV than in the initial state. The Ca 3d partial density of states is found to be close to the Fermi level in the initial state. The Ca-O(in plane) distance is shown to be a critical parameter associated with the shift of the Ca 3d states relative to the Fermi level; in particular, we have studied the effect of the out-of-plane dimpling mode of the in-plane oxygen atoms O(in plane) that will move the Ca 3d states on or off the Fermi level. This mode can therefore play a role in modulating the charge transfer between the two ${\mathrm{CuO}}_2$ planes separated by the Ca ions.