X-ray linear dichroism in cubic compounds: The case ofCr3+inMgAl2O4

Abstract

The angular dependence (x-ray linear dichroism) of the $\text{Cr}\text{ }K$ pre-edge in ${\text{MgAl}}_{2}{\text{O}}_{4}:{\text{Cr}}^{3+}$ spinel is measured by means of x-ray absorption near-edge structure spectroscopy and compared to calculations based on density functional theory (DFT) and ligand field multiplet (LFM) theory. We also present an efficient method, based on symmetry considerations, to compute the dichroism of the cubic crystal starting from the dichroism of a single substitutional site. DFT shows that the electric dipole transitions do not contribute to the features visible in the pre-edge and provides a clear vision of the assignment of the $1s\ensuremath{\rightarrow}3d$ transitions. However, DFT is unable to reproduce quantitatively the angular dependence of the pre-edge, which is, on the other side, well reproduced by LFM calculations. The most relevant factors determining the dichroism of $\text{Cr}\text{ }K$ pre-edge are identified as the site distortion and $3d\text{\ensuremath{-}}3d$ electronic repulsion. From this combined DFT, LFM approach is concluded that when the pre-edge features are more intense than 4% of the edge jump, pure quadrupole transitions cannot explain alone the origin of the pre-edge. Finally, the shape of the dichroic signal is more sensitive than the isotropic spectrum to the trigonal distortion of the substitutional site. This suggests the possibility to obtain quantitative information on site distortion from the x-ray linear dichroism by performing angular dependent measurements on single crystals.