  The angular dependence (x-ray linear dichroism) of the Cr K pre-edge in
MgAl2O4:Cr3+ spinel is measured by means of x-ray absorption near edge
structure spectroscopy (XANES) and compared to calculations based on density
functional theory (DFT) and ligand field multiplet theory (LFM). 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-->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 Cr K pre-edge are identified as the site
distortion and 3d-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.
