  We study the electronic and magnetic properties of T$_2$AlC (T=Ti and Cr)
compounds in the density-functional theory using the generalized gradient
approximation (GGA) with consideration of strong Coulomb correlations (GGA+$U$)
in the framework of the fully relativistic spin-polarized Dirac linear
muffin-tin orbital (LMTO) band-structure method. The X-ray absorption spectra
and X-ray magnetic circular dichroism (XMCD) at the Cr $L_{2,3}$ and Cr, Ti,
and C $K$ edges were investigated theoretically. The calculated results are in
good agreement with experimental data. The effect of the electric quadrupole
$E_2$ and magnetic dipole $M_1$ transitions at the Cr $K$ edge has been
investigated.
