  We have performed a theoretical study of the magnetic circular dichroism in
the x-ray absorption spectra (XMCD) of the equiatomic CoPt and FePt ordered
alloys as a function of the spin quantization axis. We found that the
magnetization axis is along the [001] direction and the magneto-crystalline
anisotropy energy (MCA) for the FePt compound is twice as large as that of the
CoPt compound in agreement with experiment. The band structure and the total
density of states confirm that all electronic states contribute to the MCA, and
not just the states at the vicinity of the Fermi level. The orbital magnetic
moments decrease with respect to the angle between the [001] axis and the spin
quantization axis, and are much larger for the CoPt compound. We show that the
orbital moment anisotropy is reflected in the XMCD signal.
