  We present density functional theory (DFT) calculations of the magnetic
anisotropy energy (MAE) of FePt, which is of great interest for magnetic
recording applications. Our data, and the majority of previously calculated
results for perfectly ordered crystals, predict an MAE of $\sim 3.0$ meV per
formula unit, which is significantly larger than experimentally measured
values. Analyzing the effects of disorder by introducing stacking faults (SFs)
and anti site defects (ASDs) in varying concentrations we are able to reconcile
calculations with experimental data and show that even a low concentration of
ASDs are able to reduce the MAE of FePt considerably. Investigating the effect
of exact exchange and electron correlation within the adiabatic-connection
dissipation fluctuation theorem in the random phase approximation (ACDFT-RPA)
reveals a significantly smaller influence on the MAE. Thus the effect of
disorder, and more specifically ASDs, is the crucial factor in explaining the
deviation of common DFT calculations of FePt to experimental measurements.
