  We present results of systematic fully relativistic first-principles
calculations of the uniaxial magnetic anisotropy energy (MAE) of a disordered
and partially ordered tetragonal Fe-Co alloy using the coherent potential
approximation (CPA). This alloy has recently become a promising system for thin
ferromagnetic films with a perpendicular magnetic anisotropy. We find that
existing theoretical approaches to homogeneous random bulk Fe-Co alloys, based
on a simple virtual crystal approximation (VCA), overestimate the maximum MAE
values obtained in the CPA by a factor of four. This pronounced difference is
ascribed to the strong disorder in the minority spin channel of real alloys,
which is neglected in the VCA and which leads to a broadening of the d-like
eigenstates at the Fermi energy and to the reduction of the MAE. The ordered
Fe-Co alloys with a maximum L1_0-like atomic long-range order can exhibit high
values of the MAE, which, however, get dramatically reduced by small
perturbations of the perfect order.
