Calculation of the magnetic anisotropy with projected-augmented-wave methodology and the case study of disordered<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Fe</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Co</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math>alloys

The magnetic anisotropy energy of tetragonally distorted disordered alloys Fe ${}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}$ is calculated by two different virtual crystal approximation methods and an averaged supercell method within the projected-augmented-wave (PAW) methodology and the magnetic force theorem. The details of the spin-orbit coupling implementation in the PAW methodology are given. We compare our results to the recent coherent potential approximation (CPA) studies, results of full potential calculations, and to the available experiments.