In principle the magnetic anisotropy energy is determined by two kinds of differences in energy, namely the difference in total energy, ∆Etot, with respect to two given (uniform) directions n1 and n2 of the magnetization and the corresponding difference in the magnetic dipole-dipole interaction energy, ∆Edd,

Ea = ∆Etot +∆Edd , (6.1) ∆Etot = Etot[n1]−Etot[n2] , ∆Edd = Edd[n1]−Edd[n2] ,

since the latter one is not provided by the Density Functional Theory, and usually is expressed classically.