The magnetocrystalline anisotropy (MA) of ferromagnetic fcc Ni, fcc Co
, and bcc Fe (001) slabs is calculated to second order in the spin-orb
it coupling constant using realistic tight-binding models with paramet
ers fitted to available first-principles electronic-structure calculat
ions. Results for slabs with 1 - 17 atomic layers show that MA favors
magnetization perpendicular to the slab for Fe but in-plane for Ni and
Co, in agreement with experiment. Fluctuations in the MA as the thick
ness is varied indicate that surface MA is not purely of local origin
in the surface atomic layer.