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The magnetocrystalline anisotropy energy E(anis) of free-standing monolayersand thin films of Fe and Ni is determined using two different semi-empiricalschemes. Within a tight-binding calculation for the 3d bands alone, we analyzein detail the relation between bandstructure and E(anis), treating spin-orbitcoupling non-pertubatively. We find important contributions to E(anis) due tothe lifting of band degeneracies near the Fermi level by SOC. The importantrole of degeneracies is supported by the calculation of the electrontemperature dependence of the magnetocrystalline anisotropy energy, whichdecreases with the temperature increasing on a scale of several hundred K. Ingeneral, E(anis) scales with the square of the SOC constant. Including 4s bandsand s-d hybridization, the combined interpolation scheme yields anisotropyenergies that quantitatively agree well with experiments for Fe and Nimonolayers on Cu(001). Finally, the anisotropy energy is calculated for systemsof up to 14 layers. Even after including s-bands and for multilayers, theimportance of degeneracies persists. Considering a fixed fct-Fe structure, wefind a reorientation of the magnetization from perpendicular to in-plane atabout 4 layers. For Ni, we find the correct in-plane easy-axis for themonolayer. However, since the anisotropy energy remains nearly constant, we donot find the experimentally observed reorientation.Comment: 15 pages, Revtex, 15 postscript figure

Magnetocrystalline anisotropy energy of transition-metal thin films: A nonperturbative theory