First-principles theory of surface magnetocrystalline anisotropy and the diatomic-pair model

The state-tracking method proposed recently is employed for the first-principles determination of the magnetocrystalline-anisotropy (MCA) energy. A close relationship of the MCA energy to the band structure is found for transition-metal monolayers that show the change of sign of the MCA with respect to the band filling (atomic species) to be determined mainly by the spin-orbit coupling within the spin-down bands. The Fe monolayer with the \ensuremath{\pi}-bonding band as the highest occupied band exhibits positive MCA (easy axis along the layer normal). However, the effect of strain on the MCA of the Fe monolayer demonstrates the effect of the spin-orbit coupling between opposite-spin states. A model for the electronic origin of the magnetic anisotropy of this two-dimensional system is presented that explains the first-principles MCA results for iron and cobalt monolayers on the basis of the bonding character between two d atoms, the band broadening due to increase in coordination, and geometry (symmetry).