Illustrative view on the magnetocrystalline anisotropy of adatoms and monolayers

Although it has been known for decades that magnetocrystalline anisotropy is linked to spin-orbit coupling (SOC), the mechanism of how it arises for specific systems is still a subject of debate. We focused on finding markers of SOC in the density of states (DOS) and on using them to understand the source of magnetocrystalline anisotropy for the case of adatoms and monolayers. Fully relativistic ab initio Korringa-Kohn-Rostoker Green's-function calculations were performed for Fe, Co, and Ni adatoms and monolayers on Au(111) to investigate changes in the orbital-resolved DOS due to a rotation of magnetization. In this way, one can see that a significant contribution to magnetocrystalline anisotropy for adatoms comes from pushing the SOC-split states above or below the Fermi level. As a result of this, the magnetocrystalline anisotropy energy depends crucially on the position of the energy bands of the adatom with respect to the Fermi level of the substrate. This view is supported by model crystal-field Hamiltonian calculations.