Magnetocrystalline Anisotropy of Fe and FeCo Thin Films

Abstract

In the race for the miniaturization of electronic devices, modern science reached the ultimate level of monoatomic layers. Whereas, magnetic tunnel junctions with perpendicular magnetic anisotropy reached the limit of about twenty atomic monolayers [1]. In our work, we systematically study the magnetic anisotropy of Fe and FeCo thin films of size from one to twenty atomic monolayers.Theoretical studies are based on calculations using the full-potential local-orbital electronic structure code FPLO [2] and generalized gradient approximation (GGA). The chemical disorder in FeCo layers was modeled using virtual crystal approximation (VCA). A set of layers with different thicknesses formed based on the bcc structure was subjected to full geometry optimization. The set of equilibrium structures was then recalculated using a fully relativistic approach for two orthogonal magnetization directions (in-plane and out-of-plane). The results of calculations allow the interpretation of parallel experimental studies in which FeCo layers on Au substrate are analyzed.The result of ab-initio calculations is a series of dependences of structural and magnetic parameters on layer thickness. Fig. 1 shows an example of the dependence of the optimized lattice constant on the Fe layer thickness. For few-atom-thick Fe layers there is a large reduction of the lattice parameter with respect to the value for bulk bcc Fe, to which the parameters determined for thicker layers converge. Fig. 2 presents the dependence of the magnetocrystalline anisotropy energy (MAE) on the Fe layer thickness. Positive values denote perpendicular magnetic anisotropy, negative values denote anisotropy in-plane. The calculated value of MAE for Fe monolayer equal to 0.58 meV/atom is in good agreement with the previous GGA result equal to 0.50 meV/atom [3]. These results were compared with measurements of the ratio of orbital to spin magnetic moment using VNA-FMR. We found that the contribution of surface anisotropy to the effective anisotropy is strong enough to overcome the shape anisotropy in Au/CoFe/Au systems.  Fig.1 Dependence of the lattice parameter on the Fe layer thickness.  Fig.2 Dependence of MAE on Fe layer thickness.