Magnetic anisotropy of Fe and Co adatoms and monolayers: Need for a proper treatment of the substrate

The magnetocrystalline contribution to the magnetic anisotropy energy (MAE) of Fe and Co adatoms, monolayers, and surface superstructures on Pt(111) is investigated. It is shown that the thickness of the slab representing the substrate and the interaction between the atoms in neighboring surface supercells affect the calculated MAE much more profoundly than they affect magnetic moments. Reliable theoretical values of MAE cannot be obtained if the substrate is represented by a slab of less than about ten atomic layers. If a surface superstructure is meant to represent an adatom by means of supercell approach, then decoupling has to be ensured by using very large supercells.

Figure 1

(Color online) Top view of $1\times 1$, $\sqrt{3}\times \sqrt{3}$, $2\times 2$, and $\sqrt{7}\times \sqrt{7}$ surface superstructures on Pt(111).

Figure 2

(Color online) Calculated magnetic moments and the MAE of full Fe (left panels) and Co (right panels) monolayers on Pt(111) with bulklike and semirelaxed structures for different thicknesses of the substrate slab. Magnetic moments inside the Fe or Co spheres obtained for magnetization perpendicular to the surface are shown in the upper panels $\left({\mu }_{\text{spin}}\right)$ and in the middle panels $\left({\mu }_{\text{orb}}\right)$. The lowermost panels display the MAE. Values for semi-infinite substrate are shown via markers close to the right edges of the panels.

Figure 3

(Color online) Calculated ${\mu }_{\text{spin}}$ induced in the Pt substrate for Fe (left panels) and Co (right panels) monolayers on Pt(111). The values of ${\mu }_{\text{spin}}\left(\text{Pt}\right)$ refer to a sum of contributions of all substrate layers and are related to one Fe or Co atom. This figure is analogous to Fig. 2.

Figure 4

(Color online) Minority-spin Bloch spectral functions $A^B\left(\mathbf{k},E\right)$ at the Co sites for a Co monolayer on Pt(111), with bulklike interlayer distances. The substrate is modeled by finite slabs of 9 and 38 layers (topmost and middle diagrams, respectively) and by a proper semi-infinite crystal (lowermost diagram). The color-coded scale of $A^B\left(\mathbf{k},E\right)$ intensities is shown at the top. In the left panels, densities of states at the Co sites are displayed. In the case of finite slabs, the DOS for the semi-infinite crystal is also shown via dotted lines for comparison (topmost and middle diagrams).

Figure 5

(Color online) Calculated magnetic properties of Fe (left panels) and Co (right panels) surface supercells on Pt(111) with bulklike and semirelaxed structures. Magnetic moments obtained for magnetization perpendicular to the surface are shown in the upper panels $\left({\mu }_{\text{spin}}\right)$ and in the middle panels $\left({\mu }_{\text{orb}}\right)$. The lowermost panels display the MAE per Fe or Co atom. The surface superstructures are depicted in Fig. 1.