Finite Electric Field Effects in the Large Perpendicular Magnetic Anisotropy Surface $\mathrm{Pt}/\mathrm{Fe}/\mathrm{Pt}(001)$: A First-Principles Study

We investigate crystalline magnetic anisotropy in the electric field (EF) for the FePt surface which has a large perpendicular anisotropy, by means of the first-principles approach. Anisotropy is reduced linearly with respect to the inward EF, associated with the induced spin density around the Fe layer. Although the magnetic anisotropy energy (MAE) density reveals large variation around the atoms, the intrinsic contribution to the MAE is found to mainly come from the Fe layer. The surface without the capping Pt layer also shows similar linear dependence.

Figure 1

(a) Schematic diagram of the computational models. (b) Magnetic anisotropy energies (MAEs) (solid dots) and the number of added electrons (crosses) as a function of the electric field for $\mathrm{Pt}/\mathrm{Fe}/\mathrm{Pt}(001)$. The inset shows the MAEs as a function of the electric field for $\mathrm{Fe}/\mathrm{Pt}(001)$. The lines are obtained by the least squares fit to the set of data.

Figure 2

Electric field change of the magnetic anisotropy energy (MAE) densities along $z$ coordinate and the contour ($\mathrm{meV}/{\AA }^3$) maps, (a)–(c) for $\mathrm{Pt}/\mathrm{Fe}/\mathrm{Pt}(001)$, and (d)–(f) for $\mathrm{Fe}/\mathrm{Pt}(001)$. The horizontal solid and dashed lines in (a),(b),(d),(e) indicate the atomic positions and the layer’s boundaries, respectively, for better visualization. The maps, (c) and (f), are shown in the (110) plane on the Fe (red or dark gray ball) and Pt (gray ball) atoms.

Figure 3

The induced majority (solid curves) and minority (dashed curves) spin charge densities along the $z$ coordinate and the contour maps of induced spin densities ($\times {10}^{-3}e/{\AA }^3$) (a),(b) for $\mathrm{Pt}/\mathrm{Fe}/\mathrm{Pt}(001)$ and (c),(d) for $\mathrm{Fe}/\mathrm{Pt}(001)$. The magnetization direction used for the figure drawing is perpendicular to the surface plane. See the caption at Fig. 2 for other explanations.