Origin of electric-field-induced modification of magnetocrystalline anisotropy at Fe(001) surfaces: Mechanism of dipole formation from first principles

First-principles full-potential linearized augmented plane-wave studies reveal that a surface magnetocrystalline anisotropy (MCA) modification by an external electric field arises from a dipole formation mechanism. The precise calculations demonstrate that the formation of dipoles on Fe(001) surface atoms, which counteract the electric-field-induced charge in the vacuum region, changes the surface states around the Fermi level in the minority-spin $d$ bands, and yields a modification of the surface MCA. These findings greatly advance our understanding of the electric-field-induced MCA modifications in itinerant ferromagnetic surfaces.

Figure 1

(Color online) (a) Difference in calculated planar-averaged charge (thick solid line) and spin (thick dashed line) densities along the $z$ axis, $\Delta \overline{n}\left(z\right)$ and $\Delta \overline{m}\left(z\right)$, between the $1\text{V}/\text{Å}$ and zero field for a nine-layer film. The thin solid and dashed lines represent the calculated planar-averaged electrostatic potential, ${\overline{V}}_{\text{s}}\left(z\right)$, at $1\text{V}/\text{Å}$ and zero field, respectively, where the reference (zero) energy sets the Fermi level. Arrows indicate nuclear positions at the surfaces. (b) Contour map of charge-density difference, $\Delta n\left(\mathbf{r}\right)$, on a (110) plane in units of ${10}^{-4}$ electrons. Each contour line differs by a factor of 2. Solid and dashed lines indicate accumulation and depletion of electrons, respectively. Their blow ups in (c) and (d) show details of the charge density difference on surface atoms at $S_{-}$ and $S_{+}$ sites, respectively, where closed circles represent the center of surface atoms.

Figure 2

(Color online) Calculated $E_{\text{MCA}}$ at $1\text{V}/\text{Å}$ (closed circles) and zero field (open circles), and their difference, $\Delta E_{\text{MCA}}$, (closed diamonds) as a function of the film thickness. The $\Delta E_{\text{MCA}}$ contributions from surface atoms at $S_{-}$ and $S_{+}$ sites are represented by open triangles.

Figure 3

(Color online) Partial DOS, $N$, of surface atoms at $S_{-}$ and $S_{+}$ sites and vacuum regions at $1\text{V}/\text{Å}$ (solid lines) and zero field (dotted lines) for a nine-layer film. The DOS in the vacuum regions are multiplied by 10. The upper figures show the difference in the DOS, $\Delta N$, between $1\text{V}/\text{Å}$ and zero field, where thin and thick solid lines represent results for surface atoms and vacuum regions, respectively.

Figure 4

(Color online) Difference in calculated DOS, $\Delta N$, between $1\text{V}/\text{Å}$ and zero field for surface atoms at $S_{-}$ and $S_{+}$ sites and vacuum regions for a nine-layer film, which are further decomposed in momentum space. Only the DOS in the minority-spin states are drawn. $p_0$ and $p_{\pm 1}$ indicate $p_z$ and $p_{x,y}$ states, and $d_0$, $d_{\pm 1}$, and $d_{\pm 2}$ are $d_{z^2}$, $d_{xz,yz}$, and $d_{x^2-y^2,xy}$ states, respectively. The upper figures show the difference in the MCA energy, $\Delta E_{\text{MCA}}$, between $1\text{V}/\text{Å}$ and zero field within a rigid-band model when the $E_{\text{F}}$ is shifted.