Giant interfacial perpendicular magnetic anisotropy in ${\mathrm{Fe}/\mathrm{CuIn}}_{1-x}{\mathrm{Ga}}_x{\mathrm{Se}}_2$ beyond Fe/MgO

We study interfacial magnetocrystalline anisotropies in various Fe/semiconductor heterostructures by means of first-principles calculations. We find that many of those systems show perpendicular magnetic anisotropy (PMA) with a positive value of the interfacial anisotropy constant $K_{\mathrm{i}}$. In particular, the ${\mathrm{Fe}/\mathrm{CuInSe}}_2$ interface has a large $K_{\mathrm{i}}$ of $\sim 2.3\mathrm{mJ}/{\mathrm{m}}^2$, which is about 1.6 times larger than that of Fe/MgO known as a typical system with relatively large PMA. We also find that the values of $K_{\mathrm{i}}$ in almost all the systems studied in this work follow the well-known Bruno's relation, which indicates that minority-spin states around the Fermi level provide dominant contributions to the interfacial magnetocrystalline anisotropies. Detailed analyses of the local density of states and wave-vector-resolved anisotropy energy clarify that the large $K_{\mathrm{i}}$ in ${\mathrm{Fe}/\mathrm{CuInSe}}_2$ is attributed to the preferable $3d$-orbital configurations around the Fermi level in the minority-spin states of the interfacial Fe atoms. Moreover, we have shown that the locations of interfacial Se atoms are the key for such orbital configurations of the interfacial Fe atoms.

Figure 1

Supercells of (a) ${\mathrm{Fe}\left(7\right)/\mathrm{CuInSe}}_2$(17), (b) ${\mathrm{Fe}\left(7\right)/\mathrm{CuIn}}_{0.5}{\mathrm{Ga}}_{0.5}{\mathrm{Se}}_2$(17), and (c) Fe(7)/MgO(13).

Figure 2

In-plane lattice constant dependence of the interfacial anisotropy constant $K_{\mathrm{i}}$ for ${\mathrm{Fe}/\mathrm{CuInSe}}_2$(001).

Figure 3

Correlation between the interfacial anisotropy constant $K_{\mathrm{i}}$ and the anisotropy of the orbital magnetic moment at the interfacial Fe layer $\mathrm{\Delta }{M}_{\mathrm{orb},\mathrm{i}}$ (see the text for details).

Figure 4

Anisotropy of the orbital magnetic moment $\mathrm{\Delta }{M}_{\mathrm{orb}}$ resolved into each Fe-layer contribution for ${\mathrm{Fe}/\mathrm{CuInSe}}_2$(001) and Fe/MgO(001). The horizontal axis shows the distance of each Fe layer from the interface.

Figure 5

The projected LDOSs for (a) Fe $3d$ states and (b) O $2p$ states at the interface of the Fe/MgO(001) heterostructure. In each panel, positive and negative values indicate the majority- and minority-spin projected LDOSs, respectively. The inset of panel (a) shows an enlarged view near the Fermi level.

Figure 6

The projected LDOSs for (a) Fe $3d$ states and (b) Se $4p$ states at the interface of the ${\mathrm{Fe}/\mathrm{CuInSe}}_2$(001) heterostructure. In each panel, positive and negative values indicate the majority- and minority-spin projected LDOSs, respectively. The inset of panel (a) shows an enlarged view near the Fermi level.

Figure 7

The direct microscopic information on PMA in the ${\mathrm{Fe}/\mathrm{CuInSe}}_2$(001) heterostructure: (a) the in-plane wave-vector (${\mathbf{k}}_{\parallel }$) dependence of $\mathrm{\Delta }E\left({\mathbf{k}}_{\parallel }\right)\equiv E_{\left[100\right]}\left({\mathbf{k}}_{\parallel }\right)-E_{\left[001\right]}\left({\mathbf{k}}_{\parallel }\right)$ and (b) the minority-spin bands along the high-symmetry lines in the ${\mathbf{k}}_{\parallel }$ Brillouin zone. In panel (b), orbital components of each band are indicated by colors.

Figure 8

Calculated $K_{\mathrm{i}}$ as a function of the change in the Fermi energy $\mathrm{\Delta }{E}_{\mathrm{F}}$ for ${\mathrm{Fe}/\mathrm{CuInSe}}_2$(001) and Fe/MgO(001). The origin of the horizontal axis $\mathrm{\Delta }{E}_{\mathrm{F}}=0$ corresponds to the original Fermi energy in each system. The changes in the valence electron number $\mathrm{\Delta }n$ at $\mathrm{\Delta }{E}_{\mathrm{F}}=\pm 1\mathrm{eV}$ are also shown in units of electrons/atom.