Perpendicular magnetic anisotropy at the Fe/MgAl$_2$O$_4$ interface: Comparative first-principles study with Fe/MgO

We present a theoretical study on interfacial magnetocrystalline anisotropy for Fe/MgAl$_2$O$_4$. This system has a very small lattice mismatch at the interface and therefore is suitable for realizing a fully coherent ferromagnet/oxide interface for magnetic tunnel junctions. On the basis of density functional theory, we calculate the interfacial anisotropy constant $K_{\rm i}$ and show that this system has interfacial perpendicular magnetic anisotropy (PMA) with $K_{\rm i} \approx 1.2\,{\rm mJ/m^2}$, which is a little bit smaller than that of Fe/MgO ($K_{\rm i} \approx$ 1.5--1.7$\,{\rm mJ/m^2}$). Second-order perturbation analysis with respect to the spin-orbit interaction clarifies that the difference in $K_{\rm i}$ between Fe/MgAl$_2$O$_4$ and Fe/MgO originates from the difference in contributions from spin-flip scattering terms at the interface. We propose that the insertion of tungsten layers into the interface of Fe/MgAl$_2$O$_4$ is a promising way to obtain huge interfacial PMA with $K_{\rm i} \gtrsim 3\,{\rm mJ/m^2}$.