Interfacial magnetic anisotropy from a 3-dimensional Rashba substrate

We study the magnetic anisotropy which arises at the interface between a thin film ferromagnet and a 3-d Rashba material. The 3-d Rashba material is characterized by the spin-orbit strength $\alpha$ and the direction of broken bulk inversion symmetry $\hat n$. We find an in-plane uniaxial anisotropy in the $\hat{z}\times\hat{n}$ direction, where $\hat z$ is the interface normal. For realistic values of $\alpha$, the uniaxial anisotropy is of a similar order of magnitude as the bulk magnetocrystalline anisotropy. Evaluating the uniaxial anisotropy for a simplified model in 1-d shows that for small band filling, the in-plane easy axis anisotropy scales as $\alpha^4$ and results from a twisted exchange interaction between the spins in the 3-d Rashba material and the ferromagnet. For a ferroelectric 3-d Rashba material, $\hat n$ can be controlled with an electric field, and we propose that the interfacial magnetic anisotropy could provide a mechanism for electrical control of the magnetic orientation.