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. We use a tight-binding model to describe the bilayer, and the 3-d Rashba material characterized by the spin-orbit strength α and the direction of broken bulk inversion symmetry n̂. We find an in-plane uniaxial anisotropy in the ẑ × n̂ direction, where ẑ is the interface normal. For realistic values of α, 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 α4 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, n̂ 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.