Determining perpendicular magnetic anisotropy in Fe/MgO/Fe magnetic tunnel junction: A DFT-based spin–orbit torque method

In our JUNPY package, we have combined the first-principles calculated self-consistent Hamiltonian with divide-and-conquer technique to successfully determine the magnetic anisotropy (MA) in an Fe/MgO/Fe magnetic tunnel junction (MTJ). We propose a comprehensive analytical derivation to clarify the crucial roles of spin–orbit coupling that mediates the exchange and spin–orbit components of spin torque, and the kinetic and spin–orbit components of spin current accumulation. The angular dependence of cumulative spin–orbit torque (SOT) indicates a uniaxial MA corresponding to the out-of-plane rotations of magnetic moments of the free Fe layers. Different from the conventional MA energy calculation and the phenomenological theory for a whole MTJ, our results provide insight into the orbital-resolved SOT for atomistic spin dynamics simulation in emergency complex magnetic heterojunctions.