Anatomy of Magnetic Anisotropy and Voltage-Controlled Magnetic Anisotropy in Metal Oxide Heterostructure from First Principles

Voltage control of magnetic anisotropy (VCMA) is one of the promising approaches for magnetoelectric control of magnetic tunnel junction (MTJ). Here, we systematically calculated the magnetic anisotropy (MA) and the VCMA energies in the well-known MTJ structure consisting of Fe/MgO interface with Cr buffer layer. In this calculation, we investigated an alloying between Fe and Cr and a strain effect. We used a spin density functional approach which includes both contributions from magnetocrystalline anisotropy energy (MCAE) originating from spin-orbit coupling and shape magnetic anisotropy energy from spin dipole-dipole interaction. In the present approach, the MCAE part, in addition to a common scheme of total energy, was evaluated using a grand canonical force theorem scheme. In the latter scheme, atom-resolved and k-resolved analyses for MA and VCMA can be performed. At first, we found that, as the alloying is introduced, the perpendicular MCAE increases by a factor of two. Next, as the strain is introduced, we found that the MCAE increases with increasing compressive strain with the maximum value of 2.2 mJ/m(2). For the VCMA coefficient, as the compressive strain increases, the sign becomes negative and the absolute value becomes enhanced to the number of 170 fJ/Vm. By using the atom-resolved and k-resolved analyses, we clarified that these enhancements of MCAE and VCMA mainly originates from the Fe interface with MgO (Fe-1) and are located at certain lines in the two dimensional Brillouin zone. The findings on MCAE and VCMA are fully explained by the spin-orbit couplings between the certain d-orbital states in the second-order perturbation theory.