First-principales calculations of the magnetic anisotropy energy of Fe-V multilayers

The magnetic anisotropy energy (MAE) of Fe$_2$V$_6$, Fe$_3$V$_5$, and Fe$_4$V$_4$ multilayers are investigated using first-principles spin-polarized and relativistic band-structure calculations based upon the full-potential linearized muffin-tin-orbital method. A strong difference in the MAE and the easy axis of magnetization (calculated for the experimental lattice parameters) is observed between the three studied multilayer systems, with easy axes of (001), (110), and (100) for Fe$_2$V$_6$, Fe$_3$V$_5$, and Fe$_4$V$_4$, respectively. The MAE of the Fe$_2$V$_6$ and Fe$_4$V$_4$ multilayers agrees well with the experimental data. The origin of this difference of behavior is analyzed, via a study of the influence of the atomic volume as well as a relaxation study of the multilayers with respect to the tetragonal deformation. The important role played by the {\it c/a} axial ratio, imposed by the alloying effects, is outlined. The magnetic anisotropy coefficients entering the expression of the MAE, as a function of the directional cosines, are extracted from a series of calculations for four independent spin directions. Finally, the band-filling effects on the MAE are analyzed as well as the different contributions in reciprocal space.