Origin of perpendicular magneto-crystalline anisotropy in L10-FeNi under tetragonal distortion

We investigated the origin of perpendicular magneto-crystalline anisotropy (MCA) in L10 ordered FeNi alloy using first-principles density-functional calculations. We found that the perpendicular MCA of L10-FeNi arises predominantly from the constituent Fe atoms, which is consistent with recent measurements of the anisotropy of the Fe orbital magnetic moment of L10-FeNi by x-ray magnetic circular dichroism. Analysis of the second-order perturbation of the spin-orbit interaction indicates that spin-flip excitations between the occupied majority-spin and unoccupied minority-spin bands make a considerable contribution to the perpendicular MCA as does the spin-conservation term in the minority-spin bands. Furthermore, the MCA energy increases as the in-plane lattice parameter decreases (increasing the axial ratio c/a). The increase in the MCA energy can be attributed to further enhancement of the spin-flip term due to modulation of the Fe d(xy) and d(x2-y2) orbital components around the Fermi level under the compressive in-plane distortion.