Theoretical Study of Spin-Orbit Coupling in Metallic Ferromagnetism

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The spin-orbit coupling is the only one interaction, which fixes the spin system to the lattice, but it is too small to make a reliable quantitative calculations in the case of 3d-transition metals. We have investigated the magnetic anisotropy energy (MAE) from the first-principles band calculations in the two cases : interstitially modified intermetallics of rare-earth (R) and 3d transition metals and X/Co or Fe (X=Pd, Pt, Ag, Au) ferromagnetic multilayr system. In the former case, the electronic structures of GdCo_5, GdFe_<12>, Gd_2Fe_<17>, GdFe_<12>N and Gd_2Fe_<17>N_3 were calculated by FLAPW method and the charge distribution around R ions were investigated carefully. Nitrogen interstitial ions make strong bondings with surrounding Fe and R ions. The bonding with Fe leads to a larger spin saturation moment, but that with R makes a strong aspherical charge distribution around R and a crystalline field (CF) as large as that of SmCo_5. We found that this large CF is the microscopic origin of the strong uniaxial magnetic anisotropy in these nitrides. In the case of X/Co or Fe system, the MAE were calculated systematically by the LMTO method including the spin-orbit interaction. We found that the general tendency of the MAE in these systems are well explained by first-principles calculations. The thickness of Co layr dependence and the strain dependence of the MAE were also investigated.