Intrinsic anomalous Hall effect in nickel: A GGA+U study

The electronic structure and intrinsic anomalous Hall conductivity of nickel have been calculated based on the generalized gradient approximation (GGA) plus on-site Coulomb interaction (GGA + U) scheme. The highly accurate all-electron full-potential linearized augmented plane-wave method is used. It is found that the intrinsic anomalous Hall conductivity (sigma(H)(xy)) obtained from the GGA + U calculations with U = 1.9 eV and J = 1.2 eV is in nearly perfect agreement with that measured recently at low temperatures while, in contrast, the sigma(H)(xy) from the GGA calculations is about 100% larger than the measured one. This indicates that, as for the other spin-orbit interaction (SOI)-induced phenomena in 3d itinerant magnets, such as the orbital magnetic magnetization and magnetocrystalline anisotropy, the on-site electron-electron correlation, though moderate only, should be taken into account properly in order to get the correct anomalous Hall conductivity. The intrinsic sigma(H)(xy) and the number of valence electrons (N-e) have also been calculated as a function of the Fermi energy (E-F). A sign change is predicted at E-F = -0.38 eV (N-e = 9.57), and this explains qualitatively why the theoretical and experimental sigma(H)(xy) values for Fe and Co are positive. It is also predicted that fcc Ni(1-x)Co(Fe,Cu)(x) alloys with x being small would also have the negative sigma(H)(xy) with the magnitude being in the range of 500-1400 Omega(-1) cm(-1). The most pronounced effect of including the on-site Coulomb interaction is that all the d-dominant bands are lowered in energy relative to the E-F by about 0.3 eV, and consequently, the small minority spin X-2 hole pocket disappears. The presence of the small X-2 hole pocket in the GGA calculations is attributed to be responsible for the large discrepancy in the sigma(H)(xy) between theory and experiment.