  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. It is found that the intrinsic
anomalous Hall conductivity ($\sigma_{xy}^H$) 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
$\sigma_{xy}^H$ 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 3$d$ 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
$\sigma_{xy}^H$ 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 explain qualitatively
why the theoretical and experimental $\sigma_{xy}^H$ 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 $\sigma_{xy}^H$ with the
magnitude being in the range of $500\sim 1400$ $\Omega^{-1}$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 $\sigma_{xy}^H$ between
theory and experiment.
