  We have calculated the intrinsic anomalous and spin Hall conductivities, spin
and orbital magnetic moments and also spin polarization of Hall currentsin
hexagonal cobalt within the density functional theory with the generalized
gradient approximation (GGA) plus on-site Coulomb interaction (GGA+$U$). The
accurate all-electron full-potential linearized augmented plane wave method is
used. We find that the anomalous Hall conductivity (AHC) ($\sigma_{xy}^A$) and
orbital magnetic moment ($m_o$) of cobalt with the magnetization being along
the c-axis ($m//c$) calculated in the GGA+$U$ scheme with $U = 1.6$ eV and $J =
0.9$ eV agree rather well with the corresponding experimental values while, in
contrast, the $\sigma_{xy}^A$ and $m_o$ from the GGA calculations are
significantly smaller than the measured ones. This suggests that moderate $U =
1.6$ eV and $J = 0.9$ eV are appropriate for Co metals. The calculated AHC and
spin Hall conductivity (SHC) ($\sigma^S$) are highly anisotropic, and the ratio
of the Hall conductivity for $m//c$ to that for the magnetization being
in-plane ($m//ab$) from the GGA+$U$ calculations, is $\sim$16.0 for the AHC and
$\sim$6.0 for the SHC. For $m//c$, the spin-up and spin-down Hall currents are
found to flow in the same direction. The magnitude of the calculated Hall
current spin polarization ($P^H$) is large and $P^H = -0.61$. Remarkably, for
$m//ab$, the spin-up and spin-down Hall currents are predicted to flow in the
opposite directions. This indicates that the Hall current contains both
spin-polarized charge current and pure spin current, resulting in the magnitude
of the Hall current spin polarization ($P^H = -1.59$) being larger than 1.0.
