  Based on first principles density functional calculations of the intrinsic
anomalous and spin Hall conductivities, we predict that the charge Hall current
in Co-based full Heusler compounds Co$_2$XZ (X = Cr and Mn; Z = Al, Si, Ga, Ge,
In and Sn) except Co$_2$CrGa would be almost fully spin-polarized even although
Co$_2$MnAl, Co$_2$MnGa, Co$_2$MnIn and Co$_2$MnSn do not have a half-metallic
band structure. Furthermore, the ratio of the associated spin current to the
charge Hall current is slightly larger than 1.0. This suggests that these
Co-based Heusler compounds, especially Co$_2$MnAl, Co$_2$MnGa and Co$_2$MnIn
which are found to have large anomalous and spin Hall conductivities, might be
called anomalous Hall half-metals and could have valuable applications in
spintronics such as spin valves as well as magnetoresistive and spin-torque
driven nanodevices. These interesting findings are discussed in terms of the
calculated electronic band structures, magnetic moments and also anomalous and
spin Hall conductivities as a function of the Fermi level.
