  It is well established that the anomalous Hall effect that a ferromagnet
displays scales with its magnetization. Therefore, an antiferromagnet that has
no net magnetization should exhibit no anomalous Hall effect. Here we show that
the non-collinear triangular antiferromagnet Mn3Ge exhibits a large anomalous
Hall effect comparable to that of ferromagnetic metals; the magnitude of the
anomalous conductivity is 500 per ohm per cm at 2 K and 50 per ohm per cm at
room temperature. The angular dependence of the anomalous Hall effect
measurements confirm that the small residual in-plane magnetic moment has no
role in the observed effect. Our theoretical calculations demonstrate that the
large anomalous Hall effect in Mn3Ge originates from a non-vanishing Berry
curvature that arises from the chiral spin structure, and which also results in
a large spin Hall effect, comparable to that of platinum. The present results
pave the way to realize room temperature antiferromagnetic spintronics and spin
Hall effect based data storage devices.
