  In most conductors current flow perpendicular to electric field direction
(Hall current) can be explained in terms of the Lorentz forces present when
charged particles flow in an external magnetic field. However, as established
in the very early work of Edwin Hall, ferromagnetic conductors such as Fe, Co,
and Ni have an anomalous Hall conductivity contribution that cannot be
attributed to Lorentz forces and therefore survives in the absence of a
magnetic field. Although the anomalous Hall effect is experimentally strong, it
has stood alone among metallic transport effects for much of the last century
because it lacked a usefully predictive, generally accepted theory. Progress
over the past decade has explained why. It is now clear that the anomalous Hall
effect in ferromagnets has contributions from both extrinsic scattering
mechanisms similar to those that determine most transport coefficients, and
from an intrinsic mechanism that is independent of scattering. The anomalous
Hall effect is also observed in paramagnets, which have nonzero magnetization
induced by an external magnetic field. Although no explicit relationship has
been established, the anomalous Hall effect in a particular material is usually
assumed to be proportional to its magnetization. In this work we point out that
it is possible to have an anomalous Hall effect in a noncollinear
antiferromagnet with zero net magnetization provided that certain common
symmetries are absent, and predict that Mn3Ir, a technologically important
antiferromagnetic material with noncollinear order that survives to very high
temperatures, has a surprisingly large anomalous Hall effect comparable in size
to those of the elemental transition metal ferromagnets.
