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Anomalous Hall effect arising from noncollinear antiferromagnetism

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.