Anomalous Hall Effect Arising from Noncollinear Antiferromagnetism

As established in the very early work of Edwin Hall, ferromagnetic conductors have an anomalous Hall conductivity contribution that cannot be attributed to Lorentz forces and therefore survives in the absence of a magnetic field. These anomalous Hall conductivities are normally assumed to be proportional to magnetization. We use symmetry arguments and first-principles electronic structure calculations to counter this assumption and to predict that ${\mathrm{Mn}}_{3}\mathrm{Ir}$, a high-temperature antiferromagnet that is commonly employed in spin-valve devices, has a large anomalous Hall conductivity.