Essential role of the anisotropic magnetic dipole in the anomalous Hall effect

We theoretically investigate the anomalous Hall effect (AHE) that requires neither a net magnetization nor an external magnetic field in collinear antiferromagnets. We show that such an emergent AHE is essentially caused by a ferroic ordering of the anisotropic magnetic dipole (AMD), which provides an effective coupling between ordered magnetic moments and electronic motion in the crystal. We demonstrate that the AMD is naturally induced by the antiferromagnetic ordering, in which the magnetic moments have a quadrupole spatial distribution. In view of the ferroic AMD ordering, we analyze the behavior of the AHE in the orthorhombic lattice system, where the AHE is largely enhanced by the large coupling between the AMD and the spin-orbit interaction. From these findings, the AMD can be used as a descriptor in general to investigate the ferromagnetic-related physical quantities in antiferromagnets including noncollinear ones, which are detectable by using the x-ray magneto-circular dichroism.