  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 is detectable by using the
x-ray magneto-circular dichroism.
