Unlike magnetic spin ordering where the antiferromagnetism can be defined by flipping the magnetization axis of two neighbor sites from a ferromagnetic configuration, flipping of the magnetization axis of a multipole is usually meaningless. Taking a  moment as an example, if one flips the z-axis by making a  rotation toward the y-axis, it just changes nothing. Therefore, a suggested definition of antiferromagnetic multipolar ordering is to flip their phases by , i.e. . In this regard, the antiferromagnetic spin ordering is just a special case of this definition, i.e. flipping the phase of a dipole moment is equivalent to flipping its magnetization axis. As for high rank multipoles, e.g. , it actually becomes a  rotation and for  it is even not any kind of rotation.