Generalization of microscopic multipoles and cross-correlated phenomena by their orderings.

The generalization of the atomic-scale multipoles is discussed. By introducing the augmented multipoles defined in the hybrid orbitals or in the site/bond-cluster, any of electronic degrees of freedom can be expressed in accordance with the crystallographic point group. These multipoles are useful to describe the cross-correlated phenomena, band-structure deformation, and generation of effective spin-orbit coupling due to antiferromagnetic ordering in a systematic and comprehensive manner. Such a symmetry-adapted multipole basis set could be a promising descriptor for materials design and informatics.