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We propose a systematic method to generate a complete orthonormal basis setof multipole expansion for magnetic structures in arbitrary crystal structure.The key idea is the introduction of a virtual atomic cluster of a targetcrystal, on which we can clearly define the magnetic configurationscorresponding to symmetry-adapted multipole moments. The magneticconfigurations are then mapped onto the crystal so as to preserve the magneticpoint group of the multipole moments, leading to the magnetic structuresclassified according to the irreducible representations of crystallographicpoint group. We apply the present scheme to pyrhochlore and hexagonal ABO3crystal structures, and demonstrate that the multipole expansion is useful toinvestigate the macroscopic responses of antiferromagnets.

Multipole expansion for magnetic structures: A generation scheme for symmetry-adapted orthonormal basis set in crystallographic point group