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

## TL;DR

This paper introduces a systematic method to generate a complete orthonormal basis set of multipole expansion for magnetic structures in arbitrary crystal structures, aiding the analysis of magnetic responses.

## Contribution

The authors develop a novel scheme to construct symmetry-adapted multipole basis sets for magnetic structures using virtual atomic clusters, applicable to any crystal symmetry.

## Key findings

- Successfully applied to pyrochlore and hexagonal ABO3 structures.
- Demonstrated usefulness in studying macroscopic responses of antiferromagnets.
- Provides a unified framework for magnetic multipole analysis.

## Abstract

We propose a systematic method to generate a complete orthonormal basis set of multipole expansion for magnetic structures in arbitrary crystal structure. The key idea is the introduction of a virtual atomic cluster of a target crystal, on which we can clearly define the magnetic configurations corresponding to symmetry-adapted multipole moments. The magnetic configurations are then mapped onto the crystal so as to preserve the magnetic point group of the multipole moments, leading to the magnetic structures classified according to the irreducible representations of crystallographic point group. We apply the present scheme to pyrhochlore and hexagonal ABO3 crystal structures, and demonstrate that the multipole expansion is useful to investigate the macroscopic responses of antiferromagnets.