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

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.

Topology analysis for anomalous Hall effect in the noncollinear antiferromagnetic states of Mn3AN (A=Ni, Cu,Huyen1, Suzuki2, Yamauchi3 et al. 2019Phys. Rev. B614302View full textAdd to dashboardCite

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“…Classification of the magnetic structures with the ordering vector q=0 in Mn3AN according to the symmetryadapted multipole20 as well as the irreducible representation (IR), magnetic point group (Mag. PG) with its principal axis (P. axis).…”

Cluster multipole dynamics in noncollinear antiferromagnets

“…Especially, there is a lack of systematic methods to obtain its effective model so far. Here, we propose a framework to derive an effective model of noncollinear AFM based on the cluster multipole theory [33,39,40]. In Mn 3 Sn, the derived model is composed of two octupole degrees of freedom and reduced into the sine-Gordon model similar to FM and collinear AFM.…”

Imaging switchable magnetoelectric quadrupole domains via nonreciprocal linear dichroism

“…agnetic symmetry of matter plays an essential role in defining their physical properties associated with magnetism, such as magnetoelectric, magnetooptical, and magnetotransport properties. Recent theoretical studies have shown that such intriguing magnetic phenomena are fully described by n-th rank magnetic multipoles and magnetic toroidal multipoles from the symmetry viewpoint 1,2 . Among them, magnetic multipoles with rank 0 (monopole) and rank 2 (quadrupole), and magnetic toroidal multipole with rank 1 (toroidal dipole) are categorized as the most fundamental parity-odd magnetic quantities.…”