Systematic investigation of emergent particles in type-III magnetic space groups

TL;DR

This paper systematically investigates emergent particles in 674 type-III magnetic space groups, revealing their classification, properties, and topological features, thus advancing the understanding of magnetic topological materials.

Contribution

It provides a comprehensive classification and tabulation of emergent particles in type-III MSGs, including symmetry details and topological characteristics, filling a gap in magnetic crystal research.

Findings

All emergent particles in type-III MSGs also exist in type-II MSGs except one case.

Explicit tabulations of emergent particles, symmetries, and topological features are provided.

The work enables efficient search for topological magnetic materials with novel quasiparticles.

Abstract

In three-dimensional (3D) crystals, emergent particles arise when two or multiple bands contact and form degeneracy (band crossing) in the Brillouin zone. Recently a complete classification of emergent particles in 3D nonmagnetic crystals, which described by the type-II magnetic space groups (MSGs), has been established. However, a systematic investigation of emergent particles in magnetic crystals has not yet been performed, due to the complexity of the symmetries of magnetically ordered structures. Here, we address this challenging task by exploring the possibilities of the emergent particles in the 674 type-III MSGs. Based on effective k.p Hamiltonian and our classification of emergent particles [Yu et al., Sci. Bull. 67, 375 (2022) DOI:10.1016/j.scib.2021.10.023], we identify all possible emergent particles, including spinful and spinless, essential and accidental particles in the type-III MSGs. We find that all emergent particles in type-III MSGs also exist in type-II MSGs, with only one exception, i.e. the combined quadratic nodal line and nodal surface (QNL/NS). Moreover, tabulations of the emergent particles in each of the 674 type-III MSGs, together with the symmetry operations, the small corepresentations, the effective k.p Hamiltonians, and the topological character of these particles, are explicitly presented. Remarkably, combining this work and our homemade SpaceGroupIrep and MSGCorep packages will provide an effcient way to search topological magnetic materials with novel quasiparticles.