Structure and Topology of Band Structures in the 1651 Magnetic Space Groups

TL;DR

This paper systematically analyzes the symmetry and topological properties of electron band structures across all 1651 magnetic space groups, revealing constraints on electron fillings, band connectivity, and topological phases in magnetic materials.

Contribution

It provides a comprehensive, systematic description of band structures in all magnetic space groups and layer groups, including constraints and topological classifications.

Findings

Constraints on electron fillings and band connectivity

Identification of band topology from MSG symmetry

Application to topological semimetals in magnetic textures

Abstract

The properties of electrons in magnetically ordered crystals are of interest both from the viewpoint of realizing novel topological phases, such as magnetic Weyl semimetals, and from the applications perspective of creating energy-efficient memories. A systematic study of symmetry and topology in magnetic materials has been challenging given that there are 1651 magnetic space groups (MSGs). Here, by using an efficient representation of allowed band structures, we obtain a systematic description of several basic properties of free electrons in all MSGs in three dimensions as well as in the 528 magnetic layer groups relevant to two dimensional magnetic materials. We compute constraints on electron fillings and band connectivity compatible with insulating behavior. Also, by contrasting with atomic insulators, we identify band topology entailed by the symmetry transformation of bands, as determined by the MSG alone. We give an application of our results to identifying topological semimetals arising in periodic arrangements of hedgehog-like magnetic textures.