Magnetic point groups and space groups

TL;DR

This paper introduces magnetic point and space groups, extending traditional symmetry descriptions to matter with magnetic properties, and discusses their structure, notation, and implications for neutron diffraction.

Contribution

It defines magnetic groups, explains their structure and notation, and provides pedagogical examples, expanding the symmetry framework for magnetic matter.

Findings

Definition and explanation of magnetic point and space groups

Examples of enumeration of magnetic groups

Discussion of magnetic selection rules in neutron diffraction

Abstract

The spatial symmetry of matter - including finite objects like molecules or atomic clusters, and extended objects like periodic or aperiodic crystals - is described using point groups and space groups. Magnetic point groups and space groups are the simplest extension of this description, to matter whose atomic constituents possess a property that can take one of two possible values, like the "up" or "down" orientations of a magnetic moment, or a spin. Magnetic groups - also known as antisymmetry groups, Shubnikov groups, Heesch groups, Opechowski-Guccione groups, as well as dichromatic, 2-color, or simply black-and-white groups - are here defined, and their structure and notation explained, while providing some pedagogical examples of their enumeration. The resulting magnetic selection rules, or extinctions, in neutron diffraction experiments are discussed. Further extensions to color groups and spin groups are briefly described.