Magnetically-ordered quasicrystals: Enumeration of spin groups and calculation of magnetic selection rules

TL;DR

This paper develops a detailed theoretical framework for magnetic symmetry in quasicrystals, enabling enumeration of spin groups and calculation of neutron scattering selection rules, demonstrated on 2D octagonal quasicrystals.

Contribution

It introduces a practical formalism for magnetic symmetry analysis in quasicrystals, extending previous outlines with detailed methods and examples.

Findings

Formalism for spin group enumeration in quasicrystals

Calculation of magnetic selection rules for neutron scattering

Application to 2D octagonal quasicrystals

Abstract

We provide the details of the theory of magnetic symmetry in quasicrystals, which has previously only been outlined. We develop a practical formalism for the enumeration of spin point groups and spin space groups, and for the calculation of selection rules for neutron scattering experiments. We demonstrate the formalism using the simple, yet non-trivial, example of magnetically-ordered octagonal quasicrystals in two dimensions. In a companion paper we shall provide complete results for octagonal quasicrystals in three dimensions.