The four-dimensional magnetic point and space groups

Abstract

AbstractThis paper describes the classification of magnetic point and space groups which are also referred to asantisymmetry groups or black-and-white groups. These groups play an important role in the description of discrete point sets in which the points are not only characterized by their spatial coordinates but also by an additional property taking one of two possible values (e.g. spinupordown). Each operation of a magnetic group may or may not switch the value of this additional property. In this paper, the methods for classifying magnetic groups in arbitrary dimensions are described in an algorithmic fashion. Results of the full classification in four-dimensional space are given and the application of the magnetic groups in this dimension to quasicrystals is indicated.