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Bernd Souvignier
The four-dimensional magnetic point and space groups
Keywords: Magnetic groups, Antisymmetry, Higher-dimensional crystallography, Quasicrystals
This paper describes the classification of magnetic point and space groups which are also referred to as antisymmetry 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. spin up or down). 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.
Zeitschrift für Kristallographie, Oldenbourg Wissenschaftsverlag
Print ISSN: 0044-2968
Volume: 221, 01/2006
Pages: 077 - 082