Magnetism in Crystalline Materials: Applications of the Groups of Cambiant Symmetry (Monographs in Natural Philosophy)

"This book is concerned with those physical properties of magnetically ordered crystalline solids which are closely related to their symmetry. In the last decade or so it has become apparent that the structures of many magnetically ordered crystals can conveniently be described in terms of cambiant symmetry, i.e. by the Heesch-Shubnikov groups or by other generalized symmetry groups. The term "cambiant" symmetry (Latin 'cambiare' = to change) was introduced by Dr. N.F.M. Henry to describe the various generalizations of crystallographic symmetry in which it is desired to specify not only the positions of the atoms in a crystal but also some physical property, such as a magnetic moment, associated with each of the atoms. Previous writings on the use of some of these generalized groups in the description of the symmetry and physical properties of magnetic crystals include the review article by Opechowski and Guccione (1965) and the book by Birss (1966); extensive use of these sources has been made in writing certain sections of this book. In addition to this material we shall also be concerned with the applications of the theory of representations and of co-representations to the physical properties of magnetic crystals. The appropriate mathematical theory is lengthy and has already been described elsewhere, see the book by Bradley and Cracknell (1972); we shall simply quote the appropriate results that are needed in connection with some physical problems.

In order to establish some of the background, we shall find it necessary in the first chapter to recall a few of the basic ideas of magnetism and of symmetry in solids. However, this is not a comprehensive treatise on either magnetism or solid state theory, and we have concentrated only on those aspects of these subjects which are particularly interesting from the point of view of symmetry considerations of the physical properties of magnetic crystals."