Time inversion in the representation analysis of magnetic structures

The representation analysis of magnetic structures (group theory) considers generally the group G k (symmetry elements of the space group G which keep unchanged the propagation vector k). There exists a certain confusion about the way and the usefulness of introducing time inversion, the operation which reverses the directions of the magnetic moments. We show here that we can define two ‘time inversion’ operators, one which is linear and one which is antilinear. While introducing the linear operator does not bring any new piece of information, introducing the antilinear operator brings more details on the possible magnetic structures. Because of this antilinearity, the corepresentations have to be used instead of the usual representations. The corepresentation theory had been introduced by Wigner for the operator ‘time inversion in quantum mechanics’, operator which, in quantum mechanics, must be antilinear. Finally we show that, for magnetic structures, using an antilinear operator instead of a linear operator, is connected with the reality of the magnetic moments. To cite this article: J. Schweizer, C. R. Physique 6 (2005).