Abstract
We develop in this chapter the general symmetry analysis method of magnetic structures of crystals on the basis of the theory of space group representations, wherein the magnetic structure is expanded in terms of the basis functions of irreducible representations of the space group of the crystal. The principal assumption of the symmetry theory of phase transitions, namely that a transition to a phase of lower symmetry takes place through an irreducible representation of the symmetry group of the initial phase, makes it possible to reduce the problem of magnetic structures which can exist in a given crystal to sorting versions of mixed basis functions of a single representation. We perform a symmetry analysis of the exchange Hamiltonian and show which information on possible magnetic structures of a crystal can be obtained from the eigenfunctions of this Hamiltonian. We establish a symmetry relation between the eigenstates of the exchange Hamiltonian and the basis functions of the irreducible representations of the space groups. This chapter expounds the principal method of using symmetry analysis in neutron diffraction and for the description of magnetic structures of crystals.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Consultants Bureau, New York
About this chapter
Cite this chapter
Izyumov, Y.A., Naish, V.E., Ozerov, R.P. (1991). Symmetry Analysis of Magnetic Structures on the Basis of the Theory of Representations. In: Neutron Diffraction of Magnetic Materials. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3658-1_2
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3658-1_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-306-11030-6
Online ISBN: 978-1-4615-3658-1
eBook Packages: Springer Book Archive