GROUP THEORY AND MAGNETIC PHENOMENA IN SOLIDS

In a brief introductory section the derivation of the Shubnikov groups and their importance in the description of the symmetries of magnetic crystals is described. The derivation of the black and white Bravais lattices and of the Shubnikov point groups and space groups is described and there is a brief discussion of spin space groups. In a later section the determination of the corepresentations of these non-unitary groups is discussed. The remainder of the article is devoted to a description of the various uses which can be made of the magnetic groups and of their corepresentations in studying various properties of magnetic crystals. These applications include: the simplification of the form of a tensor describing either some macroscopic static property or some transport property or some microscopic property of the crystal; the determination of the shape of the Brillouin zone of a magnetically ordered crystal; Landau's theory of second-order phase transitions; spontaneous currents and superconductivity; crystal field theory; space-group selection rules; the symmetry properties and degeneracies of magnons and paramagnons in magnetic or nearly-magnetic crystals; the symmetry properties and degeneracies of the electronic band structure of a ferromagnetic metal. In conclusion there is a brief discussion of the polychromatic groups.