International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. D. ch. 1.5, pp. 105-149
https://doi.org/10.1107/97809553602060000632 Chapter 1.5. Magnetic properties
a
P. L. Kapitza Institute for Physical Problems, Russian Academy of Sciences, Kosygin Street 2, 119334 Moscow, Russia, and bLabor für Neutronenstreuung, ETH Zurich, and Paul Scherrer Institute, CH-5234 Villigen PSI, Switzerland |
Footnotes
‡ Deceased.
2 By omitting its translative part, each element of is mapped on the corresponding element of the point group . This mapping also establishes a one-to-one correspondence between the representations of and those of .3 In Section 1.5.3.3, we shall show that this rule corresponds in the Landau theory of phase transitions to the general law that the magnetically ordered state is described by or , which form the basis of one of the irreducible representations of the paramagnetic space group of the crystal.
4 Table 1.5.8.1 shows that the tensor describing the magnetoelectric effect does not need to be symmetric for 31 of the 58 point groups. These 31 groups coincide with those that admit a spontaneous toroidal moment (Gorbatsevich & Kopaev, 1994); they were first determined by Ascher (1966) as the magnetic point groups admitting spontaneous currents.