Tables for
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D, ch. 1.5, pp. 105-149

Chapter 1.5. Magnetic properties

A. S. Borovik-Romanova and H. Grimmerb*

aP. 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
Correspondence e-mail:


1 The sudden death of Andrey Stanislavovich Borovik-Romanov is deeply regretted. At the age of 77, he died on 31 July 1997 in Cairns, Australia, where he was taking part in the International Conference on Magnetism ICM'97.


2 By omitting its translative part, each element of [\widetilde{\bi{D}}_{3d}^6] is mapped on the corresponding element of the point group [{\bi D}_{3d}=\bar{3}m]. This mapping also establishes a one-to-one correspondence between the representations of [\widetilde{\bi{D}}_{3d}^6] and those of [{\bi D}_{3d}=\bar{3}m].
3 In Section[link], 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 [L_{\alpha i}] or [M_i], which form the basis of one of the irreducible representations of the paramagnetic space group of the crystal.
4 Table[link] 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[link]); they were first determined by Ascher (1966[link]) as the magnetic point groups admitting spontaneous currents.