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

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. 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:  hans.grimmer@psi.ch

Footnotes

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.

Deceased.

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 1.5.3.3[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 1.5.8.1[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.