Table 1.5.5.1

Borovik-Romanov, A. S.; Grimmer, H.

doi:10.1107/97809553602060000632

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

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International Tables for Crystallography (2006). Vol. D. ch. 1.5, p. 129

Table 1.5.5.1

A. S. Borovik-Romanov^a ^‡ and H. Grimmer^b ^*

^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
Correspondence e-mail: hans.grimmer@psi.ch

Table 1.5.5.1 | top | pdf |
The numbers of the crystallographic space groups that allow a phase transition into a weakly ferromagnetic state and the invariants of lowest order that are responsible for weak ferromagnetism

Note that the standard numbering of space groups is used in this table, not the one employed by Turov (1963).

System	Nos. of the space groups	Invariants
Monoclinic	3–15	$[M_{x}L_{y}]$ , $[M_{z}L_{y}]$ , $[M_{y}L_{x}]$ , $[M_{y}L_{z}]$
Orthorhombic	16–74	$[M_{x}L_{y}]$ , $[M_{y}L_{x}]$
		$[M_{y}L_{z}]$ , $[M_{z}L_{y}]$
		$[M_{x}L_{z}]$ , $[M_{z}L_{x}]$
Tetragonal	75–88	$[M_{x}L_{y}+M_{y}L_{x}]$ , $[M_{x}L_{x}-M_{y}L_{y}]$
	89–142	$[{M_{x}L_{y}-M_{y}L_{x}}]$
		$[{M_{x}L_{y}+M_{y}L_{x}}]$
		$[{M_{x}L_{x}-M_{y}L_{y}}]$
Trigonal	149–167	$[{M_{x}L_{y}-M_{y}L_{x}}]$
Hexagonal	168–176	$[{M_{z}(L_{x}{\pm}iL_{y})^{3}}]$ , $[{(M_{x}{\pm}iM_{y})(L_{x}{\pm}iL_{y})^{2}L_{z}}]$
	177–194	$[{M_{x}L_{y}-M_{y}L_{x}}]$
		$[{iM_{z}[(L_{x}+iL_{y})^{3}-(L_{x}-iL_{y})^{3}]}]$ , $[{i[(M_{x}+iM_{y})(L_{x}+iL_{y})^{2}-(M_{x}-iM_{y})(L_{x}-iL_{y})^{2}]L_{z}}]$
		$[{M_{z}[(L_{x}+iL_{y})^{3}+(L_{x}-iL_{y})^{3}]}]$ , $[{[(M_{x}+iM_{y})(L_{x}+iL_{y})^{2}+(M_{x}-iM_{y})(L_{x}-iL_{y})^{2}]L_{z}}]$
Cubic	207–230	$[{M_{x}L_{x}(L_{y}^{2}-L_{z}^{2})+M_{y}L_{y}(L_{z}^{2}-L_{x}^{2})+M_{z}L_{z}(L_{x}^{2}-L_{y}^{2})}]$