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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. 108-109
Section 1.5.1.2.3. Helical and sinusoidal magnetics
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 |
There are many more complicated non-collinear magnetic structures. Fig. 1.5.1.4![[link]](/graphics/greenarr.gif)
(a) shows an antiferromagnetic helical structure. It consists of planes perpendicular to the z axis in which all the magnetic moments are parallel to each other and are perpendicular to z. The polar angle of the direction of the moments changes from plane to plane by some constant ![[\delta]](/teximages/bach1o3/bach1o3fi482.svg)
. Thus the magnetization vectors describe a spiral along the axis of the crystal. Such structures were observed in hexagonal rare-earth metals. A specific feature is that they often are incommensurate structures. This means that ![[2\pi /\delta ]](/teximages/dach1o5/dach1o5fi63.svg)
is not a rational number and that the period of the magnetic spiral is not a multiple of the period of the lattice.
![[Figure 1.5.1.4]](/figures/Dafig1o5o1o4thm.gif)
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Helical and sinusoidal magnetic structures. (a) An antiferromagnetic helix; (b) a cone spiral; (c) a cycloidal spiral; (d) a longitudinal spin-density wave; (e) a transverse spin-density wave. |
Similar to the antiferromagnetic helix, ferromagnetic helical or spiral structures exist [see Fig. 1.5.1.4(b)] in which the magnetizations of the layers are tilted to the axis at an angle ![[\theta]](/teximages/bach1o1/bach1o1fi82.svg)
. As a result, the vectors of the magnetization of the layers are arranged on the surface of a cone. The ferromagnetic magnetization is aligned along the z axis. This structure is called a ferromagnetic helix. It usually belongs to the incommensurate magnetic structures.
More complicated antiferromagnetic structures also exist: sinusoidal structures, which also consist of layers in which all the magnetic moments are parallel to each other. Fig. 1.5.1.4(c) displays the cycloidal spiral and Figs. 1.5.1.4(d) and (e) display longitudinal and transverse spin density waves, respectively.
