Antiferromagnets

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. 108

Section 1.5.1.2.2. Antiferromagnets

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

1.5.1.2.2. Antiferromagnets

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As discussed above, the exchange interaction, which is of prime importance in the formation of magnetic order, can lead to a parallel alignment of the neighbouring magnetic moments as well as to an antiparallel one. In the latter case, the simplest magnetic structure is the collinear antiferromagnet, schematically shown in Fig. 1.5.1.3(a). Such an antiferromagnet consists of one or several pairs of magnetic sublattices of identical magnetic ions located in equivalent crystallographic positions. The magnetizations of the sublattices are oriented opposite to each other.

Figure 1.5.1.3 | top | pdf |

Ordered arrangements of magnetic moments $[{\boldmu}_{i}]$ in: (a) an ordinary two-sublattice antiferromagnet $[{\bf L} =]$ $[(N/2)({\boldmu}_1 -]$ $[{\boldmu}_2)]$ ; (b) a weakly non-collinear four-sublattice antiferromagnet $[{\bf L}_1(x) =]$ $[(N/4)({\boldmu}_1 -]$ $[{\boldmu}_2 -]$ $[{\boldmu}_3 +]$ $[{\boldmu}_4)]$ , $[{\bf L}_2(y) =]$ $[(N/4)({\boldmu}_1 -]$ $[{\boldmu}_2 +]$ $[{\boldmu}_3 -]$ $[{\boldmu}_4)]$ ; (c) a strongly non-collinear three-sublattice antiferromagnet $[{\bf L}_1 =]$ $[(N/3)(3)^{1/2}({\boldmu}_2 -]$ $[{\boldmu}_1)]$ , $[{\bf L}_2 =]$ $[(N/3)({\boldmu}_1 +]$ $[{\boldmu}_2 -]$ $[{\boldmu}_3)]$ . The broken lines show the crystallographic primitive cell and the solid lines show the magnetic primitive cell.

Fig. 1.5.1.3(b) shows a weakly non-collinear antiferromagnet, in which the vectors of magnetization of four equivalent sublattices form a cross with a small tilting angle $[2\alpha]$ . Such a structure can be considered as an admixture of `weak antiferromagnetism' $[{\bf L}_1]$ with easy axis Ox to an ordinary antiferromagnet $[{\bf L}_2]$ with easy axis Oy. This weak antiferromagnetism is of the same origin as weak ferromagnetism. Its nature will be discussed in detail in Section 1.5.5.2.

The minimum of the exchange interaction energy of three spins located at the corners of a triangle corresponds to a structure in which the angles between two adjacent spins are 120°. Correspondingly, many hexagonal crystals possess a triangular antiferromagnetic structure like the one shown in Fig. 1.5.1.3(c). The sum of the magnetizations of the three sublattices in this structure equals zero. In tetragonal crystals, there is a possibility of the existence of a 90° antiferromagnetic structure, which consists of four equivalent sublattices with magnetizations oriented along the positive and negative directions of the x and y axes.

Finally, it is worth noting that in addition to the electronic magnetically ordered substances, there exist nuclear ferro- and antiferromagnets (below 1 mK for some insulators and below 1 µK for metals).

References

International Tables for Crystallography (2006). Vol. D. ch. 1.5, p. 108