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A historical introduction to the symmetries of magnetic structures. Part 1. Early quantum theory, neutron powder diffraction and the coloured space groups

Published online by Cambridge University Press:  14 March 2017

Andrew S. Wills
Andrew S. Wills*
Affiliation:
Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom
*
a)Author to whom correspondence should be addressed. Electronic mail: [email protected]
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Abstract

This paper introduces the historical development of the symmetries for describing magnetic structures culminating in the derivation of the black and white and coloured space groups. Beginning from the Langevin model of the Curie law, it aims to show the challenges that magnetic ordering presented and how different symmetry frameworks were developed to meet them. As well as explaining core ideas, later papers will show how the different schemes are connected. With these goals in mind, the maths related is kept to the minimum required for clarity. Those wishing to learn more details are invited to engage with the references. As well as looking back and reviewing the development of magnetic symmetry over time, particular attention is spent on explaining where the concept of time-reversal has been applied. That time-reversal has different meaning in classical and quantum mechanical situations, has created confusions which continue to propagate.

Keywords

Neelmagnetic structuresymmetryShubnikovantisymmetryspace groups
Type
Crystallography Education
Information
Powder Diffraction , Volume 32 , Issue 2 , June 2017 , pp. 148 - 155
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Copyright
Copyright © International Centre for Diffraction Data 2017 

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References

Anderson, P. W. (1950). “Antiferromagnetism. Theory of superexchange interaction,” Phys. Rev. 79, 350–356.Google Scholar
Anderson, P. W. (2011). More and Different: Notes from a Thoughtful Curmudgeon (World Scientific, Singapore).CrossRefGoogle Scholar
Barnett, S. J. (1946). “International Conference on magnetism Strasbourg, 21–24 May 1939,” Science 104, 70–73.Google Scholar
Belov, N. V. and Tarkhova, T. N. (1956). “Groups of colored symmetry,” (In Russian). Kristallografiya 1, 4–13. (English translation: Sov. Phys. Crystallogr. 1, 5–11).Google Scholar
Belov, N. V., Neronova, N. N., and Smirnova, T. S. (1955). “1651 Shubnikov groups,” (In Russian). Trudy Inst. Kristallogr. Acad. SSSR 11, 33–67.Google Scholar
Belov, N. V., Neronova, N. N., and Smirnova, T. S. (1957). “Shubnikov groups,” (In Russian). Kristall. 2, 315–325. (English translation: Sov. Phys. Crystallogr. 2, 311–322).Google Scholar
Bertaut, E. F. (1968). “Representation analysis of magnetic structures,” Acta Crystallogr. A24, 217–231.Google Scholar
Bitter, F. (1938). “A generalization of the theory of ferromagnetism,” Phys. Rev. 54, 79–86.CrossRefGoogle Scholar
Brinkman, W. F. and Elliot, R. J. (1966). “Theory of spin-space groups,” Proc. R. Soc. A294, 343–358.Google Scholar
Cracknell, A. P. (1969). “Group theory and magnetic phenomena in solids,” Rep. Progr. Phys. 32, 633–707.CrossRefGoogle Scholar
Curie, P. (1894). ” Sur la symétrie dans les phénomènes physiques, symétrie d'un champ électrique et d'un champ magnétique,” J. Phys. 3, 393–415.Google Scholar
Curie, P. (1895). “Propriétés magnétiques des corps à diverses temperatures,” (Gauthier-Villers, et fils, Paris). Ann. Chim. Phy. 7, 289–405.Google Scholar
Donnay, G., Corliss, L. M., Donnay, J. D. H., Elliot, N., and Hastings, J. M. (1958). “Symmetry of magnetic structures: magnetic structure of chalcopyrite,” Phys. Rev. 112, 1917–1923.Google Scholar
Hahn, Th. (Ed.) (1996). Interk,knational Tables for Crystallography, Volume A: Space Group Symmetry (Kluwer, London).Google Scholar
Halpern, O. and Johnson, M. H. (1939). “On the magnetic scattering of neutrons,” Phys. Rev. 55, 898–923.Google Scholar
Heesch, H. (1930). “Über die vierdimensionalen Gruppen des dreidimensionalen Raumes,” Z. Kristallogr. 73, 325–345.Google Scholar
Indenbom, V. L. (1959). “Relation of the antisymmetry and color symmetry groups to one-dimensional representations of the ordinary symmetry groups. Isomorphism of the Shubnikov and space groups. (In Russian.),” Kristallografiya 4, 619–621. (English translation: Sov. Phys. Crystallogr. 4(1960), 578–580).Google Scholar
Izyumov, Yu. A. (1980). “Neutron diffraction studies of magnetic structures of crystals,” Sov. Phys. – Usp. 23, 356–374.CrossRefGoogle Scholar
Kitz, A. (1965). “Über die Symmetriegruppenvon Spinverteilungen,” Phys. Status Sol. 10, 455–466.Google Scholar
Koptsik, V. A. (1966). Shubnilov Groups. Handbook on the Symmetry and Physical Properties of Crystal Structures (Izd. M.G.U., Moscow). [English translation: (1971) (Fysica Memo 175, Stichting, Reactor Centrum Nederlands].Google Scholar
Krishnamurty, T. S. G., Prasad, L. S. R. K., and Rama Mohana Rao, K. (1978). “On quasisymmetry (P-symmetry) groups,” J. Phys. A: Math. Gen. 11, 805–811.Google Scholar
Landau, L. D. (1933). “Possible explanation of the dependence on the field of the susceptibility at low temperatures,” Phys. Z. Sowjet 4, 675–679.Google Scholar
Landau, L. I. and Lifshitz, E. M. (1951). Statistical Physics (In Russian). (GITTL, Moscow). [English translation: (1958) (Pergamon: London)].Google Scholar
Langevin, P. (1905). “Magnétisme et thérie des electrons,” Ann. Chim. Phys. 5, 70–127.Google Scholar
Mason, T. E., Gawne, T. J., Nagler, S. E., Nestora, M. B., and Carpenter, J. M. (2013). “The early development of neutron diffraction: science in the wings of the Manhattan Project,” Acta Crystallogr. A69, 37–44.Google Scholar
Naish, V. E. (1962). “Magnetic structures of the metallic perovskites,” Phys. Met. Metall. 14, 144.Google Scholar
Néel, L. (1932). Influence des fluctuations des champs moléculaires sur les propriétés magnétiques des corps. PhD Thesis, Masson et Cie, Paris. Ann. Phys. 17, 5–105.Google Scholar
Néel, L. (1936). “Theory of constant paramagnetism. Application to manganese,” C. R. Acad. Sci. Paris 203, 304–306.Google Scholar
Niggli, A. Z. (1959). “The systematic and group-theoretical derivations of the symmetry-, antisymmetry- and degeneration-symmetry groups,” (In German). Kristallogr. 111, 288–300.Google Scholar
Opechowski, W. and Dreyfus, T. (1971). “Classifications of magnetic structures,” Acta Crystallogr. A27, 470–484.Google Scholar
Senechal, M. (1988). “Color symmetry,” Comput. Math. Appl. 16, 545–553.Google Scholar
Shubnikov, A. V. (1951). Symmetry and Antisymmetry of Finite Figures (In Russian). (USSR Academy of Sciences, Moscow).Google Scholar
Shubnikov, A. V. (1988), “On the works of Pierre Curie on symmetry,” Comput. Math. Appl. 16, 357–364.Google Scholar
Shubnikov, A. V. and Koptsik, V. A. (1972). Symmetry in Science and Art (In Russian). (Nuaka, Moscow); [English translation: (1974) (Plenum Press, New York) (1974).Google Scholar
Shull, C. G. and Smart, J. S. (1949). “Detection of antiferromagnetism by neutron diffraction,” Phys. Rev. 76, 1256–1257.Google Scholar
Shull, C. G., Strauber, W. A., and Wollan, E. O. (1951). “Neutron diffraction by paramagnetic and antiferromagnetic substances,” Phys. Rev. 83, 333–345.CrossRefGoogle Scholar
Sivardière, J. (1969). “Methode Nouvelle de Construstion des Groupes Magnétiques,” Acta Crystallogr. A25, 658–665.Google Scholar
Tavger, B. A. and Zaitsev, V. M. (1956). “Magnetic symmetry of crystals,” (In Russian). Zh. Eksp. Teor. Fiz. 30, 564–568. (English translation: Sov. Phys. JETP, 3, 430–436).Google Scholar
van Vleck, J. (1932). The Theory of Electric and Magnetic Susceptibilities (Oxford University Press, London).Google Scholar
van Vleck, J. (1941). “On the theory of antiferromagnetism,” J. Chem. Phys. 9, 85–90.CrossRefGoogle Scholar
Voigt, W. (1910). Lehrbuch der Kristallphysik: (mit Ausschluss der Kristalloptik), (Teubner, Leipzig); reprinted (1966) (Springer Fachmedien, Wiesbaden).Google Scholar
Weiss, P. (1906). “La variation du ferromagnétism avec la température,” C. R. Acad. Sci. 143, 1137–1139.Google Scholar
Weiss, P. (1907). “L'hypothèse du champ moléculaire et la propriété ferromagnétique,” J. Phys. 6, 666–690.Google Scholar
Weiss, P. and Foex, G. (1911). “Etude de l'aimantation des corps ferromagnétiques au-dessus du point de Curie,” J. Phys. Theor. Appl. 1, 805–814.Google Scholar
Wigner, E. P. (1931). Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (In German). (Friedrich Vieweg und Sohn, Braunschweig). (English translation: (1959) (Academic Press, New York).Google Scholar
Zamorzaev, A. M. (1953). Generalization of Fedorov groups. PhD Thesis, Leningrad University.Google Scholar
Zamorzaev, A. M. (1957). “Generalization of the Fedorov groups,” (In Russian). Kristallografiya 2, 15–20. (English translation: Sov. Phys. Crystallogr. 2, 10–15).Google Scholar
Zamorzaev, A. M. (1988). “Generalized antisymmetry,” Comput. Math. Appl. 16, 555–562.Google Scholar