Abstract
The solution is given to the problem regarding the derivation of the so-called space groups of magnetic symmetry with crystallographic angles of rotation of the spin vector, which was formulated as far back as the early 1970s. The crystallographic P-symmetries that should be used in the generalization with the three-dimensional space Fedorov groups G 3 are revealed. The space groups G 3 are generalized with each of these P-symmetries.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. M. Zamorzaev, A. F. Palistrant, and Yu. S. Karpova, in Proceedings of the International Seminar on Group Theoretical Methods in Physics, Zvenigorod, Moscow Region, Russia, 1982 (Nauka, Moscow, 1983), p. 346 [in Russian].
A. M. Zamorzaev, Yu. S. Karpova, A. P. Lungu, and A. F. Palistrant, P-Symmetry and Its Further Development (Shtiintsa, Kishinev, 1986) [in Russian].
A. A. Shenesheutskaya and A. F. Palistrant, Analele Ştiinţifice ale USM: Seria “Ştiinţe Fiziso-Matematise” (USM, Chişinău, 2002) [in Moldavian].
V. E. Naĭsh, Izv. Akad. Nauk SSSR, Ser. Fiz. 27, 1496 (1963).
A. M. Zamorzaev and A. F. Palistrant, Dokl. Akad. Nauk SSSR 256, 856 (1981) [Sov. Phys. Dokl. 26, 115 (1981)].
A. M. Zamorzaev, É. I. Galyarskiĭ, and A. F. Palistrant, Color Symmetry: Its Generalizations and Applications (Shitiintsa, Kishinev, 1978) [in Russian].
A. M. Zamorzaev, Theory of Simple and Multiple Antisymmetry (Shtiintsa, Kishinev, 1976) [in Russian].
A. V. Shubnikov, Kristallografiya 10(6), 775 (1965) [Sov. Phys. Crystallogr. 10 (6), 655 (1965)].
A. V. Shubnikov, Symmetry and Antisymmetry of Finite Figures (USSR Academy of Sciences, Moscow, 1951) [in Russian].
A. M. Zamorzaev, Izv. Akad. Nauk Resp. Mold., Mat., No. 1, 75 (1994).
B. K. Vainshtein, Modern Crystallography, Vol. 1: Fundamentals of Crystals: Symmetry and Methods of Structural Crystallography (Nauka, Moscow, 1979; Springer, Berlin, 1994).
A. M. Zamorzaev, Extended Abstracts of the Candidate’s Dissertation in Mathematical Physics (Leningrad, 1953).
N. V. Belov, N. N. Neronova, and T. S. Kuntsevich, Tr. Inst. Kristallogr., Akad. Nauk SSSR, No. 11, 33 (1955).
V. A. Koptsik, Shubnikov Groups (Moscow State University, Moscow, 1966) [in Russian].
N. V. Belov and T. N. Tarkhova, Kristallografiya 1(1), 4 (1956) [Sov. Phys. Crystallogr. 1 (1), 5 (1956)].
A. V. Shubnikov and V. A. Koptsik, Symmetry in Science and Art (Nauka, Moscow, 1972; Plenum, New York, 1974).
A. M. Zamorzaev, Kristallografiya 14(2), 195 (1969) [Sov. Phys. Crystallogr. 14 (2), 155 (1969)].
V. A. Koptsik and Zh.-N. M. Kuzhukeev, Kristallografiya 17(4), 705 (1972) [Sov. Phys. Crystallogr. 17 (4), 622 (1972)].
A. F. Palistrant, Doctoral Dissertation in Mathematical Physics (Kishinev, 1981).
S. V. Jablan, Acta Crystallogr., Sect. A: Found. Crystallogr. 49, 127 (1993).
S. V. Jablan and A. F. Palistrant, Kristallografiya 38(2), 4 (1993) [Crystallogr. Rep. 38 (2), 137 (1993)].
S. V. Jablan, Filomat (University of Niś, Serbia and Montenegro) 11, 1 (1997).
A. A. Shenesheutskaya, Analele Ştiinţifice ale USM: Seria “Ştiinţe Fiziso-Matematise” (USM, Chişinău, 2005) [in Moldavian].
S. V. Jablan, Publ. Inst. Math., Nouvelle Serie (Belgrade) 40(54), 33 (1986).
L. Radovĭc and S. Jablan, in Abstracts of the International Seminar on Discrete Geometry, Chişinău, 2002, p. 77.
V. A. Koptsik and I. N. Kotsev, Soobshch. Ob’edin. Inst. Yad. Issled., Dubna, R4–8066 (1974).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.F. Palistrant, 2007, published in Kristallografiya, 2007, Vol. 52, No. 6, pp. 1085–1091.
Rights and permissions
About this article
Cite this article
Palistrant, A.F. Complete derivation of space groups of magnetic symmetry of crystals by numerical construction. Crystallogr. Rep. 52, 1048–1055 (2007). https://doi.org/10.1134/S1063774507060193
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1063774507060193