On the symmetry of magnetic structures in terms of the fibre bundles

• Authors: Jerzy Warczewski , Paweł Gusin , Tamara Śliwińska , Grzegorz Urban , Józef Krok-Kowalski
• Languages of publication: EN

Abstracts

EN

The paper concerns the application of the fibre bundle approach to the description of the magnetic structures and their symmetry groups. Hence the explicit formulas describing both the variety of magnetic structures and their symmetry groups have been derived. The assumption was made that the bundle sections correspond to magnetizations of the separate crystal planes multiplied by a certain Gaussian factor defined in ℝ3, the last factor making the problem continuous and more physical.

Keywords

EN

fibre bundles; magnetic structures; symmetry groups

Discipline

• 75.10.-b: General theory and models of magnetic ordering(see also 05.50.+q Lattice theory and statistics)
• 75.10.Hk: Classical spin models

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2007
• Volume: 5
• Issue: 3
• Pages: 377-384

Dates

published

1 - 9 - 2007

online

13 - 5 - 2007

Contributors

author

Jerzy Warczewski

• Institute of Physics, University of Silesia, ul. Uniwersytecka 4, PL-40007, Katowice, Poland

author

Paweł Gusin

• Institute of Physics, University of Silesia, ul. Uniwersytecka 4, PL-40007, Katowice, Poland

author

Tamara Śliwińska

• Institute of Physics, University of Silesia, ul. Uniwersytecka 4, PL-40007, Katowice, Poland

author

Grzegorz Urban

• Institute of Physics, University of Silesia, ul. Uniwersytecka 4, PL-40007, Katowice, Poland

author

Józef Krok-Kowalski

• Institute of Physics, University of Silesia, ul. Uniwersytecka 4, PL-40007, Katowice, Poland

References

• [1] D.B. Litvin: “Spin Translation Groups and Neutron Diffraction Analysis”, Acta Crystallogr. A, Vol. 29, (1973), pp. 651–660. http://dx.doi.org/10.1107/S0567739473001658[Crossref]
• [2] D.B. Litvin and W. Opechowski: “Spin Groups”, Physica, Vol. 76, (1974), pp. 538–554. http://dx.doi.org/10.1016/0031-8914(74)90157-8[Crossref]
• [3] D.B. Litvin: “Spin Point Groups”, Acta Crystallogr. A, Vol. 33, (1977), pp. 279–287. http://dx.doi.org/10.1107/S0567739477000709[Crossref]
• [4] V.A. Koptsik and I.N. Kotzev: “K teorii i klassifikatsii grupp tsvetnoj simmetrii I. P-simmetriya” (“On the Theory and Classification of Color Symmetry Groups. I. Psymmetry”) [In Russian], In: Communications of the Joint Inst. for Nuclear Research, Dubna, 1974, pp. 4–8067.
• [5] V.A. Koptsik: “Advances in theoretical crystallography. Color symmetry of defect crystals”, Krist. Tech., Vol. 10, (1975), pp. 231–245. [Crossref]
• [6] V.A. Koptsik: “The theory of symmetry of space modulated crystal structures”, Ferroelectrics, Vol. 21, (1978), pp. 499–501.
• [7] R. Lifshitz: “Symmetry of Magnetic Ordered Quasicrystals”, Phys. Rev. Lett., Vol. 80, (1998), pp. 2717–2720. http://dx.doi.org/10.1103/PhysRevLett.80.2717[Crossref]
• [8] D.B. Litvin: “Wreath groups”, Physica, Vol. 101A, (1980), pp. 339–350. [Crossref]
• [9] D.B. Litvin: “Wreath products and the symmetry of incommensurate crystals”, Ann. Israel Phys. Soc., Vol. 3, (1980), pp. 371–374.
• [10] D. B. Litvin: “Wreath groups-symmetry of crystals with structural distortions”, Phys. Rev. B, Vol. 21, (1980), pp. 3184–3192. http://dx.doi.org/10.1103/PhysRevB.21.3184[Crossref]
• [11] R. Sulanke and P. Wintgen: Differentialgeometrie und Faserbündel, Deutscher Verlag der Wissenschaften, Berlin, 1972.
• [12] P. Gusin and J. Warczewski: “On the relations between magnetization and topological invariants of the physical system”, J. Magn. Magn. Mater., Vol. 281, (2004), pp. 178–187. http://dx.doi.org/10.1016/j.jmmm.2004.04.102[Crossref]

Identifiers

DOI

10.2478/s11534-007-0023-8