- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Magnetic Groups and Their Corepresentations

C. J. BRADLEY and B. L. DAVIES

C. J. BRADLEY and B. L. DAVIES

  • Department of Metallurgy, University of Oxford, Oxford, England

PDF

Rev. Mod. Phys. 40, 359 – Published 1 April, 1968

DOI: https://doi.org/10.1103/RevModPhys.40.359

Abstract

A review is given of the theory of magnetic groups and of their unitary corepresentations. Particular application is made to magnetic space groups, this part of the work being set in the framework of little-group theory. The symmetry problems in physics which lead to magnetic groups are analyzed and various applications of the theory to such problems are pointed out. Finally a method is given for obtaining the Kronecker products of corepresentations of magnetic groups, and an example is presented in which the unitary subgroup of the magnetic group is the point group C2v.

View figure in article

References (54)

  1. A. V. Shubnikov, Symmetry and Antisymmetry of Finite Figures (U.S.S.R. Academy of Sciences, Moscow, 1951)
  2. A. M. Zamorzaev, Generalization of the Space groups: Dissertation, Leningard University (1953)
  3. N. V. Belov, N. N. Neronova, and T. S. Smirnova, Trudy, Akad. Nauk SSSR, Inst. Kristall., 11, 33 (1955)
  4. A. V. Shubnikov and N. V. Belov, Coloured Symmetry (Pergamon Press Ltd., London, 1964)
  5. B. A. Tavger and V. M. Zaitzev, Soviet Phys.—JETP 3, 430 (1956)
  6. G. Donnay, L. M. Corliss, J. D. H. Donnay, N. Elliott, and J. M. Hastings, Phys. Rev. 112, 1917 (1958)
  7. W. Opechowski and R. Guccione, in Magnetism, G. T. Rado and H. Suhl, Eds. (Academic Press Inc., New York, 1965), Vol. IIA
  8. R. R. Birss, Symmetry and Magnetism (North-Holland Publ. Co., Amsterdam, 1964) Rept. Progr. Phys. 26, 307 (1963)
  9. S. Bhagavantam, Crystal Symmetry and Physical Properties (Academic Press Inc., New York, 1966)
  10. E. P. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (Academic Press Inc., New York, 1959)
  11. N. V. Kudryavsteva and V. A. Chaldyshev, Izv. Vysshikh Uchebn. Zavendenii Fiz. 2, 104 (1962) ibid.3, 133 (1962) ibid.4, 98 (1962) ibid.2, 46 (1963) ibid.3, 3; (1965) ibid.3, 50; (1965) ibid.9, 93 (1966)
  12. J. O. Dimmock and R. G. Wheeler, The Mathematics of Physics and Chemistry (D. Van Nostrand Co. Inc., New York, 1964), Vol. 2, Chap. 12
  13. J. O. Dimmock and R. G. Wheeler, J. Phys. Chem. Solids 23, 729 (1962)
  14. J. O. Dimmock and R. G. Wheeler, Phys. Rev. 127, 391 (1962)
  15. J. O. Dimmock, J. Math. Phys. 4, 1307 (1963)
  16. G. F. Karavaev, N. V. Kudryavsteva, and V. A. Chaldyshev, Soviet Phys.—Solid State 4, 2540 (1963)
  17. L. D. Landau and E. M. Lifshitz, Statistical Physics (Gostekhizdat, Moscow, 1951 and Pergamon Press Ltd., Oxford, England, 1958)
  18. G. Ya. Lyubarskii, The Application of Group Theory in Physics (Pergamon Press Ltd., Oxford, England, 1960)
  19. J. O. Dimmock, Phys. Rev. 130, 1337 (1963)
  20. W. F. Brinkman and R. J. Elliott, J. Appl. Phys. 37, 1457 (1966) Proc. Roy. Soc. (London) A294, 343 (1966)
  21. C. J. Bradley, J. Math. Phys. 7, 1145 (1966)
  22. G. F. Koster, Solid State Physics 5, 173, (1957)
  23. A. P. Cracknell, Progr. Theoret. Phys. (Kyoto) 33, 812 (1965)
  24. C. J. Bradley and A. P. Cracknell, Progr. Theoret. Phys. (Kyoto) 36, 648 (1966)
  25. G. F. Karavaev, Soviet Phys.—Solid State 6, 2943 (1965)
  26. V. Bargmann, J. Math. Phys. 5, 862 (1964)
  27. V. L. Indenbom, Soviet Phys.—Cryst. 4, 578 (1959)
  28. M. Hammermesh, Group Theory (Addison-Wesley Publ. Co., Inc., Reading, Mass., 1962), pp. 63-67
  29. H. Kramers, Koninkl. Ned. Akad. Wetenschap. Proc. 33, 959 (1930)
  30. J. S. Lomont, Applications of Finite Groups (Academic Press Inc., New York, 1959), p. 149
  31. S. L. Altmann and A. P. Cracknell, Rev. Mod. Phys. 37, 19 (1965)
  32. A. P. Cracknell, Progr. Theoret. Phys. (Kyoto) 35, 196 (1966)
  33. W. H. Kleiner, Phys. Rev. 142, 318 (1966)
  34. F. G. Fumi, Phys. Rev. 83, 1274 (1951) ibid.86, 561 (1952) Acta Cryst. 5, 44 (1952) Nuovo Cimento 9, 739 (1952)
  35. R. Fieschi and F. G. Fumi, Nuovo Cimento, 10, 865 (1953)
  36. R. Fieschi, Physica 24, 972 (1957)
  37. V. L. Indenbom, Soviet Phys.—Cryst. 5, 493 (1960)
  38. A. J. Coleman, Report No. 102, Quantum Chemistry Group, Uppsala University, Uppsala, Sweden
  39. P. Rudra, J. Math. Phys. 6, 1273 (1965)
  40. N. V. Kudryavtseva, Soviet Phys.—Solid State 7, 803 (1965)
  41. M. V. Murthy, J. Math. Phys. 7, 853 (1966)
  42. L. M. Corliss and J. M. Hastings, American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill Book Co., New York, 1963)
  43. E. P. Rudel and R. D. Spence, Physica 26, 1174 (1960)
  44. F. Seitz, Ann. Math. 37, 17 (1936)
  45. O. V. Kovalyev, Irreducible Representations of the Space Groups (University of Kiev, 1961 Gordon and Breach Science Publishers, Inc., New York, 1965)
  46. L. P. Bouckaert, R. Smoluchowski, and E. Wigner, Phys. Rev. 50, 58, (1936)
  47. C. Herring, J. Franklin Inst. 233, 525 (1942)
  48. J. C. Slater, Quantum Theory of Molecules and Solids, (McGraw-Hill Book Co., New York, 1965), Vol. 2
  49. C. Herring, Phys. Rev. 52, 361 (1937)
  50. R. J. Elliott and R. Loudon, J. Phys. Chem. Solids 15, 146 (1960)
  51. M. Lax and J. Hopfield, Phys. Rev. 124, 115 (1961)
  52. M. Lax, Phys. Rev. 138, A793 (1965)
  53. J. L. Birman, Phys. Rev. 127, 1093 (1962)
  54. K. P. Belov, Magnetic Transitions (Consultants Bureau Enterprises Inc., New York, 1961)

Outline

Information

Rev. Mod. Phys. 40, 359– Published 1 April, 1968

    © 1968 American Physical Society

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation