What is Noncollinear Magnetism?

  • Peter Weinberger


The terms “collinear” and “noncollinear” refer originally to a geometrical concept. Nowadays they are frequently used to classify magnetism in a rather vague sense. In the present paper an attempt is made to classify collinear and noncollinear by means of transformation properties of classical vectors (Heisenberg-like models of magnetism), and spinors and bispinors as used within a nonrelativistic and a relativistic description of magnetism based on the (local) density functional approach.


Invariance Condition Transformation Property Translational Symmetry Spin Space Band Side 
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  1. L. Udvardi et al., J. Magn. Magn. Mater.,submitted for publication; C. Uiberacker, Diplomarbeit, Technical University of Vienna, 1996.Google Scholar
  2. 2.
    For all group theoretical notations and aspects see S. L. Altmann and P. Herzig, Point-Group Theory Tables ( Clarendon Press, Oxford, 1994 ).Google Scholar
  3. 3.
    See for example: L. Jansen and M. Boom, Theory of Finite Groups: Applications to Physics (North Holland, Amsterdam, 1967 ).Google Scholar
  4. 4.
    See also the detailed discussion in P. Weinberger, Philos. Mag. B 75, 509 (1997).Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Peter Weinberger
    • 1
  1. 1.Institut für Technische Elektrochemie and Center for Computational Materials ScienceTechnical University of ViennaViennaAustria

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