Magnetic groups

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Abstract
A brief outline of conventional symmetry studies of crystalline solids using Bravais lattices, point groups and space groups is presented, leading up to the recent development by Shubnikov of the idea of antisymmetry and the subsequent derivation of the black and white Bravais lattices and of the black and white point groups and space groups. These groups are also called magnetic groups or Shubnikov groups. The results of neutron-diffraction experiments have made it clear that there are many crystals whose structures must be described by one of these Shubnikov groups rather than by one of the ordinary point groups or space groups. The relationship between a structure with the symmetry of one of the Shubnikov point groups and the magnetic properties, paramagnetism, diamagnetism, ferromagnetism, ferrimagnetism or anti-ferromagnetism, which it is able to exhibit is also considered.

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