Crystallographic magnetic point groups

Magnetic crystals with a net magnetic moment belong to one of the point groups G which contain complementary operators, but for which 0 G. If G = H + QH, where H is a halving subgroup (invariant subgroup of index 2) of G, and Q C G but Q H, then 

Type Number Color Point group Magnetic moment 

Underlines in the International notation for G show which operators are complementary ones. Alternatively, these may be identified from the classes of G H by multiplying each operator by 0 G is the ordinary crystallographic point group from which G was constructed by eq. (14.1.2) H is given first in International notation and then in Schonflies notation, in square brackets. Subscript a denotes the unit vector along [1 1 0]. 

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CsA1(S04)2 I2H2O, cubic, point group Th=(2/m)3 f) type alumn Z=4 C.S. 3, C.S.4 V—0 axes displaced from the crystallographic axes 12 different magnetic complexes VOlHjO) ... 

Brandmiiller J, Illig D and Herzig P (1999) Symmetry and Physical Properties of Matter. Rank 1, 2, 3 and 4 property tensors for the irreducible representations of the classical and magnetic, crystallographic and non-crys-tallographic point groups. IVSLA Series, Vol. 2, Amsterdam lOS Press. 

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