Symmetry analysis of modulated solid systems by line group method

Line groups are proposed to describe the symmetry properties of systems with non-collinear magnetic structure. A general method is elaborated to obtain the irreducible representation of the symmetry groups of modulated crystals by using that of the line groups. As a demonstrative example, the stuctural phase transition leading to the modulated magnetic superstructure in MnAu2 type compounds is analyzed by the employment of the line group technique. It is shown that the Dzyaloshinskii invariant is the most general one according to the symmetry properties investigated.