Symmetry analysis of antiferroquadrupolar order and accompanying atomic displacements in CeB6

Application of symmetry analysis method to description of local tensors is presented in this paper. The method is based on the decomposition of full representation of the space group, calculated for a given wave vector k→, into its irreducible representations (IR). The final ordering pattern is built up as a linear combination of basis vectors (BV) of the irreducible representations. The conditions imposed on the final solution by the quadrupolar moment tensor requirements are analyzed in detail. Here the method is applied to quadrupolar moment ordering of Ce atoms in CeB6. All possible types of quadrupolar ordering are calculated, together with their resulting final symmetry groups. An additional symmetry analysis is also carried out to determine the possible patterns of atomic displacements of the neighboring B atoms, which are consistent with the symmetry imposed by the quadrupolar ordering.