Direct observation of double-k lattice modulation in double-k magnetic structures. The case of CeAl2

Symmetry analysis is combined with x-ray scattering experiments to investigate the lattice modulation associated with the incommensurate magnetic structure in the case of a double- k structure. The expansion of the free energy shows that the components of the magnetic structure with propagation vectors k1 and k2 can couple via components of lattice modulations. It is shown that the classical diffraction peaks reflecting a 2k propagation vector, associated with magneto-elastic effects in single- k structures, will coexist with diffraction peaks with propagation vectors k1-k2 or k1+k2. The existence of these latter peaks can be considered as a signature of a double- k magnetic structure. In the case of the double- k modulated structure of CeAl2, group theory is applied directly to the study of the charge modulation. An x-ray scattering study of the 2k satellites shows that the lattice displacements of the two Ce sites of the structure are antiparallel to each other, and perpendicular to the direction of the magnetic modulation. We also confirm experimentally the existence of k1+k2 satellites.