Direct observation of double-k lattice modulation in double-k magnetic structures. The case ofCeAl2

Abstract

Symmetry analysis is combined with x-ray scattering experiments to investigate the latticemodulation 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 propagationvectors k1 and k2 can couple via components of lattice modulations. It is shown that the classical diffraction peaks reflectinga 2k propagation vector, associated with magneto-elastic effects in single-k structures, will coexist with diffraction peaks with propagation vectorsk1−k2 ork1+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 modulatedstructure of CeAl2, group theory is applied directly to the study of the charge modulation. An x-ray scattering study ofthe 2k satellites shows that the lattice displacements of the two Ce sites of thestructure are antiparallel to each other, and perpendicular to the direction ofthe magnetic modulation. We also confirm experimentally the existence ofk1+k2 satellites.