Interplay between structure and magnetism in HoxPr1-x alloys.: II.: Resonant x-ray magnetic scattering

X-ray-scattering techniques have been used to study the crystal and magnetic structures of HoxPr1-x alloys in the form of thin films. Three distinct crystal structures are found as a function of concentration x, each of which has a characteristic magnetic structure. For x greater than or equal to 0.6 a hexagonal-close-packed phase is found with the magnetic moments ordered in a basal-plane helix, whereas for 0.4 less than or equal to x<0.6 the lattice adopts the crystal structure of bulk Sm with the moments forming a six-layer c-axis antiferromagnet. At Ho concentrations x <0.4 the alloys are double hexagonal-close-packed and remain nonmagnetic down to the lowest temperatures studied. Using x-ray magnetic resonance scattering techniques, we demonstrate that a small, static spin-density wave is induced within the alloy 5d band at both the Pr and Ho sites in both of the magnetically ordered phases. The interpretation of the data is, however, complicated by the fact that the intensity branching ratio L-III/L-II differs from order unity for both Ho and Pr, in contrast to what is predicted from the simplest models of the resonance process. This suggests that an improved treatment of the full exchange interaction between the 5d and 4f moments, such as recently proposed by van Veenendaal, Goedkoop, and Thole [Phys. Rev. Lett. 78, 1162 (1997)], may be needed before quantitative estimates of the magnitudes of the induced 5d moments can be obtained. The temperature dependences of the lattice and magnetic structures, including the lattice constants, magnetic wave vectors, magnetic order parameters, and c-axis coherence lengths, are also characterized.