Temperature dependence of resonant x-ray magnetic scattering in holmium

We report the results of resonant x-ray magnetic scattering experiments on bulk and thin-film single crystals of holmium. The scattering at the principal magnetic reflection has been characterized as a function of the temperature in the spiral phases near and below their respective Néel temperatures. The integrated intensity of the principal magnetic peak in both samples shows power-law behavior versus reduced temperature with nearly equal exponents. The exponents for the scattering at the resonant second and third harmonics in the bulk sample are not simple integer multiples of the first, and motivate the consideration of simple scaling corrections to mean-field theory. We also present and compare the results of high-resolution measurements of the temperature dependence of the magnetic wave vectors, c-axis lattice constants, and correlation lengths of the magnetic scattering of the two samples in their spiral phases. Although the qualitative behavior is similar, systematic differences are found, including uniformly larger magnetic wave vectors and the suppression of the 1/6 phase in the film. The spiral magnetic structure of the film forms a domain state at all temperatures in the ordered phase. The magnetic correlation lengths of both samples are greatest near the Néel temperature, where that of the film appears to exceed the translational correlation lengths of the lattice. As the temperature decreases, the magnetic correlation lengths also decrease. These results are discussed in terms of the strain present in the samples.