Polarization and resonance studies of x-ray magnetic scattering in holmium

We report the results of an x-ray-scattering study of the polarization and resonance properties of the magnetic cross section of holmium. Off resonance, we have measured the degree of linear polarization for several different chemical and magnetic reflections, and shown that the results are consistent with a nonresonant description of the x-ray-scattering cross section. When the incident x-ray energy is tuned near the ${\mathit{L}}_{\mathrm{III}}$ absorption edge, large resonant enhancements of the magnetic scattering, and resonant integer harmonics, are observed. Detailed measurements of the dependence of the integrated magnetic intensity on the incident x-ray energy, on the x-ray momentum transfer, and on the sample temperature are described for incident x-ray energies in a range of 250 eV below and above the ${\mathit{L}}_{\mathrm{III}}$ absorption edge. In addition, we have characterized the energy dependence of the linearly σ- and π-polarized components of the magnetic scattering in this range, and fitted the resulting line shapes to a simple model of the resonant cross section, including electric dipole and quadrupole transitions among atomic orbitals. The most striking feature of the line shapes is their asymmetry, which results from the interference of the resonant and nonresonant cross sections. Smaller resonant enhancements of the magnetic scattering are reported for incident x-ray energies tuned near the ${\mathit{L}}_{\mathrm{II}}$ and ${\mathit{L}}_{\mathrm{I}}$ absorption edges.