X-ray-diffraction studies of the magnetic state of thulium

X-ray diffraction has been applied to investigate the magnetic structure of thulium. Magnetic scattering was observed at the magnetic modulation wave vector q, and charge scattering at 2q and 4q. A high-resolution study of the temperature dependence of the modulation at 2q showed two regimes: one incommensurate and the other commensurate. An analysis of the charge scattering at 2q shows that the ordering transition is continuous or almost continuous. The magnetic states of thulium were also probed by a resonance study of the magnetic scattering at the fundamental wave vector. Near the ${\mathit{L}}_{\mathrm{III}}$ absorption edge, an enhancement of the magnetic scattering of approximately 50 was observed. The results of polarization analysis of the magnetic scattering agreed with simple one-electron multipole scattering.