EuPdSn ₂ : magnetic structures in view of resonant X-ray Bragg diffraction

The magnetic properties of materials hosting Eu²⁺ (J = 7/2, 4f⁷) ions have attracted much attention in the science of strongly correlated electrons. In part because crystal electric field effects are impoverished for an S-state ion, as with Gd³⁺ intermetallics, and Eu²⁺ substitution in biological and optically active materials is resourceful. The magnetic structure of EuPdSn₂ is not wholly resolved. Ferromagnetic and antiferromagnetic structures coexist in powder neutron diffraction patterns, and compete in the ground state. Moreover, the specific heat as a function of temperature is enigmatic and indicative of J = 5/2. We present symmetry-informed analytic magnetic structure factors for single crystal resonant X-ray Bragg diffraction using Eu atomic resonances that reveal significant potential for the technique. Europium ions use Wyckoff positions that are not centres of inversion symmetry in magnetic space groups inferred from neutron diffraction. In consequence, axial and polar Eu multipoles are compulsory components of both magnetic neutron and resonant X-ray Bragg diffraction patterns. The proposed antiferromagnetic phase of EuPdSn₂ supports anapoles (magnetic polar dipoles) already observed in magnetic neutron diffraction patterns presented by Gd-doped SmAl₂, and several resonant X-ray diffraction patterns.