A recent polarized neutron diffraction experiment on the $5d^2$ rhenium double perovskite ${\mathrm{Ba}}_2\mathrm{YRe}{\mathrm{O}}_6$ held at a low temperature uncovered weak magnetic diffraction peaks. Data analysis inferred a significantly reduced Re dipole moment, and long-range order compatible with an antiferromagnetic, noncollinear motif. To interpret the experimental findings, we present a model wave function for Re ions derived from the crystal field potential, Coulomb interaction, and spin-orbit coupling that fully respects the symmetry of the low-temperature ordered state. It is used to calculate in analytic form all multipole moments visible in neutron and resonance enhanced x-ray diffraction. A minimal model consistent with available neutron diffraction data predicts significant multipolar moments up to the hexadecapole and, in particular, a dominant chargelike quadrupole moment. Calculated diffraction patterns embrace single crystal x-ray diffraction at the Re $L$ edge, and renewed neutron diffraction, to probe the presumed underlying multipolar order.

• Received 7 December 2020
• Accepted 8 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.104429