  Structural and magnetic transitions in a double perovskite hosting 5d1 Re
ions are discussed on the basis of recently published high-resolution x-ray
diffraction patterns [D. Hirai, et al., Phys. Rev. Res. 2, 022063(R) (2020)]. A
reported structural transition below room temperature, from cubic to tetragonal
symmetry, appears not to be driven by T2g-type quadrupoles, as suggested. A
magnetic motif at lower temperature is shown to be composed of two order
parameters, associated with propagation vectors k = (0, 0, 1) and k = (0, 0,
0). Findings from our studies, for structural and magnetic properties of
Ba2MgReO6, surface in predicted amplitudes for x-ray diffraction at rhenium L2
and L3 absorption edges, and magnetic neutron Bragg diffraction. Specifically,
entanglement of anapole and spatial degrees of freedom creates a quadrupole in
the neutron scattering amplitude. It would be excluded in an unexpected
scenario whereby the rhenium atomic state is a manifold. Also, a chiral
signature visible in resonant x-ray diffraction will be one consequence of
predicted electronic quadrupole and magnetic dipole orders. A model Re wave
function consistent with all current knowledge is a guide to electronic and
magnetic multipoles engaged in x-ray and neutron diffraction investigations.
