Search

Structural and magnetic transitions in a double perovskite hosting $5{d}^{1}$ Re ions are discussed in the context of recently published high-resolution x-ray diffraction patterns [D. Hirai et al., Phys. Rev. Res. 2, 022063(R) (2020)]. Our symmetry-inspired analysis of a reported structural transition below room temperature, from cubic to tetragonal symmetry, reveals order of a lone ${E}_{g}$-type charge quadrupole. A magnetic motif at lower temperature is shown to be composed of two order parameters, with propagation vectors $\mathbf{k}=(0,0,1)$ and $\mathbf{k}=(0,0,0)$, which imply a magnetic space group $Pn{n}^{\ensuremath{'}}{m}^{\ensuremath{'}}$ . A concomitant lowering of Re site symmetry adds a ${T}_{2g}$ type to permitted quadrupoles. Findings from our studies, for structural and magnetic properties of ${\mathrm{Ba}}_{2}{\mathrm{MgReO}}_{6}$, surface in predicted amplitudes for x-ray diffraction at rhenium ${L}_{2}$ and ${L}_{3}$ 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 adequately described by a single value of the total angular momentum. Quadrupoles in x-ray and neutron diffraction amplitudes possess different angular symmetries, since the former is purely electronic and the latter purely magnetic. A chiral signature visible in resonant x-ray diffraction will be one consequence of predicted chargelike 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.

Cubic double perovskites that host heavy ions with total angular momentum $J$ = 2 can exhibit a singular magnetic state epitomized by a lone octupole and bulk ferro-type magnetism. It exists in the Chen-Balents Hamiltonian with a quadrupole interaction and competing exchange forces between the ions. Our symmetry inspired analysis mirrors the Dzyaloshinskii-Man'ko theory of latent antiferromagnetic ordering, and a 3k collinear structure. Experimental tests for the singular state include neutron or resonant x-ray Bragg diffraction.

Properties of two $\mathrm{ThC}{\mathrm{r}}_{2}\mathrm{S}{\mathrm{i}}_{2}$-type materials are discussed within the context of their established structural and magnetic symmetries---the structure type accounts for more than 400 compounds of the $\mathrm{A}{\mathrm{B}}_{2}{\mathrm{X}}_{2}$ composition. Both materials develop collinear, G-type antiferromagnetic order above room temperature, and magnetic ions occupy acentric sites in centrosymmetric structures (magnetic crystal class ${4}^{\ensuremath{'}}/{m}^{\ensuremath{'}}{m}^{\ensuremath{'}}m$). We refute a previous conjecture that $\mathrm{BaM}{\mathrm{n}}_{2}\mathrm{A}{\mathrm{s}}_{2}$ is an example of a magnetoelectric material with hexadecapole order using Dirac (magnetoelectric) multipoles by exposing flaws in supporting arguments: principally, an omission of discrete symmetries enforced by the symmetry ($\overline{4}{m}^{\ensuremath{'}}{2}^{\ensuremath{'}}$) of sites used by Mn ions and, also, improper classifications of the primary and secondary order parameters. G-type antiferromagnetism using conventional magnetic dipoles provides the primary order parameter. Dirac quadrupoles are secondary, and possibly visible in Bragg diffraction patterns. Patterns caused by conventional magnetic dipoles and Dirac multipoles are predicted to be fundamentally different, which raises the intriguing possibility of a unique and comprehensive examination of the magnetoelectric state by diffraction; Dirac multipoles create Bragg spots with Miller index $l$ even (and $h+k$ even) while magnetic dipoles appear for $l$ odd (and $h+k$ odd). A rotoinversion operation ($\overline{4}$) in Mn site symmetry is the ultimate source of distinguishing features in multipole types.