Dirac multipoles in diffraction by the layered room-temperature antiferromagnets BaMn2P2 and BaMn2As2

Abstract

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.