  Properties of two ThCr2Si2-type materials are discussed within the context of
their established structural and magnetic symmetries. Both materials develop
collinear, G-type antiferromagnetic order above room temperature, and magnetic
ions occupy acentric sites in centrosymmetric structures. We refute a previous
conjecture that BaMn2As2 is an example of a magnetoelectric material with
hexadecapole order by exposing flaws in supporting arguments, principally, an
omission of discrete symmetries enforced by the symmetry of sites used by Mn
ions and, also, improper classifications of the primary and secondary
order-parameters. Implications for future experiments designed to improve our
understanding of BaMn2P2 and BaMn2As2 magnetoelectric properties, using neutron
and x-ray diffraction, are examined. Patterns of Bragg spots caused by
conventional magnetic dipoles and magnetoelectric (Dirac) multipoles are
predicted to be distinct, which raises the intriguing possibility of a unique
and comprehensive examination of the magnetoelectric state by diffraction. A
roto-inversion operation in Mn site symmetry is ultimately responsible for the
distinguishing features.
