Templates for magnetic symmetry and altermagnetism in hexagonal MnTe
S W Lovesey, D. D. Khalyavin, G. van der Laan
Abstract
The symmetry of long-range magnetic order in manganese telluride (\ensuremath{\alpha}-MnTe) is unknown. Likewise, its standing as an altermagnet. To improve the situation, we present symmetry informed Bragg diffraction patterns based on a primary magnetic order parameter for antiferromagnetic alignment between Mn dipoles. It does not break translation symmetry in a centrosymmetric structure, in keeping with an accepted definition of altermagnetism. Four templates serve x-ray diffraction that benefits from signal enhancement using a Mn atomic resonance, and neutron scattering. Even rank multipoles in magnetic neutron diffraction reflect a core requirement of altermagnetism, since they are zero for strong spin-orbit coupling presented by the ${j}_{\mathrm{eff}}=1/2$ model of an iridate, say. Symmetry in the templates demands that nuclear and magnetic contributions possess the same phase, which enables standard neutron polarization analysis on Bragg spots with overlapping contributions. Identical symmetry demands a ${90}^{\ensuremath{\circ}}$ phase shift between magnetic (time-odd) and chargelike (time-even, Templeton-Templeton) contributions to x-ray scattering amplitudes, and circular polarization in the primary beam of x-rays is rotated. We illustrate stark differences between our four templates and those of a (PT)-symmetric antiferromagnet (CuMnAs).