Group theory study of the vibrational modes and magnetic order in the topological antiferromagnet MnBi_2Te_4

摘要

We employ group theory to study the properties of the lattice vibrations and magnetic order in the antiferro-magnetic topological insulator MnBi_2Te_4, both in bulk and few-layer form. In the paramagnetic phase, we obtain the degeneracies, the selection rules, and real-space displacements for the lattice vibrational modes for different stacking configurations. We discuss how magnetism influences these results. As a representative example, we consider a double septuple layer system and obtain the form of the magnetic order allowed by the symmetries of the crystal. We derive the allowed coupling terms that describe the paramagnetic to antiferromagnetic transition. Finally, we discuss the implications of our results for Raman scattering and other optical measurements. Our work sets the stage for a deeper understanding of the interplay of lattice modes, band topology, and magnetic order in MnBi_2Te_4 and other symmetry-related materials.