Group theory study of the vibrational modes and magnetic order in the topological antiferromagnet MnBi$_2$Te$_4$

TL;DR

This study uses group theory to analyze lattice vibrations and magnetic order in MnBi$_2$Te$_4$, revealing how magnetism affects vibrational modes and providing insights for optical measurements in this topological antiferromagnet.

Contribution

The paper provides a comprehensive group theory analysis of vibrational and magnetic properties in MnBi$_2$Te$_4$, including symmetry-allowed magnetic orders and their effects on lattice vibrations.

Findings

Determined vibrational mode degeneracies and selection rules in different stacking configurations.

Identified symmetry-allowed magnetic orders and coupling terms for phase transitions.

Discussed implications for Raman and optical measurements.

Abstract

We employ group theory to study the properties of the lattice vibrations and magnetic order in the antiferromagnetic topological insulator MnBi$_2$Te$_4$, 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$_2$Te$_4$ and other symmetry-related materials.