Topological Magneto-Optical Switching in Even-Layered MnBi$_2$Te$_4$

Abstract

MnBi$_2$Te$_4$ (MBT) thin films provide a unique material platform in which magnetism, topology, and magneto-optical (MO) response can be tuned through layer-thickness and relative spin alignments. In this work, using a low-energy coupled Dirac cone model together with Wannier-based tight-binding Hamiltonian derived from \textit{ab-initio} calculations, we investigate topological MO switching in even-layered MBT films. We argue that the relative spin alignment of the outermost septuple-layers (SL) mainly controls the total Chern number, optical conductibility, and consequently, the MO response. For a 6-SL MBT thin film, we found that reversing the outermost-SL alignments from antiparallel to parallel switches the system from axion insulating state with $C=0$ and vanishing Faraday rotation to a Chern insulating state with $C=1$ and a quantized MO response, irrespective of $PT$-symmetry and net magnetization. Increasing thickness reveals an additional regime: while 8-SL MBT hosts only $C=0$ and $1$ states, a 12-SL MBT film supports a higher Chern number phase with $C=2$ with a doubled low-frequency Faraday rotation. Our results provide a thickness-dependent route to multilevel MO switching and establish MO spectroscopy as a direct probe of surface magnetism and topological order in MBT thin films.