Magneto-optical Response of 5-SL MnBi$_2$Te$_4$ in Spin-Flip States

Abstract

Magneto-optical effects like Kerr and Faraday rotations provide a direct probe of topological order in thin films of the magnetic topological insulator MnBi$_2$Te$_4$ (MBT). Motivated by recent experimental studies of spin-flip/flop transitions in MBT thin films, we investigate the interplay between interlayer spin configurations, topological order, and magneto-optical response in five septuple-layer (5-SL) MBT using first-principles calculations and a simplified coupled-Dirac-cone model. Our results reveal that, despite possessing a non-zero out-of-plane magnetization, 5-SL MBT thin films can be either ${\cal C}=+1$ topological insulators or ${\cal C}=0$ topologically trivial insulators depending on the relative spin orientations of the top and bottom SLs. We evaluate the Faraday and Kerr rotation angles using tight-binding models derived from \textit{ab-initio} calculations and by comparing our results with those of a simplified coupled Dirac-cone model clarify the macroscopic mechanisms underlying the magneto-optical response of spin-flip states. These theoretical findings highlight the tunability of topological and magneto-optical properties in MBT thin films and provide microscopic insight into the emergence of complex topological order in layered antiferromagnetic materials.