Quantized Magneto-Terahertz Effects in the Antiferromagnetic Topological Insulator MnBi$_2$Te$_4$ Thin Films

MnBi$_2$Te$_4$ (MBT) is an ideal platform for studying the interplay between magnetism and topology. Many exotic topological phenomena, such as the quantum anomalous Hall effect and the axion insulator, have been observed in few-layer MBT. A key feature in MBT is the emergence of the surface exchange gap, which lies in the milli-electron-volt range (1 THz corresponds to 4.14 meV). This makes THz spectroscopy a powerful tool to probe the associated topological physics. In this study, we report the THz spectra of Faraday and Kerr rotations in MBT thin films grown by molecular beam epitaxy. By varying the external magnetic field, we observe three magnetic states: the antiferromagnetic state, the canted antiferromagnetic state, and the ferromagnetic state. Our terahertz results show a quantized Hall state under 6 T in both 6 SL and 7 SL samples without gate voltage. These findings provide new insights into the magneto-terahertz properties of MBT and its potential for topological spintronic applications.