  Understanding the air-stability of MnBi$_2$Te$_4$ thin films is crucial for
the development and long-term operation of electronic devices based around
magnetic topological insulators. In the present work, we study MnBi$_2$Te$_4$
thin films upon exposure to atmosphere using a combination of synchrotron-based
photoelectron spectroscopy, room temperature electrical transport and atomic
force microscopy to determine the oxidation process. After 2 days air exposure
a 2 nm thick oxide passivates the surface, corresponding to oxidation of only
the top two surface layers, with the underlying layers preserved. This
protective oxide layer results in samples that still exhibit metallic
conduction even after several days air exposure. Furthermore, the work function
decreases from 4.4 eV for pristine MnBi$_2$Te$_4$ to 4.0 eV after the formation
of the oxide, along with only a small shift in the core levels indicating
minimal doping as a result of air exposure. With the oxide confined to the top
surface layers, and the underlying layers preserved, it may be possible to
explore new avenues in how to handle, prepare and passivate future
MnBi$_2$Te$_4$ devices.
