  The interplay between band topology and magnetism can give rise to exotic
states of matter. For example, magnetically doped topological insulators can
realize a Chern insulator that exhibits quantized Hall resistance at zero
magnetic field. While prior works have focused on ferromagnetic systems, little
is known about band topology and its manipulation in antiferromagnets. Here, we
report that MnBi$_2$Te$_4$ is a rare platform for realizing a
canted-antiferromagnetic (cAFM) Chern insulator with electrical control. We
show that the Chern insulator state with Chern number $C = 1$ appears as soon
as the AFM to canted-AFM phase transition happens. The Chern insulator state is
further confirmed by observing the unusual transition of the $C = 1$ state in
the cAFM phase to the $C = 2$ orbital quantum Hall states in the magnetic field
induced ferromagnetic phase. Near the cAFM-AFM phase boundary, we show that the
Chern number can be toggled on and off by applying an electric field alone. We
attribute this switching effect to the electrical field tuning of the exchange
gap alignment between the top and bottom surfaces. Our work paves the way for
future studies on topological cAFM spintronics and facilitates the development
of proof-of-concept Chern insulator devices.
