  The quantum anomalous Hall effect is a fundamental transport response of a
topologically non-trivial system in zero magnetic field. Its physical origin
relies on the intrinsically inverted electronic band structure and
ferromagnetism, and its most consequential manifestation is the
dissipation-free flow of chiral charge currents at the edges that can
potentially transform future quantum electronics. Here we report a previously
unknown Berry-curvature-driven anomalous Hall regime ('Q-window') at
above-Kelvin temperatures in the magnetic topological bulk crystals where
through growth Mn ions self-organize into a period-ordered
MnBi$_2$Te$_4$/Bi$_2$Te$_3$ superlattice. Robust ferromagnetism of the
MnBi$_2$Te$_4$ monolayers opens a large surface gap, and anomalous Hall
conductance reaches an $e^2/h$ quantization plateau when the Fermi level is
tuned into this gap within a Q-window in which the anomalous Hall conductance
from the bulk is to a high precision zero. The quantization in this new regime
is not obstructed by the bulk conduction channels and thus should be present in
a broad family of topological magnets.
