  Topological magnets are a new family of quantum materials providing great
potential to realize emergent phenomena, such as quantum anomalous Hall effect
and axion-insulator state. Here we present our discovery that stoichiometric
ferromagnet MnBi8Te13 with natural heterostructure MnBi2Te4-(Bi2Te3)3 is an
unprecedented half-magnetic topological insulator, with the magnetization
existing at the MnBi2Te4 surface but not at the opposite surface terminated by
triple Bi2Te3 layers. Our angle-resolved photoemission spectroscopy
measurements unveil a massive Dirac gap at the MnBi2Te4 surface, and gapless
Dirac cone on the other side. Remarkably, the Dirac gap (~28 meV) at MnBi2Te4
surface decreases monotonically with increasing temperature and closes right at
the Curie temperature, thereby representing the first smoking-gun spectroscopic
evidence of magnetization-induced topological surface gap among all known
magnetic topological materials. We further demonstrate theoretically that the
half-magnetic topological insulator is desirable to realize the half-quantized
surface anomalous Hall effect, which serves as a direct proof of the general
concept of axion electrodynamics in condensed matter systems.
