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Magnetically doped topological insulators enable the quantum anomalous Halleffect (QAHE) which provides quantized edge states for lossless chargetransport applications. The edge states are hosted by a magnetic energy gap atthe Dirac point but all attempts to observe it directly have been unsuccessful.The gap size is considered crucial to overcoming the present limitations of theQAHE, which so far occurs only at temperatures one to two orders of magnitudebelow its principle limit set by the ferromagnetic Curie temperature $T_C$.Here, we use low temperature photoelectron spectroscopy to unambiguously revealthe magnetic gap of Mn-doped Bi$_2$Te$_3$ films, which is present only below$T_C$. Surprisingly, the gap turns out to be $\sim$90 meV wide, which not onlyexceeds $k_BT$ at room temperature but is also 5 times larger than predicted bydensity functional theory. By an exhaustive multiscale structurecharacterization we show that this enhancement is due to a remarkable structuremodification induced by Mn doping. Instead of a disordered impurity system, itforms an alternating sequence of septuple and quintuple layer blocks, where Mnis predominantly incorporated in the septuple layers. This self-organizedheterostructure substantially enhances the wave-function overlap and the sizeof the magnetic gap at the Dirac point, as recently predicted. Mn-dopedBi$_2$Se$_3$ forms a similar heterostructure, however, only a large,nonmagnetic gap is formed. We explain both differences based on the higherspin-orbit interaction in Bi$_2$Te$_3$ with the most important consequence of amagnetic anisotropy perpendicular to the films, whereas for Bi$_2$Se$_3$ thespin-orbit interaction it is too weak to overcome the dipole-dipoleinteraction. Our findings provide crucial insights for pushing the losslesstransport properties of topological insulators towards room-temperatureapplications.

Large magnetic gap at the Dirac point in a Mn-induced Bi$_2$Te$_3$ heterostructure