  We report transport studies of Mn-doped Bi2Te3 topological insulator (TI)
films with accurately controlled thickness grown by molecular beam epitaxy. We
find that films thicker than 5 quintuple-layer (QL) exhibit the usual anomalous
Hall effect for magnetic TIs. When the thickness is reduced to 4 QL, however,
characteristic features associated with the topological Hall effect (THE)
emerge. More surprisingly, the THE vanishes again when the film thickness is
further reduced to 3 QL. Theoretical calculations demonstrate that the coupling
between the top and bottom surface states at the dimensional crossover regime
stabilizes the magnetic skyrmion structure that is responsible for the THE.
