We report transport studies of Mn-doped Bi_{2}Te_{3} topological insulator (TI) films with an accurately controlled thickness grown by molecular beam epitaxy. We find that films thicker than five quintuple layers (QLs) exhibit the usual anomalous Hall effect for magnetic TIs. When the thickness is reduced to four QLs, 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 three QLs. 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.
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