Noncollinear antiferromagnets with a D0$_{19}$ (space group = 194, P6$_{3}$/mmc) hexagonal structure have garnered much attention for their potential applications in topological spintronics. Here, we report the deposition of continuous epitaxial thin films of such a material, Mn$_{3}$Sn, and characterize their crystal structure using a combination of x-ray diffraction and transmission electron microscopy. Growth of Mn$_{3}$Sn films with both (0001) c-axis orientation and (40$bar{4}$3) texture is achieved. In the latter case, the thin films exhibit a small uncompensated Mn moment in the basal plane, quantified via magnetometry and x-ray magnetic circular dichroism experiments. This cannot account for the large anomalous Hall effect simultaneously observed in these films, even at room temperature, with magnitude $sigma_{mathrm{xy}}$ ($mu_{0}H$ = 0 T) = 21 $mathrm{Omega}^{-1}mathrm{cm}^{-1}$ and coercive field $mu_{0}H_{mathrm{C}}$ = 1.3 T. We attribute the origin of this anomalous Hall effect to momentum-space Berry curvature arising from the symmetry-breaking inverse triangular spin structure of Mn$_{3}$Sn. Upon cooling through the transition to a glassy ferromagnetic state at around 50 K, a peak in the Hall resistivity close to the coercive field indicates the onset of a topological Hall effect contribution, due to the emergence of a scalar spin chirality generating a real-space Berry phase. We demonstrate that the polarity of this topological Hall effect, and hence the chiral-nature of the noncoplanar magnetic structure driving it, can be controlled using different field cooling conditions.
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