  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.
