  The presence of non-trivial magnetic topology can give rise to non-vanishing
scalar spin chirality and consequently a topological Hall or Nernst effect. In
turn, topological transport signals can serve as indicators for topological
spin structures. This is particularly important in thin films or nanopatterned
materials where the spin structure is not readily accessible. Conventionally,
the topological response is determined by combining magnetotransport data with
an independent magnetometry experiment. This approach is prone to introduce
measurement artifacts. In this study, we report the observation of large
topological Hall and Nernst effects in micropatterned thin films of
Mn$_{1.8}$PtSn below the spin reorientation temperature $T_\mathrm{SR} \approx
190$K. The magnitude of the topological Hall effect
$\rho_\mathrm{xy}^\mathrm{T} = 8$ n$\Omega$m is close to the value reported in
bulk Mn$_2$PtSn, and the topological Nernst effect $S_\mathrm{xy}^\mathrm{T} =
115$ nV K$^{-1}$ measured in the same microstructure has a similar magnitude as
reported for bulk MnGe ($S_\mathrm{xy}^\mathrm{T} \sim 150$ nV K$^{-1}$), the
only other material where a topological Nernst was reported. We use our data as
a model system to introduce a topological quantity, which allows to detect the
presence of topological transport effects without the need for independent
magnetometry data. Our approach thus enables the study of topological transport
also in nano-patterned materials without detrimental magnetization related
limitations.
