Recently non-collinear magnetic structures have attracted renewed attention due to the novel Hall effects that they display. In earlier work evidence for a non-collinear magnetic structure has been reported for the ferromagnetic Heusler compound Mn₂RhSn. Using sputtering techniques we have prepared high quality epitaxial thin films of Mn₂RhSn by high temperature growth on MgO (001) substrates. The films are tetragonally distorted with an easy magnetization axis along the c-axis. Moreover, we find evidence for an anomalous Hall effect whose magnitude increases strongly below the Curie temperature that is near room temperature. Consistent with theoretical calculations of the anomalous Hall conductivity that we have carried out by deriving the Berry curvature from the electronic structure of perfectly ordered Mn₂RhSn, the sign of the anomalous Hall conductivity is negative, although the measured value is considerably smaller than the calculated value. We attribute this difference to small deviations in stoichiometry and chemical ordering. We also find evidence for a topological Hall resistivity of about 50 nΩ cm, which is ∼5% of the anomalous Hall effect, for temperatures below 100 K. The topological Hall effect signifies the presence of a chiral magnetic structure that evolves from the non-collinear magnetic structure that Mn₂RhSn is known to exhibit
