In-plane magnetic field induced double fan spin structure with $\textit{c}$-axis component in metallic kagome antiferromagnet YMn$_{6}$Sn$_{6}$

The geometrical frustration nature of the kagome lattice makes it a great host to flat electronic band, non-trivial topological properties, and novel magnetisms. Metallic kagome antiferromagnet YMn$_{6}$Sn$_{6}$ exhibits the topological Hall effect (THE) when an in-plane magnetic field is applied. THE is typically associated with the nanometer-sized non-coplanar spin structure of skyrmions in non-centrosymmetric magnets with large Dzyaloshinskii-Moriya interaction. Here we use single crystal neutron diffraction to determine the field/temperature dependence of the magnetic structure in YMn$_{6}$Sn$_{6}$. We find that the observed THE cannot arise from a magnetic skyrmion lattice, but instead from an in-plane field-induced double fan spin structure with $\textit{c}$-axis components (DFC). Our work provides the experimental basis from which a microscopic theory can be established to understand the observed THE.