Multiple unconventional Hall effects induced by noncoplanar spin textures in $\mathrm{SmM}{n}_{2}G{e}_2$

The search for materials exhibiting multiple topological transport properties such as large anomalous Hall effect (AHE) and robust topological Hall effect (THE) are crucial for novel nanospintronic devices. However, such multiple unconventional Hall responses materials are rare in nature. Here, we report the coexistence of a giant AHE and robust THE in single crystals of $\mathrm{SmM}{n}_{2}G{e}_2$ with a noncoplanar spin texture. A giant anomalous Hall conductivity of $1715{\Omega }^{-1}c{m}^{-1}$ is observed for $H\text{//}a$ and $I\text{//}b$ whereas a large THE is observed for $H\text{//}c$ and $I\text{//}b$. A scaling analysis suggests that the giant AHE in this compound has an overwhelmingly large extrinsic contribution due to the unconventional skew scattering induced by short-range conical spin clusters with scalar spin chirality. The large THE originates from the real-space magnetic skyrmionic bubbles which are observed using the Lorenz transmission electron microscopy. Additionally, a planar topological Hall effect (PTHE) is observed when the magnetic field and the current are coplanar. The PTHE is related to a noncoplanar spin texture with nonzero spin chirality. These observations of multiple topological transport responses contribute to a deeper understanding of the noncoplanar $\mathrm{SmM}{n}_{2}G{e}_2$ material and advance their application in spintronic devices.