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Spin Hall effect in van der Waals ferromagnet Fe$_{5}$GeTe$_{2}$

We investigate the spin Hall effect (SHE) in a van der Waals (vdW) ferromagnet Fe$_{5}$GeTe$_{2}$ (FGT) with a Curie temperature $T_{\rm C}$ of 310 K utilizing the spin-torque ferromagnetic resonance method. In synchronization with the emergence of the ferromagnetic phase resulting in the anomalous Hall effect (AHE), a noticeable enhancement in the SHE was observed below $T_{\rm C}$. On the other hand, the SHE shows a different temperature dependence from the AHE: the effective spin Hall conductivity is clearly enhanced with decreasing temperature unlike the anomalous Hall conductivity, reflecting the variation of band-structure accompanied by the complicated magnetic ordering of the FGT. The results provide a deep understanding of the SHE in magnetic materials to open a new route for novel functionalities in vdW materials-based spintronic devices.