Negative orbital Hall effect in germanium

Our investigation reveals a groundbreaking discovery of a negative inverse orbital Hall effect (IOHE) in $\mathrm{Ge}$ thin films. We employed the spin pumping technique where the spin-orbital coupled current is injected into $\mathrm{Ge}$ films using $\mathrm{YIG}/\mathrm{Pt}(2)/\mathrm{Ge}({t}_{\mathrm{Ge}})$ and $\mathrm{YIG}/\mathrm{W}(2)/\mathrm{Ge}({t}_{\mathrm{Ge}})$ heterostructures. Through comprehensive analysis, we observe significant reductions in the signals generated by coherent (rf-driven) and incoherent (thermal-driven) spin-orbital pumping techniques. These reductions are attributed to the presence of a remarkably strong negative IOHE in $\mathrm{Ge}$, showing its magnitude comparable with the spin-to-charge signal in $\mathrm{Pt}$. Our findings reveal that, although the spin-to-charge conversion in $\mathrm{Ge}$ is negligible, the orbital-to-charge conversion exhibits a large magnitude. Our results are innovative and pioneering in the investigation of negative IOHE by the injection of spin-orbital currents.