Negative orbital Hall effect in Germanium

Our investigation reveals a groundbreaking discovery of a negative inverse orbital Hall effect (IOHE) in Ge thin films. We employed the innovative orbital pumping technique where spin-orbital coupled current is injected into Ge films using YIG/Pt(2)/Ge($t_{Ge}$) and YIG/W(2)/Ge($t_{Ge}$) 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 remarkable strong negative IOHE in Ge, showing its magnitude comparable to the spin-to-charge signal in Pt. Our findings reveal that although the spin-to-charge conversion in Ge is negligible, the orbital-to-charge conversion exhibits large magnitude. Our results are innovative and pioneering in the investigation of negative IOHE by the injection of spin-orbital currents.