Fig. 2: First-principles results.
a Spin Hall conductivity \({\sigma }_{{{{{\rm{SH}}}}}}^{{{{{\rm{NM}}}}}}\) and orbital Hall conductivity \({\sigma }_{{{{{\rm{OH}}}}}}^{{{{{\rm{NM}}}}}}\) of Pt and β-Ta. b Orbital-to-spin conversion efficiency \({C}_{{FM}}\) of Fe, CoFe, Co, and Ni. c \({\sigma }_{{{{{\rm{SH}}}}}}^{{{{{\rm{NM}}}}}}+{C}_{{{{{\rm{FM}}}}}}{\sigma }_{{{{{\rm{OH}}}}}}^{{{{{\rm{NM}}}}}}\) of FM/Pt bilayers (FM = Fe, Co, CoFe, and Ni). d \({\sigma }_{{{{{\rm{SH}}}}}}^{{{{{\rm{NM}}}}}}+{C}_{{{{{\rm{FM}}}}}}{\sigma }_{{{{{\rm{OH}}}}}}^{{{{{\rm{NM}}}}}}\) of FM/Ta bilayers (FM = Fe, Co, CoFe, and Ni). In (b), the value of \({C}_{{{{{\rm{FM}}}}}}\) depends on the ratio \({T}_{L}/{T}_{S}\), where the spin (orbital) transparency \({T}_{S}\) (\({T}_{L}\)) denotes the likelihood of spin (orbital) Hall current gets transmitted through the FM/NM interface. The ratio \({T}_{L}/{T}_{S}\) is assumed to be 0.3 in (b), considering that the orbital relaxation is expected to be faster than the spin relaxation.
