  In a magnetic multilayer, the spin transfer between localized magnetization
dynamics and itinerant conduction spin arises from the interaction between a
normal metal and an adjacent ferromagnetic layer. The spin-mixing conductance
then governs the spin-transfer torques and spin pumping at the magnetic
interface. Theoretical description of spin-mixing conductance at the magnetic
interface often employs a single conduction-band model. However, there is
orbital hybridization between conduction $s$ electron and localized $d$
electron of the heavy transition metal, in which the single conduction-band
model is insufficient to describe the $s$-$d$ orbital hybridization. In this
work, using the generalized Anderson model, we estimate the spin-mixing
conductance that arises from the $s$-$d$ orbital hybridization. We find that
the orbital hybridization increases the magnitude of the spin-mixing
conductance.
