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Enhancement of spin mixing conductance by $s$-$d$ orbital hybridization in heavy metals

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.