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In the normal metal/ferromagnetic insulator bilayer (such asPt/Y$_{3}$Fe$_{5}$O$_{12}$) and the normal metal/ferromagnetic metal/oxidetrilayer (such as Pt/Co/AlO$_{x}$) where spin injection and ejection areachieved by the spin Hall effect in the normal metal, we propose a minimalmodel based on quantum tunneling of spins to explain the spin-transfer torqueand spin pumping caused by the spin Hall effect. The ratio of theirdamping-like to field-like component depends on the tunneling wave functionthat is strongly influenced by generic material properties such as interface$s-d$ coupling, insulating gap, and layer thickness, yet the spin relaxationplays a minor role. The quantified result renders our minimal model aninexpensive tool for searching for appropriate materials.

Minimal Model of Spin-Transfer Torque and Spin Pumping caused by Spin Hall Effect