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

In the normal-metal-ferromagnetic-insulator bilayer (such as Pt/Y_{3}Fe_{5}O_{12}) and the normal-metal-ferromagnetic-metal-oxide trilayer (such as Pt/Co/AlO_{x}) where spin injection and ejection are achieved by the spin Hall effect in the normal metal, we propose a minimal model based on quantum tunneling of spins to explain the spin-transfer torque and spin pumping caused by the spin Hall effect. The ratio of their dampinglike to fieldlike component depends on the tunneling wave function that is strongly influenced by generic material properties such as interface s-d coupling, insulating gap, and layer thickness, yet the spin relaxation plays a minor role. The quantified result renders our minimal model an inexpensive tool for searching for appropriate materials.