Spin circuit representation of spin pumping

Circuit theory has been tremendously successful in translating physical equations into circuit elements in organized form for further analysis and proposing creative designs for applications. With the advent of new materials and phenomena in the field of spintronics and nanomagnetics, it is imperative to construct the spin circuit representations for different materials and phenomena. Spin pumping is a phenomenon by which a pure spin current can be injected into the adjacent layers. If the adjacent layer is a material with a high spin orbit coupling, a considerable amount of charge voltage can be generated via inverse spin Hall effect, allowing spin detection. Here we develop the spin circuit representation of spin pumping. We then combine it with the spin circuit representation for the materials having spin Hall effect to show that it reproduces the standard results in literature. We further show how complex multilayers can be analyzed by simply writing a netlist.