Phenomenological model for the direct and inverse Edelstein effects

We have developed a phenomenological model that connects the direct and the inverse Edelstein effects. Our model implies a trade-off relation between the conversion coefficients for the direct and inverse effects. Thus, a large conversion coefficient for the inverse effect does not necessarily bring a large conversion coefficient for the direct effect. Instead of these coefficients, we propose a figure of merit of Edelstein effects which consists of two factors; one of them represents the magnitude of the spin-orbit coupling, and the other represents the strength of the hybridization between bulk and interface states. Both of them are quit important for the efficient conversion through Edelstein effects. To test our model, we measured the inverse and direct Edelstein effects at the Bi2O3/Cu interface using spin absorption method with a non-local spin valve structure and calculated the conversion coefficients. The effective spin Hall angle reaches ~0.09 in this system. This relatively large value is attributable to not only the large spin-orbit coupling but also the strong hybridization between the interface and bulk states at the Bi2O3/Cu interface.