Phenomenological model for the direct and inverse Edelstein effects

We have developed a phenomenological model that connects the direct and 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. The other represents the strength of the hybridization between bulk and interface states. Both of them are important for efficient conversion through Edelstein effects. To test our model, we measured the inverse and direct Edelstein effects at the Bi2O3/Cu interface using the spin absorption method with a nonlocal spin valve structure and calculated the conversion coefficients. The effective spin Hall angle reaches similar to 0.09 in this system. This relatively large value of the spin Hall angle is attributable to the large spin-orbit coupling and the strong hybridization between the interface and bulk states at the Bi2O3/Cu interface.