Theory of electric reactance emerging from spin Hall effect

The spin Hall effect in a heavy metal intercorrelates an AC electric current to the magnetization dynamics in an adjacent ferromagnet, which manifests as an electric reactance in the system's current–voltage response. We present a comprehensive theoretical analysis for this emergent reactance contribution in the frequency regime relevant to transport measurements up to a few GHz. Our analysis reveals that the reactance becomes inductor-like at low frequency below the ferromagnetic resonance. Crucially, we find that the sign of the reactance is directly governed by the spin transfer mechanism at the interface, which depends on the competition between its damping-like and field-like components parametrized by the spin mixing conductance. This characteristic behavior in the reactance offers a powerful transport observable in distinguishing the interfacial spin transfer processes in spintronic materials.