The inverse spin-Hall effect (ISHE) induced by the spin pumping has been investigated systematically in simple ferromagnetic/paramagnetic bilayer systems. The spin pumping driven by ferromagnetic resonance injects a spin current into the paramagnetic layer, which gives rise to an electromotive force transverse to the spin current using the ISHE in the paramagnetic layer. In a Ni81Fe19/Pt film, we found an electromotive force perpendicular to the applied magnetic field at the ferromagnetic resonance condition. The spectral shape of the electromotive force is well reproduced using a simple Lorentz function, indicating that the electromotive force is due to the ISHE induced by the spin pumping; extrinsic magnetogalvanic effects are eliminated in this measurement. The electromotive force varies systematically by changing the microwave power, magnetic-field angle, and film size, being consistent with the prediction based on the Landau–Lifshitz–Gilbert equation combined with the models of the ISHE and spin pumping. The electromotive force was observed also in a Pt/Y3Fe4GaO12 film, in which the metallic Ni81Fe19 layer is replaced by an insulating Y3Fe4GaO12 layer, supporting that the spin-pumping-induced ISHE is responsible for the observed electromotive force.

We derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis of an entropy-current analysis. The first and second laws of local thermodynamics constrain possible structures of the constitutive relations including a spin current and the antisymmetric part of the (canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations within the linear-mode analysis, we find spin-diffusion modes, indicating that spin density is damped out after a characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the energy-momentum tensor in the entropy-current analysis. This is a consequence of mutual convertibility between spin and orbital angular momentum.