Symmetry and transport property of spin current induced spin-Hall effect

We study the spin current induced spin-Hall effect that a longitudinal spin-dependent chemical potential qV(s=x,y,z) induces transverse spin conductances G(ss'). A four-terminal system with the Rashba and Dresselhaus spin-orbit interactions (SOIs) in the scattering region is considered. By using Landauer-Buttiker formula with the aid of Green's function, various spin current induced spin-Hall conductances G(ss') are calculated. With the charge chemical potential qV(c) or spin chemical potential qV(s=x,y,z), there are 16 elements for the transverse conductances G(p)(mu nu)=J(p,mu)/V-nu, where mu,nu=x,y,z,c. Due to the symmetry of our system, these elements are not independent. For the system with C-2 symmetry half of the elements are zero when only the Rashba SOI or the Dresselhaus SOI exists in the center region. The numerical results show that of all the conductance elements, the spin current induced spin-Hall conductances G(ss') are usually much greater (about one or two orders of magnitude) than the spin-Hall conductances G(sc) and the reciprocal spin-Hall conductances G(cs). So the spin current induced spin-Hall effect dominates in the present device.