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We calculate spin Hall conductivities in the two dimensional electron systemswith Rashba spin-orbit interaction. The salient feature is that, apart from theusual spin-Hall conductivity \sigma^z_{xy} which corresponds to the inductionof out-of-plane spin-current due to the application of transverse chargecurrent, there is a novel spin-Hall conductivity \sigma^\perp_{xy} which arisesdue to the induction of transverse spin-polarized current in the transversedirection by the application of in-plane spin-polarized current. Thisphenomenon which we call as `spin-spin' Hall effect is a spin analog ofconventional Hall effect, but with no magnetic field. This contribution may beunderstood through the spin-diffusive equation.Comment: 9 pages; converted into a detailed paper; accepted in J. Phys.:  Condensed Matte

‘Spin–spin’ Hall effect in two dimensional electron systems with spin–orbit interaction