Spin Hall conductivity in insulators with nonconserved spin
We study the linear response of a spin current to a small electric field in a two-dimensional crystalline insulator with nonconserved spin. We adopt the spin current operator proposed in J. Shi et al. [Phys. Rev. Lett. 96, 076604 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.076604], which satisfies a continuity equation and fits the Onsager relations.