Intrinsic Second Order Spin Current

In recent years, nonlinear Hall effect has attracted great attention with three different terms contributed by Drude effect, Berry curvature dipole and Berry connection polarizability. In this work, we theoretically predict an intrinsic second order spin current induced by spin-dependent Berry curvature polarizability based on time-independent perturbation theory. And we show other two second order spin conductivities contributed by the group velocity and spin-dependent Berry curvature dipole. A two-dimensional Rashba-Dresselhaus spin-orbit coupled system is studied as an example, and the value of intrinsic spin conductivity exhibits a maximum at zero chemical potential μ and decreases rapidly with increasing μ; while the extrinsic contribution remains unchanged in the region of μ 0. Thus, the dependence of spin conductivity on chemical potential is expected to distinguish the extrinsic and intrinsic contributions experimentally. Our calculation provides a theoretical basis for understanding the nonlinear spin transport.