  Spin current plays a central role in spintronics. In particular, finding more
efficient ways to generate spin current has been an important issue and studied
actively. For example, representative methods of spin current generation
include spin polarized current injections from ferromagnetic metals, spin Hall
effect, and spin battery. Here we theoretically propose a new mechanism of spin
current generation based on nonlinear phenomena. By using Boltzmann transport
theory, we show that a simple application of the electric field $\bf{E}$
induces spin current proportional to $\bf{E^2}$ in noncentrosymmetric
spin-orbit coupled systems. We demonstrate that the nonlinear spin current of
the proposed mechanism is supported in the surface state of three-dimensional
topological insulators and two-dimensional semiconductors with the Rashba
and/or Dresselhaus interaction. In the latter case, the angular dependence of
the nonlinear spin current can be manipulated by the direction of the electric
field and by the ratio of the Rashba and Dresselhaus interactions. We find that
the magnitude of the spin current largely exceeds those in the previous methods
for a reasonable magnitude of the electric field. Furthermore, we show that
application of AC electric fields (e.g. terahertz light) leads to the
rectifying effect of the spin current where DC spin current is generated. These
findings will pave a new route to manipulate the spin current in
noncentrosymmetric crystals.
