Electric polarization due to spin-orbit coupling

The electric dipole of the electron due to spin-orbit coupling plays an essential role in spintronics theory. We have found that this dipole is directly related to the antisymmetric components of the spin current tensor. It not only induces the observable electromagnetic effects directly but also is related to the force and torque that the electron feels in the electric field, which provides the possibility to manipulate the spin by electrical means.