The contribution of spin torque to spin Hall coefficient and spin motive   force in spin-orbit coupling system
  We derive rigorously the relativistic angular momentum conservation equation by means of quantum electrodynamics. The novel nonrelativistic spin current and torque in the spin-orbit coupling system, up to the order of $1/c^{4}$, are exactly investigated by using Foldy-Wouthuysen transformation. We find a perfect spin Hall coefficient including the contribution of spin torque dipole. A novel spin motive force, analogue to the Lorentz force, is also obtained for understanding of the spin Hall effect. 
Yong-Ping Fu, Dong Wang, F. J. Huang, Y. D. Li, W. M. Liu
cond-mat.str-el