The charge and spin currents for Spinor Boltzmann equation beyond gradient approximation

Based on Spinor Boltzmann equation beyond gradient approximation, we establish the continuity equations satisfied by the charge current and spin current, a generalized spin transfer torque is given when the potential in the system change rapidly. The numerical results for charge density, charge current, spin accumulation, spin current and spin transfer torque are illustrated by a system with periodic potential, they are obviously influenced by the rapid potential, whatever external electric field applied on the system or magnetization therein, where the gradient approximation fails.