The definition of the spin current: The angular spin current and its physical consequences

We find that in order to completely describe the spin transport, apart from spin current (or linear spin current), one has to introduce the angular spin current. The two spin currents respectively describe the translational and rotational motion (precession)of a spin. The definitions of these spin current densities are given and their physical properties are discussed. Both spin current densities appear naturally in the spin continuity equation. Moreover we predict that the angular spin current can also induce an electric field $\vec{E}$, and in particular $\vec{E}$ scales as $1/r^2$ at large distance $r$, whereas the $\vec{E}$ field generated from the linear spin current goes as $1/r^3$.