  We derive the spin continuity equation by using the Noether's theorem. A new
type of spin-tensor Hall current is found in the continuity equation. The
spin-tensor Hall current is originating from the coupling of the spin-tensor
and the momentum. The intrinsic spin Hall effect in the two-dimensional fermion
model with the spin-orbit coupling and spin-tensor-momentum coupling is
studied. The total spin Hall conductivity with the presence of the spin-tensor
Hall current is calculated. The numerical results indicate that the total spin
Hall conductivity is enhanced by the contribution of the spin-tensor-momentum
coupling. The spin-tensor-momentum coupling may increase the spin transport in
the intrinsic spin Hall effect.
