  In this letter, we propose the average spin Chern number (ASCN) as an
indicator of the topological significance of the spin degree of freedom within
insulating materials. Whenever this number is a non-zero even integer, it
distinguishes the material as a spin Chern insulator and the number is a
topological invariant. If this number is not zero, it indicates that the
material has non-trivial spin transport properties, and it lies close to the
value of the spin Hall conductivity (SHC) within the bandgap. For materials
where spin-orbit coupling (SOC) is small, the ASCN matches the SHC. When the
SOC cannot be neglected, both values are non-zero simultaneously. The ASCN is
therefore a good complement for the intrinsic contribution of the SHC, and
permits to detect topological information of the material which is not possible
alone from the value of the SHC.
