  We consider a disordered topological insulator thin film placed on the top of
a ferromagnetic insulator with a perpendicular exchange field $M$ and subjected
to a perpendicular electric field. The presence of ferromagnetic insulator
causes that bottom surface states of the topological insulator thin film become
spin polarized and the electric field provides a potential difference $V$
between the two surface states, resulting in breaking of time-reversal and
inversion symmetry in the system. Using Kubo formalism and employing the first
Born approximation as well as the self-consistent Born approximation, we
calculate the spin Hall conductivity. We find that for small values of $V$, a
large spin conductivity can be generated through large values of $M$ away from
the charge neutrality point. But for large values of $V$, the spin conductivity
can be promoted even with small values of $M$ around the charge neutrality
point. The effect of vertex corrections and the stability of the obtained large
spin conductivity against disorders are also examined.
