  We delve into spin Hall effect in generic spin-orbit coupled two-dimensional
fermionic systems. We derive analytically the spin-orbit force responsible for
the spin Hall effect, and find that it has `Lorentz force'-like form. We also
derive the pseudo magnetic field responsible for this force. We establish the
relation between the spin Hall conductivity, flux quanta and this pseudo
magnetic field, similar to the one between charge Hall conductivity, flux
quanta and the external field. We also present an exact closed-form expression
of the spin Hall conductivity in a generic spin-orbit coupled system. Depending
on the dimensionality of the spin-orbit interactions, the spin Hall
conductivity depends on different combinations of Rashba parameter and fermion
density.
