  We report on magneto-transport measurements of a two-dimensional electron gas
confined in a Cd$_{0.997}$Mn$_{0.003}$Te quantum well structure under
conditions of vanishing Zeeman energy. The electron Zeeman energy has been
tuned via the $s-d$ exchange interaction in order to probe different quantum
Hall states associated with metallic and insulating phases. We have observed
that reducing Zeeman energy to zero does not necessary imply the disappearing
of quantum Hall states, i.e. a closing of the spin gap. The spin gap value
under vanishing Zeeman energy conditions is shown to be dependent on the
filling factor. Numerical simulations support a qualitative description of the
experimental data presented in terms of a crossing or an avoided-crossing of
spin split Landau levels with same orbital quantum number $N$.
