Quantum Hall states under conditions of vanishing Zeeman energy

We report on magnetotransport measurements of a two-dimensional electron gas confined in a ${\text{Cd}}_{0.997}{\text{Mn}}_{0.003}\text{Te}$ quantum well structure under conditions of vanishing Zeeman energy. The electron Zeeman energy has been tuned via the $s\text{\ensuremath{-}}d$ 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 $N$.