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

Quantum Hall states under conditions of vanishing Zeeman energy