Fractional quantum Hall effect in a dilute magnetic semiconductor

We report the observation of the fractional quantum Hall effect in the lowest Landau level of a two-dimensional electron system (2DES), residing in the diluted magnetic semiconductor ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$. The presence of magnetic impurities results in a giant Zeeman splitting leading to an unusual ordering of composite fermion Landau levels. In experiment, this results in an unconventional opening and closing of fractional gaps around the filling factor $\ensuremath{\nu}=3/2$ as a function of an in-plane magnetic field, i.e., of the Zeeman energy. By including the s-d exchange energy into the composite Landau level spectrum the opening and closing of the gap at filling factor $5/3$ can be modeled quantitatively. The widely tunable spin-splitting in a diluted magnetic 2DES provides a means to manipulate fractional states.