Measurements of Landau-level crossings and extended states in magnetic two-dimensional electron gases

We present longitudinal and Hall magnetoresistance measurements of a ``magnetic'' two-dimensional electron gas formed in modulation-doped ${\mathrm{Zn}}_{1\ensuremath{-}x\ensuremath{-}y}{\mathrm{Cd}}_{x}{\mathrm{Mn}}_{y}\mathrm{Se}$ quantum wells. The electron spin splitting is temperature and magnetic field dependent, resulting in striking features as Landau levels of opposite spin cross near the Fermi level. Magnetization measurements on the same sample probe the total density of states and Fermi energy, allowing us to fit the transport data using a model involving extended states centered at each Landau level and two-channel conduction for spin-up and spin-down electrons. A mapping of the extended states over the whole quantum Hall effect regime shows no floating of extended states within experimental resolution as Landau levels cross near the Fermi level.