  Quantum wells of HgTe doped with Mn display the quantum anomalous Hall effect
due to the magnetic moments of the Mn ions. In the presence of a magnetic
field, these magnetic moments induce an effective nonlinear Zeeman effect,
causing a nonmonotonic bending of the Landau levels. As a consequence, the
quantized (spin) Hall conductivity exhibits a reentrant behavior as one
increases the magnetic field. Here, we will discuss the appearance of different
types of reentrant behavior as a function of Mn concentration, well thickness,
and temperature, based on the qualitative form of the Landau-level spectrum in
an effective four-band model.
