  Using analytical formulas as well as a finite-difference scheme, we
investigate the magnetic field dependence of the energy spectra and magnetic
edge states of HgTe/CdTe-based quantum wells in the presence of perpendicular
magnetic fields and hard walls, for the band-structure parameters corresponding
to the normal and inverted regimes. Whereas one cannot find counterpropagating,
spin-polarized states in the normal regime, below the crossover point between
the uppermost (electron-like) valence and lowest (hole-like) conduction Landau
levels, one can still observe such states at finite magnetic fields in the
inverted regime, although these states are no longer protected by time-reversal
symmetry. Furthermore, the bulk magnetization and susceptibility in HgTe
quantum wells are studied, in particular their dependence on the magnetic
field, chemical potential, and carrier densities. We find that for fixed
chemical potentials as well as for fixed carrier densities, the magnetization
and magnetic susceptibility in both the normal and the inverted regimes exhibit
de Haas-van Alphen oscillations, whose amplitude decreases with increasing
temperature. Moreover, if the band structure is inverted, the ground-state
magnetization (and consequently also the ground-state susceptibility) is
discontinuous at the crossover point between the uppermost valence and lowest
conduction Landau levels. At finite temperatures and/or doping, this
discontinuity is canceled by the contribution from the electrons and holes and
the total magnetization and susceptibility are continuous. In the normal
regime, this discontinuity of the ground-state magnetization does not arise and
the magnetization is continuous for zero as well as finite temperatures.
