  Magneto-optical spectroscopy based on the transverse magneto-optical Kerr
effect (TMOKE) is a sensitive method for investigation of magnetically-ordered
media. However, in magnetic materials the optical transitions are usually
characterized by spectrally broad resonances with widths considerably exceeding
the Zeeman splitting in the magnetic field. Here we investigate experimentally
and theoretically the TMOKE in the vicinity of relatively narrow optical
resonances provided by confined quantum systems. For experimental demonstration
we use the exciton resonance in a (Cd,Mn)Te diluted magnetic semiconductor
quantum well, where the strong exchange interaction with magnetic ions enables
the giant Zeeman splitting of exciton spin states $\Delta$ in magnetic fields
of a few Tesla. In the weak coupling regime, when the splitting $\Delta$ is
smaller than the spectral broadening of the optical transitions $\Gamma$, the
TMOKE magnitude grows linearly with the increase of the Zeeman splitting and
its spectrum has an S-shape, which remains virtually unchanged in this range.
In the strong coupling regime ($\Delta>\Gamma$) the TMOKE magnitude saturates,
while its spectrum is strongly modified resulting in the appearance of two
separate peaks. The TMOKE is sensitive not only to the sample surface but can
be used to probe the confined electronic states in depth if the upper layer is
sufficiently transparent. Our results demonstrate that TMOKE of spectrally
narrow resonances serves as a versatile tool for probing the charge and spin
structure of electronic states in various confined quantum systems and can be
used for spin tomography in combination with the conventional polar Kerr
effect.
