  Magnetic tuning of the bound exciton states and corresponding giant Zeeman
splitting (GZS) between {\sigma}^{+} and {\sigma}^{-} excitonic transitions in
CdTe/Cd_{1-x}Mn_{x}Te quantum ring has been investigated in the Faraday
configuration for various concentrations of Mn^{2+} ions, using the variational
technique in the effective mass approximation. The sp-d exchange interaction
between the localized magnetic impurity ions and the delocalized charge
carriers has been accounted via mean-field theory with the inclusion of a
modified Brillouin function. The enhancement of the GZS, and in turn, the
effective g-factor with the application of an external magnetic field, is
strikingly manifested in type-I - type-II transition in the band structure,
which has been well explained by computing the overlap integral between the
electron and hole, and the in-plane exciton radius. This highlights the
extraordinary magneto-optical properties, including the giant Faraday rotation
and associated Verdet constant, which have been calculated using single
oscillator model. The oscillator strength and exciton lifetime have been
estimated, and are found to be larger than in the bulk diluted magnetic
semiconductors (DMS) and quantum wells, reflecting stronger confinement inside
the quantum ring. The results show that the DMS-based quantum ring exhibits
more extensive Zeeman splitting, which gives rise to ultra-high Verdet constant
of 2.6 \times 10^{9}rad/Tesla/m, which are a few orders of magnitude larger
than in the existing quantum systems and magneto-optical materials.
