Coulomb enhancement of Faraday rotation in semimagnetic semiconductors

We investigate the influence of the excitonic Coulomb interaction on the linear Faraday rotation in the ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ system. Experimental results for two samples ($x=\frac{0.053}{0.097}$) at different temperatures (5 and 77 K) and magnetic fields up to 2 T are presented. They are modeled qualitatively and quantitatively in a microscopic model by calculating the complex dielectric function. The anisotropy and $k$ dependence of the magnetic spin-exchange interaction and the Coulomb interaction between optically excited bound and unbound electron-hole pairs are considered.