Interband Faraday rotation in diluted magnetic semiconductors: ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te and ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te

Faraday rotation as a function of ${\mathrm{Mn}}^{2+}$ concentration (x), temperature, and magnetic field is measured in the zinc-blende diluted magnetic semiconductors ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te and ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te. The effects of the large exchange interaction between d electrons of ${\mathrm{Mn}}^{2+}$ and the ${\Gamma }_6$ conduction-band electrons as well as the ${\Gamma }_8$ valence-band electrons are strikingly manifested in the interband Faraday effect leading to very large rotations. For large x, the effects of ${\mathrm{Mn}}^{2+}$-${\mathrm{Mn}}^{2+}$ antiferromagnetic exchange interaction are observed in the temperature dependence of the Faraday rotation.