Faraday spectroscopy in diluted-magnetic-semiconductor superlattices

We investigate the wavelength and magnetic-field dependence of the Faraday rotation in ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Mn}}_{\mathit{x}}$Te/CdTe superlattices in order to probe the strength of the spin-exchange interaction between the excited carriers and the ${\mathrm{Mn}}^{2+}$ ions in these systems. Using a modulation technique we are able to optically record changes of the density of aligned ${\mathrm{Mn}}^{2+}$ spin states 〈${\mathit{S}}_{\mathit{z}}$〉 in the order of 〈${\mathit{S}}_{\mathit{z}}$〉/${\mathit{S}}_{\mathrm{sat}}$=6×${10}^{\mathrm{-}5}$, where ${\mathit{S}}_{\mathrm{sat}}$ is the saturation density. We observe a steplike behavior at the absorption edge reflecting the density of states and a strong excitonic resonance, which is difficult to resolve by conventional spectroscopic methods like photoluminescence excitation or transmission spectroscopy. With decreasing barrier width ${\mathit{L}}_{\mathit{B}}$ we observe below ${\mathit{L}}_{\mathit{B}}$=4 nm a decrease of the strength of the spin-exchange interaction indicating the effects of reduced dimensionality.