Effect of the reduction of dimensionality on the exchange parameters in semimagnetic semiconductors

We present experimental results showing a variation of the exchange parameters between carrier spins and Mn spins as a function of quantum-well width in semimagnetic heterostructures. Relative changes of the exchange parameters of about 0.1 are observed by analyzing the Zeeman splittings of the free-exciton states in epitaxially grown ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}/{\mathrm{Cd}}_{1-x-y}{\mathrm{Mn}}_x{\mathrm{Mg}}_y\mathrm{Te}$ quantum wells with no discontinuity of the Mn content at the interfaces. We attribute the well-width dependence of the Zeeman splittings to a k-vector dependence of the exchange parameters.