Confinement-induced reduction of the effective exchange parameters in semimagnetic semiconductor nanostructures

We present a theoretical study of the effect of reduced dimensionality on the Zeeman splittings of the electron and hole states. It is based on the effective mass approximation for the confined states and the wave vector dependence of the sp-d exchange interaction parameters in the bulk semimagnetic semiconductor. We find that the ratio of the exciton Zeeman splitting to the magnetization in a nanostructure is reduced with respect to the bulk by a factor rho that depends on the degree of confinement. The effect is relatively small (a few percent) in quantum wells, but rho as a function of the well width shows a minimum, in qualitative agreement with experimental data in Cd1-xMnxTe/Cd1-x-yMnxMgyTe heterostructures. In small-size quantum dots of Cd1-xMnxTe the predicted reduction is drastic: rho approximate to 0.5 for the dot radius R = 10 Angstrom; it increases rapidly with R and then saturates to about 0.84. We account for the available magnetoabsorption data in the wurtzite-structure nanocrystals of Cd1-xMnxSe, where uniaxial anisotropy also contributes to a reduction of the average Zeeman splitting. [S0163-1829(98)03547-4].