Exciton magnetic polaron in semimagnetic semiconductor nanocrystals

We present a theoretical study of the magnetic polaron associated with an electron-hole pair in a diluted magnetic semiconductor quantum dot. It is based on the effective-mass approximation in the strong confinement regime, which incorporates the coupling between the light- and heavy-hole bands. The magnetic polaron, arising from the sp-d exchange interaction between the confined carriers and the magnetic ions, is treated in a self-consistent mean-field approach that leads to coupled nonlinear Schrodinger equations for the electron and the hole: The local response to the effective field is modeled by the experimental high-field magnetization curve in the bulk. The electron-hole Coulomb interaction is taken into account. An exact numerical solution of the three coupled equations is used to calculate the equilibrium polaron size, binding energy (E-p), and spin (S-p). Results are first presented for Cd1-xMnxTe nanocrystals with x = 0.11. E-p decreases and the orbital contraction increases with an increasing quantum dot radius (a). In small dots, approaching saturation in the core region, E-p decreases slowly as the temperature (T) increases. In large dots E-p(T) decreases rapidly towards the fluctuation regime, where E-p proportional to a(-3). A similar temperature dependence is obtained for S-p; the fluctuation-regime value is, however, size independent. The light-induced magnetization enhancement due to polaron formation is considered and an optimal quantum dot radius is predicted to be similar to 30 Angstrom. We have also calculated E-p as a function of an applied magnetic field, which shows a decreasing behavior that depends on a and T. Theoretical results for Cd1-xMnxSe nanocrystals show a good agreement with recently reported experimental data on the photoluminescence Stokes shift versus magnetic field.