Exciton fine structure and coherent spin precession in transition-metal-doped semiconductor quantum dots

The optical properties of quantum dots (QDs) containing a single magnetic impurity are studied within a multiband envelope function formalism. We present a unified treatment of different kinds of Mn-doped semiconductor QDs: spherical and ellipsoidal nanocrystals (NCs) and self-assembled quantum dots (SAQDs), focusing on their respective potentialities for optical detection and manipulation of the Mn spin state. The zero-field splitting of the exciton arising from the confinement-enhanced $sp\text{\ensuremath{-}}d$ and electron-hole exchange interactions is deduced. The optical absorption spectrum shows a strong dependence on the Mn spin orientation with respect to the polarization of light, promising for optical detection. The theoretical results are in accord with the reported optical and magneto-optical properties of Mn-doped ZnSe NCs and $\mathrm{Cd}\mathrm{Te}∕\mathrm{Zn}\mathrm{Te}$ SAQDs. Predictions for ellipsoidal wurtzite-structure CdSe NCs are also presented. Typically, NCs are smaller in size than SAQDs and show a correspondingly larger spin coupling and overall splitting. However, the splitting pattern is simpler in SAQDs, with fewer components, making for easier spin detection. The coherent precession of the Mn spin induced by a resonant circularly polarized laser pulse is also studied. A zero-field precession of substantial amplitude is obtained in nearly spherical NCs with strongly allowed hole-Mn spin flips. The amplitude is negligibly small in typical SAQDs, but the application of a transverse magnetic field (Voigt configuration) makes it measurable. Interestingly, in SAQDs containing a resident hole such as neutral GaAs:Mn or positively charged II-VI:Mn QDs, a significant zero-field spin precession of single frequency is predicted.