Optical orientation of a single Mn spin in a quantum dot: Role of carrier spin relaxation

In order to explain the recently observed phenomenon of optical orientation of a single Mn spin residing inside a CdTe quantum dot, a process of Mn spin relaxation with characteristic time scale of tens of nanosecond had been invoked. We show that after taking into account the mixing of states of the exciton and the Mn spin (due to the $sp\text{−}d$ exchange interaction), the observed Mn optical orientation time can be explained by invoking only the processes of carrier spin relaxation.

Figure 1

(Color online) Photoluminescence spectrum of the dot with a single Mn spin calculated using the parameters given in the text. All levels are assumed to be equally populated. The contribution from the mostly dark states to the total PL is plotted with the dashed line. Line broadening of 0.1 meV was used.

Figure 2

(Color online) Time dependence of the occupation of the empty dot $|-3/2⟩$ Mn level upon pumping of the $|-5/2,-1⟩$ transition with different light intensities (corresponding to different exciton generation rates $G$), with normalization $p_{-3/2}+p_{-5/2}=1$. The spontaneous recombination rate is ${\Gamma }_{\text{rec}}=5{\text{ns}}^{-1}$ and the hole spin-relaxation rate is ${\Gamma }_h=0.1{\text{ns}}^{-1}$. The exciton spin relaxation rate ${\Gamma }_{\text{X}}$ is assumed to be zero with exception of the dashed line for $G=0.1{\Gamma }_{\text{rec}}$, for which ${\Gamma }_{\text{X}}=1{\text{ns}}^{-1}$. The other parameters are given in the text.

Figure 3

(Color online) The same as in Fig. 2, only for $G/{\Gamma }_{\text{rec}}=1$ and with various holes spin-relaxation times $T_h={\Gamma }_h^{-1}$.