Dynamics of a Mn spin coupled to a single hole confined in a quantum dot

Using the emission of the positively charged exciton as a probe, we analyze the dynamics of the optical pumping and the dynamics of the relaxation of a Mn spin exchange coupled with a confined hole spin in a II-VI semiconductor quantum dot. The hole-Mn spin can be efficiently initialized in a few tens of ns under optical injection of spin-polarized carriers. We show that this optical pumping process and its dynamics are controlled by electron-Mn flip-flops within the positively charged exciton-Mn complex. The pumping mechanism and its magnetic field dependence are theoretically described by a model including the dynamics of the electron-Mn complex in the excited state and the dynamics of the hole-Mn complex in the ground state of the positively charged quantum dot. We measure at zero magnetic field a spin-relaxation time of the hole-Mn spin in the $\mu \text{s}$ range or shorter. This hole-Mn spin relaxation is induced by the presence of valence-band mixing in self-assembled quantum dots.

Figure 1

(a) Color-scale plot of the PL intensity of a Mn-doped QD (QD1) in a Schottky structure as a function of emission energy and bias voltage for a cw excitation at ${\lambda }_{\text{exc}}=594\text{nm}$. The series of emission lines can be assigned to the recombination of the neutral exciton ($X$-Mn), positively charged exciton ($X^{+}\text{−}\mathrm{Mn}$), and negatively charged exciton ($X^{-}\text{−}\mathrm{Mn}$). (b) PL under cocircularly polarized excitation and detection of a positively charged Mn-doped QD. Inset: Experimental and calculated linearly polarized spectra along two orthogonal directions (left) and a simplified scheme of the energy levels of the ground ($h$-Mn) and excited states ($e$-Mn) of a positively charged Mn-doped QD (right). For $h$-Mn, the dotted arrows show the states coupled two by two by the valence-band mixing. The states $|-1/2,{\uparrow }_e\rangle$ and $|+1/2,{\downarrow }_e\rangle$ (green arrow) are mixed and split. (c) Experimental (left) and calculated (right) color-scale plot of the dependence of the PL of $X^{+}\text{−}\mathrm{Mn}$ on the direction of a linear analyzer. Four lines in the center of the structure are linearly polarized. The parameters used in the model are listed in Table 1.

Figure 2

(a) Co- and cross-circularly polarized PL spectra of a Mn-doped QD (QD1) inserted in a Schottky structure for three different gate voltages. Inset (top): Circularly polarized PL spectra obtained under circular (black) and linear (blue) excitation. (b) Excitation power dependence of the ratio of intensity of the high energy (HE) and low energy (LE) lines $(I_{\text{HE}}-I_{\text{LE}})/(I_{\text{HE}}+I_{\text{LE}})$ of $X^{+}\text{−}\mathrm{Mn}$ under cocircularly polarized cw excitation and detection. (c) Transverse magnetic field dependence of the ratio of intensity of the high- and low-energy lines for $X$-Mn and $X^{+}\text{−}\mathrm{Mn}$. Inset: Cocircularly polarized spectra of $X^{+}\text{−}\mathrm{Mn}$ with and without transverse magnetic field.

Figure 3

Scheme of the optical pumping mechanism of the spin of the hole-Mn complex under $\sigma$+ excitation. The electron-Mn flip-flops controlled by ${\mathcal{H}}_{e\text{-Mn}}$ and the electron-Mn coherence time $T_2^{e\text{Mn}}$ prepare the Mn spin in the state $S_z=-5/2$. See the text for a detailed description of the pumping process.

Figure 4

(a) Co- and cross-circularly polarized PL of $X^{+}\text{−}\mathrm{Mn}$ in QD2. Inset: Time evolution of the PL of the high-energy line (8) under polarization switching of the excitation. (b) Time evolution of the circularly polarized PL of the different lines of $X^{+}\text{−}\mathrm{Mn}$ [labeled from (1) to (8)] under polarization switching of the excitation. (c) Excitation power dependence of the PL transient measured on the high-energy line (8). Inset: Power dependence of the pumping time. (d) Transverse magnetic field dependence of the PL transient measured on the high-energy line of $X^{+}\text{−}\mathrm{Mn}$. Inset: Magnetic field dependence of the amplitude of the optical pumping transient $\Delta I/I$.

Figure 5

(a) Co- and cross-circularly polarized PL of $X^{+}\text{−}\mathrm{Mn}$ and $X$-Mn in a Mn-doped QD (QD3). (b) Transverse magnetic field dependence of the amplitude of the optical pumping transients measured on the high-energy line of $X$-Mn and on the high-energy line of $X^{+}\text{−}\mathrm{Mn}$ in QD3. (c) Transverse magnetic field dependence of the amplitude of the optical pumping transients measured on the high-energy line of $X^{+}\text{−}\mathrm{Mn}$ compared for five different QDs from QD1 to QD5. The corresponding half widths at half maximum of the depolarization curves are listed in Table 1.

Figure 6

Optical pumping signal calculated with the parameters of QD2 (see Table 1). (a) Calculated intensity ratio of the high- and low-energy lines of $X^{+}\text{−}\mathrm{Mn}$ and population of the Mn spin states presented as a function of the generation rate of excitons under $\sigma +$ excitation ($g=g_{|+1\rangle }=g_{|-2\rangle }=1/{\tau }_g$). (b) Time evolution of the population of the different electron-Mn states under excitation with alternate circular polarization (${\tau }_g=4\text{ns}$). The curves are shifted for clarity. (c) Transverse magnetic field dependence of the pumping transient observed on the high-energy line (${\tau }_g=4\text{ns}$). For (a), (b), and (c) the parameters used in the calculation are ${\tau }_{\text{Mn}}=5\mu \text{s}$, ${\tau }_h=1\text{ns}$, ${\tau }_r=0.3\text{ns}$, $T_2^{h\text{Mn}}=0.5\text{ns}$, $T_2^{e\text{Mn}}=0.1\text{ns}$, $T=10$ K, $a=0.32\mu \text{eV}$, $D_0=6\mu \text{eV}$, $E=0.5\mu \text{eV}$, $g_{\text{Mn}}=2$, $g_h=0.6$, and $g_e=-0.4$. (d) Amplitude of the optical pumping transient as a function of transverse magnetic field calculated with the previous parameters (black); with $D_0=0\mu \text{eV}$, $E=0\mu \text{eV}$, $\eta =0\mu \text{eV}$ (red); with $T_2^{e\text{Mn}}=\infty$ (i.e., lifetime limited coherence of $e$-Mn) (blue); and with $T_2^{e\text{Mn}}=\infty$, $T_2^{h\text{Mn}}=1\text{ns}$ (dotted blue).

Figure 7

(a) Optical pumping transient obtained on the high-energy line of $X^{+}\text{−}\mathrm{Mn}$ in QD5 under excitation with circularly polarized light trains of 300 ns separated by a dark time of ${\tau }_{\text{dark}}=8$ $\mu \mathrm{s}$ (the excitation sequence is displayed on the top). Inset: Evolution of the amplitude of the optical pumping transient with ${\tau }_{\text{dark}}$ for $B=0$ T and $T=7$ K. (b) Calculated time evolution in the dark of the population of the Mn spin state $S_z=-5/2$ initially pumped by a $\sigma +$ cw excitation (excitation sequence displayed at the top). The calculations are performed with the exchange couplings parameters of QD5 (see Table 1), ${\tau }_{\text{Mn}}=5\mu s$, ${\tau }_h=1\text{ns}$, ${\tau }_r=0.3\text{ns}$, $T_2^{e\text{Mn}}=0.1\text{ns}$, $T=10$ K, $a=0.32\mu \text{eV}$, $D_0=6$ $\mu \mathrm{eV}$, $E=0.5$ $\mu \mathrm{eV}$, and different amplitudes of valence-band mixing ${\rho }_s/{\Delta }_{lh}$ and hole-Mn coherence time $T_2^{h\text{Mn}}$.