Influence of nonequilibrium phonons on the spin dynamics of a single Cr atom

We analyze the influence of optically generated nonequilibrium phonons on the spin relaxation and effective spin temperature of an individual Cr atom inserted in a quantum dot. Using a three-pulse pump-probe technique, we show that the spin relaxation measured in resonant optical pumping experiments strongly depends on the optical excitation conditions. We observe for an isolated Cr in the dark a heating time shorter than a few hundred nanoseconds after an initial high-power nonresonant excitation pulse. A cooling time larger than a few tens of microseconds, independent of the excitation, is obtained in the same experimental conditions. We show that a tunable spin-lattice coupling dependent on the density of nonequilibrium phonons can explain the observed dynamics. Low-energy excitation conditions are found where the Cr spin states $S_z=\pm 1$ can be efficiently populated by a nonresonant optical excitation, prepared and read out by resonant optical pumping and conserved in the dark for a few microseconds.

Figure 1

PL characteristic of a singly Cr-doped CdTe/ZnTe QD measured at $T=5$ K. (a) Co and cross-circularly polarized PL spectra. (b) PL spectra recorded along two orthogonal directions, $x$ and $y$. (c) Linear polarization intensity map. (d) Intensity map of the photoluminescence excitation spectra.

Figure 2

Energy spin level structure of a Cr atom with (X-Cr) and without (Cr) the presence of an exciton in a CdTe/ZnTe QD. Only the populated states with $S_z=0$ or $S_z=\pm 1$ are presented. $|{\Uparrow }_h\rangle$ and $|{\Downarrow }_h\rangle$ correspond to the heavy-hole spin up and down, while ${|\uparrow }_e\rangle$ and ${|\downarrow }_e\rangle$ illustrate the spin up and down of the electron. The optical and main spin relaxation paths involved in the optical pumping are presented for a $\sigma$ resonant excitation on the HE line. A nonresonant excitation populates the spin state $S_z=\pm 1$ via the generation of nonequilibrium acoustic phonons and the spin-lattice coupling ${\tau }_{sl}$ ($T_{\mathrm{eff}}^{\mathrm{ph}}$). The hole-Cr flip-flop ${\tau }_{h\mathrm{Cr}}$ transfers the Cr spin from $S_z=-1$ to $S_z=0$.

Figure 3

(a) Resonant optical pumping transients recorded on the central line for cross-circularly resonant excitation on the high-energy line. (b) Resonant excitation power dependence $P^{\mathrm{res}}$ of the pumping transient. Comparison of the pumping transient recorded (c) on the central line (C) for an excitation on the high-energy line (HE), (d) on C for an excitation on the low-energy line (LE), and (e) on LE for an excitation on HE. Note the difference in the vertical scales of (e). The optical excitation sequence is shown in (a).

Figure 4

Evolution of the resonant pumping signal as a function of the power of the nonresonant pulse 1, $P^{n-\mathrm{res}}$. The inset shows the excitation power dependence of the amplitude of the transient $\mathrm{\Delta }{I}_1$. Vertical lines indicate the excitation powers used in the time-resolved optical pumping experiments reported in Fig. 5.

Figure 5

Nonresonant excitation power dependence of the Cr spin relaxation time measured in a three-pulse resonant pumping experiment: Pulse 1 populates the spin sates $\pm 1$, pulse 2 initializes the Cr spin (empties $+1$ or $-1$), and pulse 3 probes the relaxation in the dark. Pulse 2 can be suppressed to probe the cooling of the Cr using only pulse 3. (a) and (b) Pumping transients obtained at high nonresonant excitation power $P_0^{n-\mathrm{res}}$ for two different dark times ${\tau }_d$. (c)–(e) Evolution as a function of ${\tau }_d$ of the normalized amplitudes $\mathrm{\Delta }{I}_2/\mathrm{\Delta }{I}_1$ and $\mathrm{\Delta }{I}_3/\mathrm{\Delta }{I}_1$ for three different nonresonant excitation intensities: $P_0^{n-\mathrm{res}}$, $0.4P_0^{n-\mathrm{res}}$, and $0.125P_0^{n-\mathrm{res}}$, respectively. The black line in (d) is an exponential fit with a characteristic time of 2.5 $\mu \text{s}$.

Figure 6

Evolution of the resonant pumping transients as a function of the power of the nonresonant pulse 1 $P^{n-\mathrm{res}}$ for a fixed dark time ${\tau }_d=2\mu \mathrm{s}$. The inset shows the $P^{n-\mathrm{res}}$ dependence of the normalized amplitudes $\mathrm{\Delta }{I}_2/\mathrm{\Delta }{I}_1$ and $\mathrm{\Delta }{I}_3/\mathrm{\Delta }{I}_1$.