Spin dynamics of quadrupole nuclei in InGaAs quantum dots

Photoluminescence polarization is experimentally studied for samples with (In,Ga)As/GaAs self-assembled quantum dots in transverse magnetic field (Hanle effect) under slow modulation of the excitation light polarization from fractions of Hz to tens of kHz. The polarization reflects the evolution of strongly coupled electron-nuclear spin systems in the quantum dots. Strong modification of the Hanle curves under variation of the modulation period is attributed to the peculiarities of the spin dynamics of quadrupole nuclei, which states are split due to deformation of the crystal lattice in the quantum dots. Analysis of the Hanle curves is fulfilled in the framework of a phenomenological model considering a separate dynamics of a nuclear field $B_{Nd}$ determined by polarization of the $\pm 1/2$ nuclear spin states and of a nuclear field $B_{Nq}$ determined by polarization of the split-off states $\pm 3/2, \pm 5/2$, etc. It is found that the characteristic relaxation time for the nuclear field $B_{Nd}$ is of order a fraction of a second, while the relaxation of the field $B_{Nq}$ is faster by about two orders of magnitude.

Figure 1

Hanle curves for sample A (left panel) and sample B (right panel) measured at the optical excitation of one circular polarization (cw) as well as with the modulated polarization with periods given in the legends. Excitation power $P=14$ mW for sample A and 10 mW for sample B. Diameter of laser spots on the samples, $d\approx 60\mu \mathrm{m}$. Sample temperature $T=1.8$ K.

Figure 2

Examples of the Hanle curve simulations for samples A (a) and B (b) for different modulation periods given in the legends. Symbols are the experimental data and solid lines are the fits.

Figure 3

Examples of the magnetic field dependencies of the longitudinal and transverse components of the dipole and quadrupole nuclear fields calculated for sample B using Eq. (8). The parameters used in the calculation are extracted from the Hanle curve measured at the modulation period $T_{\mathrm{mod}}=300$ ms. The magnetic field dependence of $B_e$ is taken from the experimentally measured Hanle curve. Inset shows behavior of components of the dipole field at small magnetic fields. $B_{Ndz}=300\mathrm{mT}$ at zero magnetic field.

Figure 4

Dependencies of the dipole field $B_{Nd}$, quadrupole field $B_{Nq}$, and the field of nuclear spin fluctuations $B_f$ on modulation period $T_{\mathrm{mod}}$ for sample A (a) and sample B [(b), (c)]. Symbols are the values extracted from the analysis of experimental data. Solid lines are the fits by Eqs. (12) and (13) with characteristic times as follows: for sample A, ${\tau }_{Nd}=1.6\pm 0.4$ ms, ${\tau }_{Nq}=1.4\pm 0.2$ ms, ${\tau }_f=0.5\pm 0.2$ ms; for sample B, ${\tau }_{Nd}=190\pm 11$ ms, ${\tau }_{1Nq}=0.2\pm 0.01$ ms, ${\tau }_{2Nq}=330\pm 80$ ms, ${\tau }_{1f}=0.2\pm 0.01$ ms, ${\tau }_{2f}=470\pm 80$ ms.