Nuclear spin warm up in bulk $n$-GaAs

We show that the spin-lattice relaxation in $n$-type insulating GaAs is dramatically accelerated at low magnetic fields. The origin of this effect, which cannot be explained in terms of well-known diffusion-limited hyperfine relaxation, is found in the quadrupole relaxation, induced by fluctuating donor charges. Therefore, quadrupole relaxation, which governs low field nuclear spin relaxation in semiconductor quantum dots, but was so far supposed to be harmless to bulk nuclei spins in the absence of optical pumping, can be studied and harnessed in the much simpler model environment of $n$-GaAs bulk crystal.

Figure 1

Sketch of the NSS warm up. (a) Magnetic field dependence of the two contributions to the nuclear spin-lattice relaxation: diffusion-limited hyperfine interaction at rate $1/T_D$ (dashed line) and quadrupole-induced warm up at rate $1/T_Q$. (b) Relevant processes in a nuclei-electron coupled system: fast nuclear spin warm up under donor orbits via hyperfine interaction (characterized by time $T_{hf})$, and warm up of all other nuclei via spin diffusion towards the donor sites and quadrupole interaction.

Figure 2

A scheme of the three-stage experimental protocol. Each stage is characterized by (a) the presence/absence of the pump, and (b) the value of the magnetic field applied during the dark stage. (c) The corresponding values of the PL polarization degree. (d) A set of measurements of ${\rho }_{\mathrm{dark}}\propto B_N$ for a given applied field $B_{\mathrm{dark}}=8$ G, obtained at different values of dark intervals $T_{\mathrm{dark}}$ (symbols). The solid line is the fit to the exponential decay, which determines the NSS warm-up time $T_1$. Inset: the same data recalculated in terms of the nuclear spin temperature.

Figure 3

(a) The NSS warm-up rate $1/T_1$ measured as a function of the applied magnetic field (symbols). Solid lines are fits to the Lorentz function. Values of the HWHM (b), $T_1$ at $B=\infty$ and $B=0$ (c) extracted from the fitting procedure at different temperatures. (b) The solid line is the value of local field due to spin-spin interactions, $B_{SS}$ [22], and the dashed line is the average value of the HWHM extracted from the data, which we interpret as $B_L$. (c) The solid line is a calculated value of the diffusion-limited relaxation time $T_D$.

Figure 4

(a) The enhancement of the NSS warm-up rate measured at different temperatures. The solid line is a fit to Eq. (13), with the only fitting parameter $k/{\tau }_c^c$. (b) The electrical sheet resistance measured as a function of the inverse temperature. Solid lines are fits to the exponential behavior with two different activation energies, and the Mott law at $T\le 5$ K.