Doping and temperature dependence of nuclear spin relaxation in $n$-type GaAs

We investigate the strong field nuclear spin relaxation rate in $n$-type GaAs for doping densities from the quasi-insulating over the metal-to-insulator up to the quasimetallic regime. The rate measured at 6.5 K increases in the quasi-insulating regime with doping density due to nuclear spin diffusion to the donor electrons and shows a distinct maximum at the critical density of the Mott metal-to-insulator transition. The density dependence of the nuclear spin relaxation rate can be quantitatively calculated over the whole density regime taking into account the effective number of localized electrons and the interaction of free electrons via the Korringa mechanism. Only the nuclear spin relaxation rate of the very lowest doped sample shows a significant deviation from these calculations. Temperature-dependent measurements suggest in this case an additional nuclear spin relaxation channel which is negligible at higher doping densities and is linked to the electron spin relaxation time.

Figure 1

Measured NSR rate $\mathrm{\Gamma }$ (black squares) as a function of $B_{\text{dark}}$ for $n_d=1.73\times {10}^{16}$ ${\mathrm{cm}}^{-3}$ at $T=6.5K$. The solid line is a fit to the data according to Eq. (3) with $\xi =8.79\left(74\right)$ and $B_L=0.39\left(4\right)\mathrm{mT}$. Inset: Measured nuclear magnetic field $B_N$ (black squares) in dependence on $t_{\mathrm{dark}}$. The blue line depicts a single exponential fit yielding $\mathrm{\Gamma }$.

Figure 2

Dependence of the high field NSR rate $\mathrm{\Gamma }$, in bulk $n$-type GaAs on doping density measured at $T=6.5K$. Here only the fully delocalized fraction of $n_d$ enters the Korringa rate according to Eq. (2). The values $n_{\mathrm{c}1}$ and $n_{\mathrm{c}2}$ denote critical densities (see text).

Figure 3

Temperature dependence of $\mathrm{\Gamma }$ for a doping density of $n_d=1.2\times {10}^{15}{\mathrm{cm}}^{-3}$ measured at $B_{\text{dark}}$. The NSR due to quadrupolar two-phonon process ${\mathrm{\Gamma }}_P$ is shown with respect to the right axis. Please note the different scale.

Figure 4

Schematic representation of the experimental setup for measuring nuclear spin relaxation rates in $n$-type GaAs samples via a Hanle-type depolarization scheme.

Figure 5

The black squares depict a typical Hanle curve measured with 50-kHz modulation of the excitation polarization, i.e., without relevant optical pumping of the nuclear spin system, and the red solid line a corresponding Lorentzian fit according to Eq. (A1). The green triangles depict in contrast the measured Hanle curve for excitation with right circularly polarized light where dynamic nuclear spin pumping changes the shape of the Hanle curve drastically [2]. Both Hanle curves are normalized to their respective maxima.

Figure 6

Hanle depolarization transients recorded after different dark times for $n_d=6.02\times {10}^{16}{\mathrm{cm}}^{-3}$, $B_{\mathrm{dark}}=1.17\mathrm{mT}$, and $\mathrm{T}=6.5\mathrm{K}$. The opening of the laser shutter defines $t=0$ s. The inset shows the density dependence of the local magnetic field which has been extracted from the measured $\mathrm{\Gamma }\left(B_{\mathrm{dark}}\right)$ according to Eq. (4) (blue squares). The other symbols depict for comparison a compilation of $B_L$ from literature.

Figure 7

Dependence of the localization fraction $\eta$ on doping density.