Electron-spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition

We have measured the electron-spin-relaxation rate and the integrated spin noise power in $n$-doped GaAs for temperatures between 4 and 80 K and for doping concentrations ranging from $2.7\times {10}^{15}$ to $8.8\times {10}^{16}{\text{cm}}^{-3}$ using spin noise spectroscopy. The temperature-dependent measurements show a clear transition from localized to free electrons for the lower doped samples and confirm mainly free electrons at all temperatures for the highest doped sample. While the sample at the metal-to-insulator transition shows the longest spin-relaxation time at low temperatures, a clear crossing of the spin-relaxation rates is observed at 70 K and the highest doped sample reveals the longest spin-relaxation time above 70 K.

Figure 1

(Color online) (a) Spin noise spectroscopy setup. The external magnetic field shifts the center frequency of the spin noise signal by the electron Larmor frequency. (b) Typical spin noise spectrum acquired by subtracting spin noise spectra measured at $B=6$ and 0 mT for sample ${\text{C}}^{\text{MIT}}$ at 4 K. (c) Typical spin noise difference spectrum acquired by selective suppression of spin noise with a liquid-crystal retarder for sample ${\text{B}}^{\text{low}}$ at 10 K.

Figure 2

(Color online) (a) Temperature depended measurement of the spin-relaxation rate for the samples B–D using a large focus and a large detuning of the laser wavelength from the optical transitions (probe laser wavelength $\lambda =840\text{nm}$) and the spin-relaxation rate for sample A at 8 K. The solid lines are fits to the data. The fit parameters are listed in Table . (b) Temperature dependence of the integrated spin noise power for samples B–D. The noise powers have been scaled to account for the different thicknesses of the samples. The inset shows the low-temperature noise power for samples C and D on a linear scale.

Figure 3

(Color online) Temperature dependence of the degree of electron ionization for the three lowest doped samples calculated by Blakemore’s equation (Ref. 14). The validity of Blakemore’s equation decreases with increasing doping concentration due to the formation of impurity bands, i.e., the calculation for sample C is only of limited significance.

Figure 4

(Color online) Temperature dependence of the spin relaxation in the hopping regime depends on the conductivity. Hopping transport describes the temperature dependence well for temperatures below 60 K.