Current-induced spin polarization in InGaAs and GaAs epilayers with varying doping densities

The current-induced spin polarization and momentum-dependent spin-orbit field were measured in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ epilayers with varying indium concentrations and silicon doping densities. Samples with higher indium concentrations and carrier concentrations and lower mobilities were found to have larger electrical spin generation efficiencies. Furthermore, current-induced spin polarization was detected in GaAs epilayers despite the absence of measurable spin-orbit fields, indicating that the extrinsic contributions to the spin-polarization mechanism must be considered. Theoretical calculations based on a model that includes extrinsic contributions to the spin dephasing and the spin Hall effect, in addition to the intrinsic Rashba and Dresselhaus spin-orbit coupling, are found to reproduce the experimental finding that the crystal direction with the smaller net spin-orbit field has larger electrical spin generation efficiency and are used to predict how sample parameters affect the magnitude of the current-induced spin polarization.

Figure 1

Spin drag measurements for the determination of the SO field for Sample C. (a) Amplitude $A_0\left(x\right)$ vs pump-probe spatial separation for 0 V (black), 1 V (red), and 2 V (green), and pump-probe time delay $\mathrm{\Delta }t=13$ ns. The location of the center gives the drift velocity. (b) Drift velocity vs applied voltage. (c) Faraday rotation vs magnetic field for the same in-plane voltages as (a) at the center of the spin packet. Fits to Eq. (2) give the SO field. (d) The perpendicular component of the SO field at the center of the spin packet vs drift velocity. The slope $\kappa$ gives the strength of the SO field.

Figure 2

(a) CISP measurements for 1V (black), 2V (red), and 3V (blue), showing an odd-Lorentzian lineshape for Sample A. The spin density ${\rho }_{\text{el}}$ (b) and lifetime $\tau$ (c) are used to calculate the spin generation rate $\gamma$ (d). The slope $\eta$ of $\gamma$ with respect to the drift velocity is used to characterize the strength of the CISP.

Figure 3

(a) $\eta$ (CISP) vs $\kappa$ (SO splitting) for all five InGaAs samples. Squares indicate samples with higher indium concentration (2.4%-2.6%) and triangles indicate samples with 2.0% indium. Filled in and open symbols are for measurements along the $\left[1\overline{1}0\right]$ and [110] crystal axes, respectively. $r=\alpha /\beta$ characterizes the anisotropy of the SO field. There was a negative differential relationship observed between the two parameters in all five samples. (b) Theoretical calculations for $\eta$ based on the model [Eq. (5)] using the material parameters for the five InGaAs samples. The model predicts the observed negative differential relationship.

Figure 4

Measured values of $\eta$ (CISP) for the $\left[1\overline{1}0\right]$ and [110] crystal axes as a function of (a) carrier concentration and (b) mobility. Squares indicate samples with higher indium concentration (2.4%-2.6%) and triangles indicate samples with 2.0% indium. Red and black symbols are for measurements along the $\left[1\overline{1}0\right]$ and [110] crystal axes, respectively. Calculations for $\eta$ as a function of (c) carrier concentration and (d) mobility using material parameters for Sample D.