Mechanical control of spin-orbit splitting in GaAs and ${\mathrm{In}}_{0.04}{\mathrm{Ga}}_{0.96}\mathrm{As}$ epilayers

Time-resolved Kerr rotation spectroscopy as a function of pump-probe distance, voltage, and magnetic field is used to measure the momentum-dependent spin splitting energies in GaAs and InGaAs epilayers. The strain of the samples can be reproducibly controlled in the cryostat using three- and four-point bending applied with a mechanical vise. We find that the magnitude of the spin splitting increases linearly with applied tension and voltage. A strain-drift-diffusion model is used to determine the value of the spin-strain coupling coefficient for a strained GaAs epilayer.

Figure 1

(Color) (a) Patterned sample. Mesa is shown in gray, and metal contacts are shown in gold. (b) Measurement geometry showing orientation of sample, mechanical vise, electric and magnetic fields, and optical measurement. (c) (Top) Kerr rotation at temperature $T=60\mathrm{K}$ on $2\times {10}^{16}{\mathrm{cm}}^{-3}$ GaAs epilayer as a function of applied magnetic field for electric field $E=32\mathrm{V}{\mathrm{cm}}^{-1}$ and pump-probe separation $d=38\mu \mathrm{m}$ at time delay $\Delta t=13\mathrm{ns}$ for strain $\epsilon =(9.4\pm 2.4)\times {10}^{-4}$ (black), $(1.4\pm 0.2)\times {10}^{-3}$ (red), $(1.9\pm 0.2)\times {10}^{-3}$ (green), and $(2.4\pm 0.2)\times {10}^{-3}$ (blue). (Bottom) Kerr rotation on ${\mathrm{In}}_{0.04}{\mathrm{Ga}}_{0.96}\mathrm{As}$ epilayer when unstrained (black) and strained with a three-point mechanical vise (red).

Figure 2

(Color) Kerr rotation at temperature $T=60\mathrm{K}$ and time delay $\Delta t=13\mathrm{ns}$ as a function of applied magnetic field $B$ and pump-probe separation $d$ on $2\times {10}^{16}{\mathrm{cm}}^{-3}$ GaAs epilayer sample for electric field $E=32\mathrm{V}{\mathrm{cm}}^{-1}$ for (a) $\epsilon =(9.4\pm 2.4)\times {10}^{-4}$, (b) $(1.4\pm 0.2)\times {10}^{-3}$, (c) $(1.9\pm 0.2)\times {10}^{-3}$, and (d) $(2.4\pm 0.2)\times {10}^{-3}$. The color scale is the same for all four plots.

Figure 3

(Color) (a) Effective magnetic field $B_{\mathrm{int}}$ and (b) amplitude $A$ as a function of pump-probe separation $d$ on the $2\times {10}^{16}{\mathrm{cm}}^{-3}$ GaAs epilayer sample for strain $\epsilon =(1.9\pm 0.2)\times {10}^{-3}$ and electric field $E=8$ (black), 16 (red), 24 (green), 32 (blue), 40 (cyan), and $48\mathrm{V}{\mathrm{cm}}^{-1}$ (magenta). Symbols are data, and lines are fits as described in the text.

Figure 4

(Color) Spin-splitting energy ${\Delta }_0$ as a function of drift velocity $v_d$ for $2\times {10}^{16}{\mathrm{cm}}^{-3}$ GaAs epilayer sample when unstrained $\epsilon =(0.0\pm 2.4)\times {10}^{-4}$ (black symbols) and for $\epsilon =(4.7\pm 2.4)\times {10}^{-4}$ (red), $(9.4\pm 2.4)\times {10}^{-4}$ (blue), $(1.4\pm 0.2)\times {10}^{-3}$ (green), $(1.9\pm 0.2)\times {10}^{-3}$ (orange), and $(2.4\pm 0.2)\times {10}^{-3}$ (purple). Linear fits are also shown. (Inset) $\beta$ $\left(\mathrm{neV}\mathrm{ns}\mu {\mathrm{m}}^{-1}\right)$ as a function of strain $\epsilon$. The dashed line indicates $\beta$ from measurements on a GaAs membrane in Ref. 6.

Figure 5

(Color) (a) $\beta$ as a function of the spin-strain coefficient $C_3$ for strain $\epsilon =(4.7\pm 2.4)\times {10}^{-4}$ (red), $(9.4\pm 2.4)\times {10}^{-4}$ (blue), $(1.4\pm 0.2)\times {10}^{-3}$ (green), and $(1.9\pm 0.2)\times {10}^{-3}$ (orange). Lines are obtained from solutions to a spin-drift-diffusion model, as described in the text, and the symbols show $\beta$ obtained from measurements on the $2\times {10}^{16}{\mathrm{cm}}^{-3}$ GaAs epilayer sample. (b) $\beta$ as a function of strain $\epsilon$ from data (symbols) and the model using $C_3=0.8\mathrm{eV}\mathrm{\AA }$ (line).