Figure 1

(a) Measured $S_z\left(t\right)$ for $w=8$ nm at $B_{\mathrm{ext}}=0.93$ T and various $\delta k$ (labels 1–4). (Upper inset) The fitted spin precession frequency $\nu$ strongly varies with $\delta k$. The regime of $\left|\nu \right|<1$ GHz (dotted line) is not accessible because of the fast signal decay. (Lower inset) No oscillation is observed for this signal (label 3); it decays exponentially with ${\tau }_s\approx {\tau }_z$. (b) Variation of $\langle k_z^2\rangle$ with $w$ for an infinite and a finite GaAs/Al${}_{0.3}$Ga${}_{0.7}$As square potential well. Shown are analytically (circles) and numerically (+) calculated values for $n_{\mathrm{s}}=0$ and $1.2\times {10}^{15}$ m${}^{-2}$. (c) Kerr excitation energy $E_{\mathrm{exc}}$ and (d) $g$ factor vs $\langle k_z^2\rangle$. Note the sign change of $g$ at $w\approx 7$ nm (arrow).Reuse & Permissions

Figure 2

Measured Zeeman and drift-induced Dresselhaus SO splitting $h\nu =g{\mu }_{\mathrm{B}}{B}_{\mathrm{ext}}+2{\beta }^{*}\delta k$ as a function of $\delta k$ for 6- to 30-nm-wide QWs and for $B_{\mathrm{ext}}>0$ (open symbols). For $B_{\mathrm{ext}}<0$, we plot $-h\nu$ (solid symbols). The Zeeman splitting $g{\mu }_{\mathrm{B}}{B}_{\mathrm{ext}}$ changes sign between $w=6$ and 8 nm. $2{\beta }^{*}$ is obtained from the slopes $\partial \left(h\nu \right)/\partial \delta k$ in the regime of $\left|\delta k\right|<2\times {10}^6$ m${}^{-1}$ (solid lines in the vicinity of $\delta k=0$). For $w=6$ and 8 nm, we used the regime of $\left|\nu \right|>|{\nu }_0|$ and $\left|\delta k\right|<1\times {10}^6$ m${}^{-1}$.Reuse & Permissions

Figure 3

(a) Measured ${\beta }_1$ (open symbols) and data from Ref. 7 (solid symbol) vs $\langle k_z^2\rangle$ are fit to $-\gamma \langle k_z^2\rangle$ (solid line). (Dotted lines) $95\%$ confidence interval. (Horizontal error bars) $\pm 0.5$ nm variation in $w$. (Vertical error bar) $\pm 30\%$ variation in $n_{\mathrm{s}}$ and estimated uncertainty in the fitted $\nu$. (b) Spin decay rates ${\tau }_s^{-1}$ (circles) and ${\tau }_z^{-1}$ (squares) vs $\langle k_z^2\rangle$. (c) Comparison of $\tau$ and ${\tau }_p^{*}$; $\tau$ was calculated from the mobility $\mu$, ${\tau }_p^{*}$ was calculated from ${\tau }_s$, ${\beta }_1$ and $k_{\mathrm{F}}^2$ (circles), and from ${\tau }_s$, $-\gamma \langle k_z^2\rangle$, and $k_{\mathrm{F}}^2$ (diamonds).Reuse & Permissions