Optical investigation of electrical spin injection into an inverted two-dimensional electron gas structure

We report on electrical spin injection from (Ga,Mn)As into a high-mobility two-dimensional electron gas confined at an (Al,Ga)As/GaAs interface. Besides standard nonlocal electrical detection, we use a magneto-optical approach which provides cross-sectional images of the spin accumulation at the cleaved edge of the sample, yielding spin decay lengths on the order of $2\mu \mathrm{m}$. In some cases we find a nonmonotonic bias voltage dependence of the spin signal, which may be linked to ballistic tunneling effects during spin injection. We observe a clear Hanle depolarization using a technique which is free of dynamic nuclear polarization effects. Fitting the data with the standard drift-diffusion model of spin injection suggests averaged in-plane spin lifetimes on the order of 1 ns.

Figure 1

(a) Sample layout and measurement techniques. (b) Nonlocal voltage $V_{\mathrm{nl}}$ as a function of the applied magnetic field $H_z$ for $V_{\mathrm{b}}=+0.75\mathrm{V}$. The amplitude of the spin valve signal $\mathrm{\Delta }{V}_{\mathrm{nl}}$ is a measure for the spin polarization. (c) Kerr rotation ${\theta }_{\mathrm{K}}$ in the 2DEG channel as a function of the applied magnetic field $H_z$ for $V_{\mathrm{b}}=+0.75\mathrm{V}$. The height of the hysteresis loop $\mathrm{\Delta }{\theta }_{\mathrm{K}}$ is strictly proportional to the injected spin polarization.

Figure 2

(a) Microphotoluminescence measurement of the topmost layers of the heterostructure. (b) Kerr rotation spectrum in the transport channel measured under spin extraction conditions.

Figure 3

Kerr rotation scans along the 2DEG channel for spin injection ($V_{\mathrm{b}}=-0.75\mathrm{V}$) and spin extraction ($V_{\mathrm{b}}=+0.75\mathrm{V}$) in sample $B$. The bias voltage is applied between the $2-\mu \mathrm{m}$-wide contact at $x=0\mu \mathrm{m}$ and the reference contact on the right-hand side. The contacts are indicated by shaded regions. The red and orange lines represent exponential fits to the data in the field-free region with the corresponding values of the spin decay lengths ${\lambda }_s$. The inset illustrates the current path within the sample.

Figure 4

(a) Bias dependence of the Kerr rotation signal $\mathrm{\Delta }{\theta }_{\mathrm{K}}$ for two different contacts of sample $A$. (b) Kerr rotation normalized to the current $I$ plotted vs $V_{3\mathrm{T}}$ for the same contacts as in (a).

Figure 5

(a) and (b) Hanle depolarization curves of sample $A$ for both contacts of Fig. 4 using magneto-optical detection. The fits yield spin lifetimes of (a) $(1.5\pm 0.1)\mathrm{ns}$ for contact 1 and (b) $(1.4\pm 0.2)\mathrm{ns}$ for contact 2. (c) Hanle depolarization curve of sample $B$ using optical detection. The fit yields a spin lifetime of $(0.96\pm 0.09)\mathrm{ns}$. (d) Hanle depolarization curve of sample $B$ using nonlocal detection (no laser illumination). The fit yields a spin lifetime of $(1.6\pm 0.5)\mathrm{ns}$.