Diffusive Spin Transport in Narrow Two-Dimensional-Electron-gas Channels

Using the geometry of the spin field-effect transistor, we investigate the spin transport of in-plane spins in an array of narrow channels formed in a two-dimensional electron gas confined in an $(\mathrm{In},\mathrm{Ga})\mathrm{As}$ quantum well. We demonstrate a clear enhancement of the spin-diffusion length with decreasing channel width, yielding up to 10 µm for the narrowest channels. We discuss the observed enhancement in terms of the suppression of the Dyakonov-Perel mechanism of spin relaxation, which has been invoked in previous studies in the case of diffusion of out-of-plane oriented spins. We also show that the spin signal is significantly higher when injecting into an array of narrow channels, compared with injecting into a single narrow channel.

Figure 1

(a) Sketch of the lateral spin-injection device. Narrow ferromagnetic $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ contacts on top of the channel, 500 nm and 700 nm wide, are used to inject/detect spin accumulation in the 2DEG. Additional contacts on both ends of the channel (R1, R2), far away from the spin aligning contacts, serve as a reference. (b) Scanning electron microscope pictures of two samples, representing two geometries used in the experiments. The scale bar corresponds to the length of 10 µm. Left panel: standard geometry with the width of the spin-transport channel w_c equal to the total width of the mesa w₁. Right panel: array geometry, with an array of N narrow wires, each of width w_c, in region 2 between injector and detector contacts. The total width of the 2DEG available for the spin transport is $w_2=w_c=w_1$ for the standard geometry and $w_2=N{w}_c$ for the array geometry. (c) Typical spin-valve signals measured for the standard geometry (left panel) and the array geometry with N = 13 and w_c= 1 µm (right panel). The red an black lines correspond to the magnetic field swept towards positive and negative values, respectively. The current used is I= −20 µA and distance between the contacts d= 6 µm. Horizontal dashed lines indicate the spin-independent offset voltage $V_{\mathrm{NL}}^{\mathrm{off}}$.

Figure 2

(a) Distance dependence of $\mathrm{\Delta }{V}_{\mathrm{NL}}$ for the standard sample with w_c= 20 µm and the wire sample with w_c= 400 nm for an injection current I= −20 μA. The values of the spin-diffusion length are obtained assuming exponential decay of the spin accumulation. (b) Spin-diffusion length versus the width of the transport channel w_c. The shown values are averages of values measured for currents of $I=-10,-20,-40,\mathrm{and}-100\mu \mathrm{A}$ [27]. Solid (open) symbols indicate the array (standard) geometry. The horizontal dashed line indicates the average spin-diffusion length obtained for wide channels, i.e., for the 2D case. The other dashed line shows the expected ${\lambda }_s(w_c)\propto {w_c}^{-1}$ dependence based on the diffusive theory. The solid blue line is just a guide for the eye. Inset: spin relaxation time ${\tau }_s(w_c)={{\lambda }_s}^2/D$ calculated using D values determined from magnetotransport measurements.

Figure 3

(a) Dependence of the spin signal on the total width of the spin-transport channel w₂ for the standard and the wire samples, for the injector-detector separation $d=12\mu \mathrm{m}$. The dashed curves are plotted using Eq. (1) (black) and Eq. (2), assuming constant ${\lambda }_2={\lambda }_1={\lambda }_s^{2D}$ (blue), and ${\lambda }_2={\lambda }_2(w_c)$ (red), as obtained from the measurements for I = −20 µA. For calculations we use a spin-injection efficiency of $P=0.55$. In the case of Eq. (2) we use $w_1=20\mu \mathrm{m}$, as in experiments. (b) Spin-injection efficiency extracted from the measurements with the injection current I = −20 µA, as a function of the voltage drop across the interface $V_{\mathrm{int}}$, for all measured samples (closed symbols, array geometry; open symbols, standard geometry). The solid line shows a typical drop of P with increasing $V_{\mathrm{int}}$, as measured for the standard sample with $w_c=40\mu \mathrm{m}$, with $V_{\mathrm{int}}$ adjusted by the injection current.