Hanle spin precession in a two-dimensional electron system

We investigate the nonlocal Hanle effect in high mobility two-dimensional electron systems using (Ga,Mn)As/GaAs spin Esaki diodes as spin selective contacts. Spin signals in these systems can be strongly affected by dynamic nuclear polarization, which mimics long spin-relaxation times extracted from the measured Hanle curves. Here, we introduce a method which largely suppresses these effects by using an ac injection-detection setup. This allows us to extract from the measurements realistic spin lifetimes on the order of single nanoseconds. As the detection of Hanle signals is also strongly affected by offset signals we discuss the magnetic field dependence of these background voltages observed in lateral nonlocal spin injection devices. We show how the strength of the background magnetoresistance can be minimized by choosing a proper device geometry.

Figure 1

(a) Sketch of a lateral spin injection device. Narrow ferromagnetic (FM) (Ga,Mn)As contacts on top of the channel are used to inject/detect spin accumulation in the 2DES. Each sample features typically two to six FM contacts with widths varying between 500 and 2000 nm. Additional contacts on both ends of the channel (R1, R2), far away from the spin aligning contacts, serve as reference. (b) Schematic of the wafer layout. (c) I-V curve of one of the spin injection contacts; the characteristic negative differential resistance dip is observed between 300 and 450 mV. (d) Typical magnetotransport traces taken from the high mobility 2DES at the inverted (Al,Ga)As/GaAs interface.

Figure 2

dc nonlocal measurement at low (a) and at a high (b) negative bias, as well as for (c) high forward bias. Both NLSV (black and red lines) and Hanle curves (olive and blue symbols) are shown. The dashed orange line is the magnetoresistance of the background voltage $V_{\text{NL}}^{\text{base}}\left({\mathit{B}}_z\right)=(V_{\text{NL}}^{\text{AP}}+V_{\text{NL}}^{\text{P}})/2$. (d) Bias dependence of the nonlocal spin signal $\mathrm{\Delta }{V}_{\text{NL}}$ (black diamonds) together with the corresponding nonlocal baseline $V_{\text{NL}}^{\text{base}}$ voltage (red circles) at ${\mathit{B}}_z=0$. The right $y$ axis labels the spin-density polarization $P_n$ calculated from $\mathrm{\Delta }{V}_{\text{NL}}$ using Eq. (5). (e) and (f) show Hanle curves after removing the background from the measurements shown in (a) and (b), respectively. Red solid lines are simulated Hanle curves using Eq. (2) with corresponding spin-relaxation times ${\tau }_s$. The measurements were performed on the sample with $w_y=10\mu \mathrm{m}$ and for $L=3.6\mu \mathrm{m}$ with $x\parallel \left[010\right]$ and $y\parallel \left[100\right]$ crystallographic direction.

Figure 3

(a) ac measurement ($I_{\text{rms}}^{\text{ac}}=1\mu \mathrm{A}$ and $f=13$ Hz) of the NLSV signal (black and red lines) and the Hanle effect (blue and olive symbols) for parallel (P) and antiparallel (AP) contact configuration of the same contacts as in Fig. 2. The dashed orange line shows the magnetoresistance of the background voltage $V_{\text{NL}}^{\text{base}}\left({\mathit{B}}_z\right)=(V_{\text{NL}}^{\text{AP}}+V_{\text{NL}}^{\text{P}})/2$. (b) Hanle fit to the data, after removing the background, yielding a spin lifetime of 800 ps.

Figure 4

(a) Low-amplitude ($I_{\text{rms}}^{\text{ac}}=700\mathrm{nA}$), low-frequency ($f=13$ Hz) ac measurements with an in-plane component ${\mathit{B}}_y=+2$ mT. (b) and (c) Measurements like in (a) but with an additional dc bias across the injector. Satellite peaks appear in (c) for $I^{\text{dc}}=-5\mu \mathrm{A}$. Measurements were performed on a sample with $w_y=2.5\mu \mathrm{m}$ with the injector-detector separation $L=3.75\mu \mathrm{m}$. Insets illustrate the relative orientation of the external field ${\mathit{B}}_{\text{ext}}$ and the nuclear field ${\mathit{B}}_N$ in each case. Arrows mark the position of satellite peaks at ${\mathit{B}}_{\mathit{\text{ext}}}=-{\mathit{B}}_{\mathit{N}}$ (d) Spin-relaxation time extracted from ac measurements for different values of excitation current. Measurements were performed on a sample with $w_y=5\mu \mathrm{m}$ and with the contacts aligned along $\left[1\overline{1}0\right]$ direction.

Figure 5

ac Hanle traces for different injector-detector separations L, measured on devices with a $10-\mu \mathrm{m}$-wide (a) and $2.5-\mu \mathrm{m}$-wide (b) channel. Red dashed lines are quadratic fits to the background magnetoresistance. Blue triangles indicate field values at which the spin signal is restored due to alignment of spins along ${\mathit{B}}_z$, after the magnetization of the the contacts has been rotated out of plane. The magnitude of the Hanle signal $\mathrm{\Delta }{R}_{\text{NL}}^{\text{Hanle}}$ and the change of the nonlocal background resistance $\mathrm{\Delta }{R}_{\text{NL}}^{\text{base}}$ for $B=0.1$ T are also indicated. The $10-\mu \mathrm{m}$-wide ($2.5-\mu \mathrm{m}$-wide) sample has its contacts aligned along [100] ($\left[1\overline{1}0\right]$) crystallographic direction.

Figure 6

(a) Distance dependence of $\mathrm{\Delta }{R}_{\text{NL}}^{\text{base}}\left(B\right)$ at $B=0.1$ T (black) and of nonlocal Hanle signal $\mathrm{\Delta }{R}_{\text{NL}}^{\text{Hanle}}$ (red). Diamonds and circles represent the measurements for 2.5- and $10-\mu \mathrm{m}$-wide channels, respectively. Solid red lines are exponential fits of $\mathrm{\Delta }{R}_{\text{NL}}^{\text{Hanle}}$, with the corresponding ${\lambda }_{sf}\approx 12$ and $6\mu \mathrm{m}$ for $w_y=2.5$ and $10\mu \mathrm{m}$, respectively. Black lines are guides to the eye. (b) Signal-to-background ratios obtained from measurements on ten different samples plotted vs aspect ration $L/w_y$. Red circles and diamonds correspond to data shown in (a); other symbols correspond to samples with various $w_y$, as indicated in the legend. Open (full) symbols correspond to channels along the [110] ([010]) crystallographic direction. Estimated error bars are smaller than the size of the symbols. The line is a guide to the eye.

Figure 7

Spin-relaxation times obtained from ac Hanle measurements ($I_{\text{rms}}^{\text{ac}}=700\text{nA}$) for seven different samples with various widths $w_y$ and different crystallographic orientation of the channel and of the ferromagnetic contacts. Same symbols correspond to different detector contacts of the same device. For any given sample, we use also the same symbols as in Fig. 6.