Spin Accumulation and Spin Relaxation in a Large Open Quantum Dot

We report electronic control and measurement of an imbalance between spin-up and spin-down electrons in micron-scale open quantum dots. Spin injection and detection were achieved with quantum point contacts tuned to have spin-selective transport, with four contacts per dot for realizing a nonlocal spin-valve circuit. This provides an interesting system for studies of spintronic effects since the contacts to reservoirs can be controlled and characterized with high accuracy. We show how this can be used to extract in a single measurement the relaxation time for electron spins inside a ballistic dot (${\tau }_{\mathrm{sf}}\approx 300\mathrm{ps}$) and the degree of spin polarization of the contacts ($P\approx 0.8$).

Figure 1

(a) Electron microscope image of the device, with labels for current and voltage contacts, and depletion gates $V_{gi}$ and $V_{pi}$. Gate $V_{p1}$ is a shape-distorting gate. Fully switching gate $V_{p2a}$ or gates $V_{p2b}$ on or off sets the overall size of the dot, but fine-tuning these gates is also used for controlling small shape distortions. (b) Resistor model for the most typical experiment (see text), for the case of ideal spin polarization of the contacts to the $I+$ and $V+$ reservoirs. The spin-up (top) and spin-down (bottom) populations inside the dot are contained within the dashed line. The spin-flip resistance $R_{\mathrm{sf}}$ represents spin relaxation inside the dot.

Figure 2

(a) Nonlocal resistance results $⟨R_{\mathrm{nl}}{⟩}_{\mathrm{fc}}$ as a function of gate voltage $V_{g1}$ (controlling the number of open modes in the $I+$ QPC, corresponding conductance plateaus are indicated at the top axis) for the dot with area (a) $1.2$ and (b) $2.9\mu {\mathrm{m}}^2$, measured at $B=+8.5\mathrm{T}$. Gray lines show $R_{\mathrm{nl}}$ values from the resistor model, with the spin-flip resistance $R_{\mathrm{sf}}$ and polarization $P$ as in the figure labels. The inset in (a) shows fluctuations of $R_{\mathrm{nl}}$ as a function of shape gate $V_{p1}$ with all QPCs at a conductance of $2e^2/h$.

Figure 3

Averaged nonlocal resistance $⟨R_{\mathrm{nl}}{⟩}_{\mathrm{fc}}$ as a function of the conductance $G_{V-}$ of the $V-$ QPC, for $A=1.2\mu {\mathrm{m}}^2$. Gray lines show $R_{\mathrm{nl}}$ values from the resistor model, with the spin-flip resistance $R_{\mathrm{sf}}$ and polarization $P$ as labeled.

Figure 4

(a) Averaged nonlocal resistance $⟨R_{\mathrm{nl}}⟩$ as a function of $B$, for $I+$ and $V+$ at the $e^2/h$ spin-polarized conductance plateau (open symbols) and for $I+$ at $2e^2/h$ (not spin-selective) and only $V+$ at $e^2/h$ (solid symbols). The $I-$ and $V-$ QPCs are at $2e^2/h$, $A=1.2\mu {\mathrm{m}}^2$. The difference in $⟨R_{\mathrm{nl}}⟩$ for the traces in (a) defines the focusing corrected nonlocal resistance $⟨R_{\mathrm{nl}}{⟩}_{\mathrm{fc}}$, shown in (b). The gray line in (b) is a fit of the model where the polarization $P$ of QPCs (right axis) increases with Zeeman splitting (see text). Arrows indicate $B$ that was applied for measuring the data of Figs. 2, 3.