Nonlinear spin filter for nonmagnetic materials at zero magnetic field

The ability to convert spin accumulation to charge currents is essential for applications in spintronics. In semiconductors, spin-to-charge conversion is typically achieved using the inverse spin Hall effect or using a large magnetic field. Here we demonstrate a general method that exploits the nonlinear interactions between spin and charge currents to perform all-electrical, rapid, and noninvasive detection of spin accumulation without the need for a magnetic field. We demonstrate the operation of this technique with ballistic GaAs holes as a model system with strong spin-orbit coupling, in which a quantum point contact provides the nonlinear energy filter. This approach is generally applicable to electron and hole systems with strong spin-orbit coupling.

Figure 1

(a) A schematic of the experimental setup. A current $I_{\mathrm{sd}}$ flows between terminals 1 and 2, resulting in a voltage difference $V_{\mathrm{sd}}$ across the drive channel. (b),(c) Near the quantum point contact (QPC), opposite spin orientations ${\sigma }_{+}$ and ${\sigma }_{-}$ accumulate on opposite sides of the drive channel. The QPC acts as an energy filter: Spin-to-charge conversion occurs due to the difference in the transmission probability through the QPC between each spin species. In the linear regime (d), this difference arises from a different kinetic energy caused by, for instance, a Zeeman interaction. (e) In the nonlinear regime, the different local chemical potentials for ${\sigma }_{+}$ and ${\sigma }_{-}$ give rise to different transmission probabilities. In both (f) linear and (g) nonlinear cases, spin-polarized holes accumulate after passing through the QPC, resulting in a voltage $V_3$ between terminals 2 and 3. Note that the schematics in (a)–(g) are not to scale.

Figure 2

Device image and linear spin-to-charge conversion. (a) A scanning electron microscope image of the device. Light gray regions denote the surface gates, dark gray regions represent the AlGaAs/GaAs heterostructure, while light blue squares depict terminals 1–3. (b) QPC conductance vs QPC gate voltage $V_{\mathrm{QPC}}$. The dashed lines denote the second and third conductance risers as well as the second conductance plateau. (c) Color map of the two-terminal resistance $V_{\mathrm{sd}}/I_{\mathrm{sd}}$ across the channel as a function of $V_{\mathrm{QPC}}$ and $B$, showing a symmetric dependence on $B$. (d) Line cuts of $V_{\mathrm{sd}}/I_{\mathrm{sd}}$ from (c) along the second and third QPC conductance risers, as well as along the middle of the second conductance plateau. (e) Color map of the three-terminal resistance $V_3\left(\omega \right)/I_{\mathrm{sd}}$ as a function of $V_{\mathrm{QPC}}$ and $B$. Its asymmetry in $B$ indicates a spin accumulation. (f) Line cuts of $V_3\left(\omega \right)/I_{\mathrm{sd}}$ from (e) along the second and third QPC conductance risers, as well as along the middle of the second conductance plateau. The asymmetry of $V_3\left(\omega \right)/I_{\mathrm{sd}}$ in $B$ is present at a QPC conductance riser but absent at a plateau. (g) The asymmetry $\mathrm{\Delta }\left(\omega \right)\equiv (\partial V_3/\partial B){|}_{B=0}/I_{\mathrm{sd}}$ of $V_3\left(\omega \right)/I_{\mathrm{sd}}$ as a function of $V_{\mathrm{QPC}}$ around the second riser at different $I_{\mathrm{sd}}$. The asymmetry of $V_3\left(\omega \right)/I_{\mathrm{sd}}$ persists up to $I_{\mathrm{sd}}=10\mathrm{nA}$, but it becomes hard to correlate to the transconductance at 32 nA. The $\mathrm{\Delta }\left(\omega \right)$ traces are offset by 25 $\mathrm{\Omega }/T$ for clarity. The quantity ${\mathrm{\Delta }}^{\prime }\left(\omega \right)$ measures the amplitude of the asymmetry $\mathrm{\Delta }\left(\omega \right)$ relative to the background.

Figure 3

(a) The nonlinear resistance $V_3\left(2\omega \right)/I_{\mathrm{sd}}^2$ as a function of $V_{\mathrm{qpc}}$ and $B$. (b) The nonlinear voltage $V_3\left(2\omega \right)$ as a function of $V_{\mathrm{QPC}}$ for various $I_{\mathrm{sd}}$ is proportional to the QPC transconductance at $B=0$ T.

Figure 4

(a) The amplitude ${\mathrm{\Delta }}^{\prime }\left(\omega \right)I_{\mathrm{sd}}$ of the linear signal relative to the background, which is obtained by subtracting the lowest adjacent $\mathrm{\Delta }\left(\omega \right)$ minimum [see also Fig. 2] from $\mathrm{\Delta }\left(\omega \right)$ at the second QPC riser. (b) $V_3\left(2\omega \right)$ vs $I_{\mathrm{sd}}$ at $B=0$. The dashed lines in (a) and (b) are guides to the eye, suggesting that the linear and nonlinear spin signals saturate at $\sim 5–10\mathrm{nA}$. (c) The asymmetry $\mathrm{\Delta }\left(\omega \right)$ of the linear signal and (d) the nonlinear resistance $V_3\left(2\omega \right)/I_{\mathrm{sd}}^2$ vs $B$. Parts (c) and (d) show that at low excitation currents (e.g., $I_{\mathrm{sd}}=5\mathrm{nA}$), the spin signal gradually decreases as a function of $B$, whereas at high excitation currents (e.g., $I_{\mathrm{sd}}=32\mathrm{nA}$), it is almost unaffected by $B$. The difference in the $B$ dependence of the low and high $I_{\mathrm{sd}}$ signals suggests that at low $I_{\mathrm{sd}}$ the three-terminal voltages are of spin origin.