[Paper Review] Electrical spin protection and manipulation via gate-locked spin-orbit fields

Florian Dettwiler, Jiyong Fu+5 more|arXiv (Cornell University)|Mar 14, 2014

Quantum and electron transport phenomena3 citations

TL;DR

This paper demonstrates electrically tunable, gate-locked spin-orbit (SO) fields in GaAs quantum wells, enabling simultaneous control and protection of electron spins via independent tuning of Rashba ($\alpha$) and Dresselhaus ($\beta$) SO fields. By using dual top and back gates, the authors achieve continuous, in-situ locking of $\alpha = \beta$, suppressing spin relaxation and enabling broad, tunable spin protection essential for spintronic devices.

ABSTRACT

The spin-orbit (SO) interaction couples electron spin and momentum via a relativistic, effective magnetic field. While conveniently facilitating coherent spin manipulation in semiconductors, the SO interaction also inherently causes spin relaxation. A unique situation arises when the Rashba and Dresselhaus SO fields are matched, strongly protecting spins from relaxation, as recently demonstrated. Quantum computation and spintronics devices such as the paradigmatic spin transistor could vastly benefit if such spin protection could be expanded from a single point into a broad range accessible with in-situ gate-control, making possible tunable SO rotations under protection from relaxation. Here, we demonstrate broad, independent control of all relevant SO fields in GaAs quantum wells, allowing us to tune the Rashba and Dresselhaus SO fields while keeping both locked to each other using gate voltages. Thus, we can electrically control and simultaneously protect the spin. Our experiments employ quantum interference corrections to electrical conductivity as a sensitive probe of SO coupling. Finally, we combine transport data with numerical SO simulations to precisely quantify all SO terms.

Motivation & Objective

• To achieve broad, in-situ electrical control of spin-orbit (SO) fields in GaAs quantum wells while maintaining spin protection.
• To decouple and independently tune the Rashba ($\alpha$) and Dresselhaus ($\beta$) SO fields using top and back gates.
• To demonstrate that spin relaxation is strongly suppressed when $\alpha = \beta$, enabling long spin coherence times.
• To precisely quantify the cubic Dresselhaus term ($\beta_3$) and its impact on spin dephasing using transport measurements and simulations.
• To establish a method for tuning SO fields across multiple regimes (Rashba, Dresselhaus, balanced) for spintronic applications.

Proposed method

• Employed dual-gate geometry (top and back gates) to independently control carrier density ($n$) and Rashba SO field ($\alpha$) via gate voltages $V_T$ and $V_B$.
• Used weak localization (WL) and weak antilocalization (WAL) magnetoconductance measurements as a sensitive probe of SO coupling strength and symmetry.
• Applied self-consistent Schrödinger-Poisson simulations to extract $\alpha$, $\langle k_z^2 \rangle$, and $\beta_1$, with $\gamma$ extracted from $\alpha = \beta$ condition.
• Calculated spin dephasing time $\tau_{\rm SO}$ from WAL curve minima using $\tau_{\rm SO} = \hbar / (4e D B_{\rm SO})$, where $B_{\rm SO}$ is the magnetic field at minimum.
• Used effective spin dephasing time $\tau_{\rm eff}$ from D’yakonov-Perel mechanism, averaging over spin quantization axes, with corrections for the cubic $\beta_3$ term.
• Validated results by fitting simulations to experimental WAL/WL data, extracting $\gamma = 11.6 \pm 1\ \mathrm{eV\AA^3}$ with $\sim 10\%$ uncertainty.

Experimental results

Research questions

• RQ1 Can Rashba and Dresselhaus spin-orbit fields be independently tuned in a GaAs 2DEG using dual-gate control?
• RQ2 Can the condition $\alpha = \beta$ be maintained over a broad range of gate voltages to enable extended spin protection?
• RQ3 What is the role of the cubic Dresselhaus term ($\beta_3$) in limiting spin lifetime even at $\alpha = \beta$?
• RQ4 How does gate-induced tuning of $\alpha$ and $\beta_3$ affect spin dephasing times and lengths in the presence of SO coupling?
• RQ5 Can the bulk Dresselhaus parameter $\gamma$ be consistently extracted across different quantum well widths and doping profiles?

Key findings

• Dual-gate control enables independent tuning of Rashba field ($\alpha$) and carrier density ($n$), with $\alpha$ continuously adjustable and capable of changing sign.
• By tuning $\beta_3$ via back gate voltage while locking $\alpha = \beta$, the authors achieve broad, in-situ spin protection across a range of $\alpha$ values.
• The Dresselhaus parameter $\gamma$ was extracted as $11.6 \pm 1\ \mathrm{eV\AA^3}$, consistent across asymmetrically doped quantum wells with varying widths.
• The cubic Dresselhaus term ($\beta_3$) significantly affects spin dephasing at high densities ($n = 9 \cdot 10^{11}\ \mathrm{cm^{-2}}$), where WAL persists even at $\alpha = \beta$.
• Spin dephasing time $\tau_{\rm SO}$ was extracted from WAL minima, yielding $\tau_{\rm SO} \propto 1/B_{\rm SO}$, with $B_{\rm SO}$ determined from experimental curves.
• Effective spin dephasing length $\lambda_{\rm eff} = \sqrt{2D\tau_{\rm eff}}$ was calculated, with $\tau_{\rm eff}$ including corrections from the $\beta_3$ term, especially at high $n$.